Kazimir Majorinc
                     
http://kazimirmajorinc.blogspot.com
http://instprog.com

Lot of Reduced Lambda Expressions
  
 
  
  ------  1/1. ------  

  1. ==[ start ]==> a

     REDUCED to normal form.

  ------  2/2. ------  

  1. ==[ start ]==> (^a.a)
  2. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3/3. ------  

  1. ==[ start ]==> (a a)

     REDUCED to normal form.

  ------  4/5. ------  

  1. ==[ start ]==> (^a.(^a.a))
  2. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  5/6. ------  

  1. ==[ start ]==> (a (^a.a))
  2. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  6/9. ------  

  1. ==[ start ]==> ((^a.a) a)
  2. ==[ alpha ]==> ((^x.x) a)
  3. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  7/11. ------  

  1. ==[ start ]==> (^a.(a a))
  2. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  8/12. ------  

  1. ==[ start ]==> (a (a a))

     REDUCED to normal form.

  ------  9/15. ------  

  1. ==[ start ]==> ((^a.a)(^a.a))
  2. ==[ alpha ]==> ((^x.x)(^y.y))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  10/18. ------  

  1. ==[ start ]==> ((a a) a)

     REDUCED to normal form.

  ------  11/20. ------  

  1. ==[ start ]==> (^a.b)
  2. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  12/21. ------  

  1. ==[ start ]==> (a b)

     REDUCED to normal form.

  ------  13/24. ------  

  1. ==[ start ]==> ((^a.a)(a a))
  2. ==[ alpha ]==> ((^x.x)(a a))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  14/27. ------  

  1. ==[ start ]==> ((a a)(^a.a))
  2. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  15/32. ------  

  1. ==[ start ]==> (^a.(^a.(^a.a)))
  2. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  16/33. ------  

  1. ==[ start ]==> (a (^a.(^a.a)))
  2. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  17/36. ------  

  1. ==[ start ]==> ((^a.a) b)
  2. ==[ alpha ]==> ((^x.x) b)
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  18/39. ------  

  1. ==[ start ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  19/45. ------  

  1. ==[ start ]==> ((^a.(^a.a)) a)
  2. ==[ alpha ]==> ((^x.(^y.y)) a)
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  20/47. ------  

  1. ==[ start ]==> (^a.(a (^a.a)))
  2. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  21/48. ------  

  1. ==[ start ]==> (a (a (^a.a)))
  2. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  22/51. ------  

  1. ==[ start ]==> ((^a.a)(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  23/54. ------  

  1. ==[ start ]==> ((a a) b)

     REDUCED to normal form.

  ------  24/60. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.a))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  25/63. ------  

  1. ==[ start ]==> ((a (^a.a)) a)
  2. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  26/69. ------  

  1. ==[ start ]==> ((^a.a)(a (^a.a)))
  2. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  27/72. ------  

  1. ==[ start ]==> ((a a)(^a.(^a.a)))
  2. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  28/78. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a a))
  2. ==[ alpha ]==> ((^x.(^y.y))(a a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  29/81. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.a))
  2. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  30/86. ------  

  1. ==[ start ]==> (^a.(^b.a))
  2. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  31/87. ------  

  1. ==[ start ]==> (a (^b.a))
  2. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  32/93. ------  

  1. ==[ start ]==> ((a a)(a (^a.a)))
  2. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  33/99. ------  

  1. ==[ start ]==> ((^a.(^a.a)) b)
  2. ==[ alpha ]==> ((^x.(^y.y)) b)
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  34/102. ------  

  1. ==[ start ]==> ((a (^a.a))(a a))
  2. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  35/110. ------  

  1. ==[ start ]==> (^a.((^a.a) a))
  2. ==[ alpha ]==> (^x.((^y.y) x))
  3. ==[ eta   ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  36/111. ------  

  1. ==[ start ]==> (a ((^a.a) a))
  2. ==[ alpha ]==> (a ((^x.x) a))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  37/114. ------  

  1. ==[ start ]==> ((^a.a)(^b.a))
  2. ==[ alpha ]==> ((^x.x)(^y.a))
  3. ==[ beta  ]==> (^y.a)
  4. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  38/123. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  39/126. ------  

  1. ==[ start ]==> ((a (^a.a)) b)
  2. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  40/135. ------  

  1. ==[ start ]==> (((^a.a) a) a)
  2. ==[ alpha ]==> (((^x.x) a) a)
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  41/141. ------  

  1. ==[ start ]==> ((^a.a)((^a.a) a))
  2. ==[ alpha ]==> ((^x.x)((^y.y) a))
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  42/144. ------  

  1. ==[ start ]==> ((a a)(^b.a))
  2. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  43/150. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  44/153. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  45/162. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.a))
  2. ==[ alpha ]==> (((^x.x) a)(^y.y))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  46/167. ------  

  1. ==[ start ]==> (^a.(^a.(a a)))
  2. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  47/168. ------  

  1. ==[ start ]==> (a (^a.(a a)))
  2. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  48/174. ------  

  1. ==[ start ]==> ((a a)((^a.a) a))
  2. ==[ alpha ]==> ((a a)((^x.x) a))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  49/183. ------  

  1. ==[ start ]==> ((a (^a.a))(a (^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  50/192. ------  

  1. ==[ start ]==> (((^a.a) a)(a a))
  2. ==[ alpha ]==> (((^x.x) a)(a a))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  51/198. ------  

  1. ==[ start ]==> ((^a.(a a)) a)
  2. ==[ alpha ]==> ((^x.(x x)) a)
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  52/200. ------  

  1. ==[ start ]==> (^a.(a (a a)))
  2. ==[ alpha ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  53/201. ------  

  1. ==[ start ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  54/204. ------  

  1. ==[ start ]==> ((^a.a)(^a.(a a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  55/213. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.a))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  56/225. ------  

  1. ==[ start ]==> (((^a.a) a) b)
  2. ==[ alpha ]==> (((^x.x) a) b)
  3. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  57/231. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.a))
  2. ==[ alpha ]==> ((^x.(x x))(^y.y))
  3. ==[ beta  ]==> ((^y.y)(^y.y))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  58/234. ------  

  1. ==[ start ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  59/240. ------  

  1. ==[ start ]==> ((^a.a)(a (a a)))
  2. ==[ alpha ]==> ((^x.x)(a (a a)))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  60/243. ------  

  1. ==[ start ]==> ((a a)(^a.(a a)))
  2. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  61/249. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  62/252. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.a))
  2. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  63/261. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z)))
  3. ==[ beta  ]==> (a (^y.(^z.z)))
  4. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  64/267. ------  

  1. ==[ start ]==> ((^a.(a a))(a a))
  2. ==[ alpha ]==> ((^x.(x x))(a a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  65/270. ------  

  1. ==[ start ]==> ((a (a a))(^a.a))
  2. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  66/275. ------  

  1. ==[ start ]==> (^a.(^b.(^a.a)))
  2. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  67/276. ------  

  1. ==[ start ]==> (a (^b.(^a.a)))
  2. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  68/282. ------  

  1. ==[ start ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  69/291. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a) a))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y) a))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  70/300. ------  

  1. ==[ start ]==> (((^a.a) a)(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)(a (^y.y)))
  3. ==[ beta  ]==> (a (a (^y.y)))
  4. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  71/306. ------  

  1. ==[ start ]==> ((^a.(a a)) b)
  2. ==[ alpha ]==> ((^x.(x x)) b)
  3. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  72/309. ------  

  1. ==[ start ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  73/317. ------  

  1. ==[ start ]==> (^a.((^a.a)(^a.a)))
  2. ==[ alpha ]==> (^x.((^y.y)(^z.z)))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  74/318. ------  

  1. ==[ start ]==> (a ((^a.a)(^a.a)))
  2. ==[ alpha ]==> (a ((^x.x)(^y.y)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  75/321. ------  

  1. ==[ start ]==> ((^a.a)(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  76/330. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  77/348. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^y.(^z.z)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  78/351. ------  

  1. ==[ start ]==> ((a (a a)) b)

     REDUCED to normal form.

  ------  79/360. ------  

  1. ==[ start ]==> (((^a.a)(^a.a)) a)
  2. ==[ alpha ]==> (((^x.x)(^y.y)) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  80/366. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  81/369. ------  

  1. ==[ start ]==> ((a a)(^b.(^a.a)))
  2. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  82/375. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  83/378. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(a a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  84/387. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.a))
  2. ==[ alpha ]==> (((^x.x) a)(^y.a))
  3. ==[ beta  ]==> (a (^y.a))
  4. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  85/393. ------  

  1. ==[ start ]==> ((^a.(a a))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))(a (^y.y)))
  3. ==[ beta  ]==> ((a (^y.y))(a (^y.y)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  86/396. ------  

  1. ==[ start ]==> ((a (a a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  87/405. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  88/417. ------  

  1. ==[ start ]==> ((a a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  89/426. ------  

  1. ==[ start ]==> ((a (^a.a))(a (a a)))
  2. ==[ alpha ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  90/435. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a) a))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y) a))
  3. ==[ beta  ]==> (a ((^y.y) a))
  4. ==[ alpha ]==> (a ((^x.x) a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  91/444. ------  

  1. ==[ start ]==> ((a (a a))(a (^a.a)))
  2. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  92/453. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  93/461. ------  

  1. ==[ start ]==> (^a.((a a) a))
  2. ==[ alpha ]==> (^x.((x x) x))

     REDUCED to normal form.

  ------  94/462. ------  

  1. ==[ start ]==> (a ((a a) a))

     REDUCED to normal form.

  ------  95/474. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  96/492. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.a))
  2. ==[ alpha ]==> ((^x.(x x))(^y.a))
  3. ==[ beta  ]==> ((^y.a)(^y.a))
  4. ==[ alpha ]==> ((^x.a)(^y.a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  97/504. ------  

  1. ==[ start ]==> (((^a.a)(^a.a)) b)
  2. ==[ alpha ]==> (((^x.x)(^y.y)) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  98/513. ------  

  1. ==[ start ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  99/519. ------  

  1. ==[ start ]==> ((^a.a)((a a) a))
  2. ==[ alpha ]==> ((^x.x)((a a) a))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  100/528. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  101/531. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  102/540. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(y y)))
  3. ==[ beta  ]==> (a (^y.(y y)))
  4. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  103/546. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y) a))
  3. ==[ beta  ]==> (((^y.y) a)((^y.y) a))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y) a))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  104/549. ------  

  1. ==[ start ]==> ((a (a a))(^b.a))
  2. ==[ alpha ]==> ((a (a a))(^x.a))

     REDUCED to normal form.

  ------  105/558. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  106/567. ------  

  1. ==[ start ]==> (((a a) a)(^a.a))
  2. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  107/572. ------  

  1. ==[ start ]==> (^a.(^a.b))
  2. ==[ alpha ]==> (^x.(^y.b))

     REDUCED to normal form.

  ------  108/573. ------  

  1. ==[ start ]==> (a (^a.b))
  2. ==[ alpha ]==> (a (^x.b))

     REDUCED to normal form.

  ------  109/579. ------  

  1. ==[ start ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  110/588. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  111/597. ------  

  1. ==[ start ]==> (((^a.a) a)(a (a a)))
  2. ==[ alpha ]==> (((^x.x) a)(a (a a)))
  3. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  112/606. ------  

  1. ==[ start ]==> ((a (a a))((^a.a) a))
  2. ==[ alpha ]==> ((a (a a))((^x.x) a))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  113/615. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  114/624. ------  

  1. ==[ start ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  115/630. ------  

  1. ==[ start ]==> ((^a.b) a)
  2. ==[ alpha ]==> ((^x.b) a)
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  116/632. ------  

  1. ==[ start ]==> (^a.(a b))
  2. ==[ alpha ]==> (^x.(x b))

     REDUCED to normal form.

  ------  117/633. ------  

  1. ==[ start ]==> (a (a b))

     REDUCED to normal form.

  ------  118/636. ------  

  1. ==[ start ]==> ((^a.a)(^a.b))
  2. ==[ alpha ]==> ((^x.x)(^y.b))
  3. ==[ beta  ]==> (^y.b)
  4. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  119/663. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(y y)))
  3. ==[ beta  ]==> ((^y.(y y))(^y.(y y)))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(y y)))

     IRREDUCIBLE: cycle.

  ------  120/684. ------  

  1. ==[ start ]==> (((a a) a) b)

     REDUCED to normal form.

  ------  121/690. ------  

  1. ==[ start ]==> ((^a.b)(^a.a))
  2. ==[ alpha ]==> ((^x.b)(^y.y))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  122/693. ------  

  1. ==[ start ]==> ((a b) a)

     REDUCED to normal form.

  ------  123/699. ------  

  1. ==[ start ]==> ((^a.a)(a b))
  2. ==[ alpha ]==> ((^x.x)(a b))
  3. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  124/702. ------  

  1. ==[ start ]==> ((a a)(^a.b))
  2. ==[ alpha ]==> ((a a)(^x.b))

     REDUCED to normal form.

  ------  125/708. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  126/720. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z)))
  3. ==[ beta  ]==> (a (^y.(^z.z)))
  4. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  127/726. ------  

  1. ==[ start ]==> ((^a.(a a))(a (a a)))
  2. ==[ alpha ]==> ((^x.(x x))(a (a a)))
  3. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  128/729. ------  

  1. ==[ start ]==> ((a (a a))(^a.(a a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(x x)))

     REDUCED to normal form.

  ------  129/738. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  130/747. ------  

  1. ==[ start ]==> (((a a) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  131/753. ------  

  1. ==[ start ]==> ((^a.b)(a a))
  2. ==[ alpha ]==> ((^x.b)(a a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  132/756. ------  

  1. ==[ start ]==> ((a b)(^a.a))
  2. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  133/761. ------  

  1. ==[ start ]==> (^a.(^b.(a a)))
  2. ==[ alpha ]==> (^x.(^y.(x x)))

     REDUCED to normal form.

  ------  134/762. ------  

  1. ==[ start ]==> (a (^b.(a a)))
  2. ==[ alpha ]==> (a (^x.(a a)))

     REDUCED to normal form.

  ------  135/768. ------  

  1. ==[ start ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  136/777. ------  

  1. ==[ start ]==> ((a (^a.a))((a a) a))
  2. ==[ alpha ]==> ((a (^x.x))((a a) a))

     REDUCED to normal form.

  ------  137/786. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z)))
  3. ==[ beta  ]==> (a ((^y.y)(^z.z)))
  4. ==[ alpha ]==> (a ((^x.x)(^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  138/795. ------  

  1. ==[ start ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  139/804. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a))
  3. ==[ beta  ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  140/813. ------  

  1. ==[ start ]==> (((a a) a)(a (^a.a)))
  2. ==[ alpha ]==> (((a a) a)(a (^x.x)))

     REDUCED to normal form.

  ------  141/819. ------  

  1. ==[ start ]==> ((^a.b) b)
  2. ==[ alpha ]==> ((^x.b) b)
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  142/822. ------  

  1. ==[ start ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  143/830. ------  

  1. ==[ start ]==> (^a.((^a.a)(a a)))
  2. ==[ alpha ]==> (^x.((^y.y)(x x)))
  3. ==[ beta  ]==> (^x.(x x))

     REDUCED to normal form.

  ------  144/831. ------  

  1. ==[ start ]==> (a ((^a.a)(a a)))
  2. ==[ alpha ]==> (a ((^x.x)(a a)))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  145/834. ------  

  1. ==[ start ]==> ((^a.a)(^b.(a a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  3. ==[ beta  ]==> (^y.(a a))
  4. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  146/843. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.b))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  147/861. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^y.(^z.z)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  148/888. ------  

  1. ==[ start ]==> ((^a.b)(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  149/891. ------  

  1. ==[ start ]==> ((a b) b)

     REDUCED to normal form.

  ------  150/900. ------  

  1. ==[ start ]==> (((^a.a)(a a)) a)
  2. ==[ alpha ]==> (((^x.x)(a a)) a)
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  151/906. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  152/909. ------  

  1. ==[ start ]==> ((a a)(^b.(a a)))
  2. ==[ alpha ]==> ((a a)(^x.(a a)))

     REDUCED to normal form.

  ------  153/915. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a b))
  2. ==[ alpha ]==> ((^x.(^y.y))(a b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  154/918. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.b))
  2. ==[ alpha ]==> ((a (^x.x))(^y.b))

     REDUCED to normal form.

  ------  155/933. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((^y.y)(^z.z))((^y.y)(^z.z)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1)))
  5. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  7. ==[ beta  ]==> ((^y.y)(^z.z))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  156/936. ------  

  1. ==[ start ]==> ((a (a a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  157/945. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  158/954. ------  

  1. ==[ start ]==> (((a a) a)(^b.a))
  2. ==[ alpha ]==> (((a a) a)(^x.a))

     REDUCED to normal form.

  ------  159/960. ------  

  1. ==[ start ]==> ((^a.b)(a (^a.a)))
  2. ==[ alpha ]==> ((^x.b)(a (^y.y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  160/963. ------  

  1. ==[ start ]==> ((a b)(^a.(^a.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  161/972. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  162/984. ------  

  1. ==[ start ]==> ((a a)((^a.a)(a a)))
  2. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  163/993. ------  

  1. ==[ start ]==> ((a (^a.a))(a b))
  2. ==[ alpha ]==> ((a (^x.x))(a b))

     REDUCED to normal form.

  ------  164/1002. ------  

  1. ==[ start ]==> (((^a.a) a)((a a) a))
  2. ==[ alpha ]==> (((^x.x) a)((a a) a))
  3. ==[ beta  ]==> (a ((a a) a))

     REDUCED to normal form.

  ------  165/1011. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  166/1020. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  167/1029. ------  

  1. ==[ start ]==> (((a a) a)((^a.a) a))
  2. ==[ alpha ]==> (((a a) a)((^x.x) a))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  168/1035. ------  

  1. ==[ start ]==> ((^a.b) c)
  2. ==[ alpha ]==> ((^x.b) c)
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  169/1038. ------  

  1. ==[ start ]==> ((a b)(a (^a.a)))
  2. ==[ alpha ]==> ((a b)(a (^x.x)))

     REDUCED to normal form.

  ------  170/1047. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a a))
  2. ==[ alpha ]==> (((^x.x)(a a))(a a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  171/1055. ------  

  1. ==[ start ]==> (^a.((a a)(^a.a)))
  2. ==[ alpha ]==> (^x.((x x)(^y.y)))

     REDUCED to normal form.

  ------  172/1056. ------  

  1. ==[ start ]==> (a ((a a)(^a.a)))
  2. ==[ alpha ]==> (a ((a a)(^x.x)))

     REDUCED to normal form.

  ------  173/1068. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  174/1113. ------  

  1. ==[ start ]==> ((^a.b)(^b.a))
  2. ==[ alpha ]==> ((^x.b)(^y.a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  175/1116. ------  

  1. ==[ start ]==> ((a b) c)

     REDUCED to normal form.

  ------  176/1125. ------  

  1. ==[ start ]==> (((^a.a)(a a)) b)
  2. ==[ alpha ]==> (((^x.x)(a a)) b)
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  177/1134. ------  

  1. ==[ start ]==> (((a a)(^a.a)) a)
  2. ==[ alpha ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  178/1140. ------  

  1. ==[ start ]==> ((^a.a)((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  179/1149. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  180/1152. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(a a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(a a)))

     REDUCED to normal form.

  ------  181/1161. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.b))
  2. ==[ alpha ]==> (((^x.x) a)(^y.b))
  3. ==[ beta  ]==> (a (^y.b))
  4. ==[ alpha ]==> (a (^x.b))

     REDUCED to normal form.

  ------  182/1167. ------  

  1. ==[ start ]==> ((^a.(a a))((a a) a))
  2. ==[ alpha ]==> ((^x.(x x))((a a) a))
  3. ==[ beta  ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  183/1179. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  184/1188. ------  

  1. ==[ start ]==> (((a a) a)(^a.(a a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(x x)))

     REDUCED to normal form.

  ------  185/1194. ------  

  1. ==[ start ]==> ((^a.b)((^a.a) a))
  2. ==[ alpha ]==> ((^x.b)((^y.y) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  186/1197. ------  

  1. ==[ start ]==> ((a b)(^b.a))
  2. ==[ alpha ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  187/1206. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  188/1215. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.a))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  189/1227. ------  

  1. ==[ start ]==> ((a a)((a a)(^a.a)))
  2. ==[ alpha ]==> ((a a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  190/1236. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  191/1245. ------  

  1. ==[ start ]==> (((^a.a) a)(a b))
  2. ==[ alpha ]==> (((^x.x) a)(a b))
  3. ==[ beta  ]==> (a (a b))

     REDUCED to normal form.

  ------  192/1254. ------  

  1. ==[ start ]==> ((a (a a))((a a) a))

     REDUCED to normal form.

  ------  193/1263. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  194/1272. ------  

  1. ==[ start ]==> (((a a) a)(a (a a)))

     REDUCED to normal form.

  ------  195/1281. ------  

  1. ==[ start ]==> ((a b)((^a.a) a))
  2. ==[ alpha ]==> ((a b)((^x.x) a))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  196/1290. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (^y.y)))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  197/1299. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a a))
  2. ==[ alpha ]==> (((a a)(^x.x))(a a))

     REDUCED to normal form.

  ------  198/1307. ------  

  1. ==[ start ]==> (^a.(b a))
  2. ==[ alpha ]==> (^x.(b x))
  3. ==[ eta   ]==> b

     REDUCED to normal form.

  ------  199/1308. ------  

  1. ==[ start ]==> (a (b a))

     REDUCED to normal form.

  ------  200/1338. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.b))
  2. ==[ alpha ]==> ((^x.(x x))(^y.b))
  3. ==[ beta  ]==> ((^y.b)(^y.b))
  4. ==[ alpha ]==> ((^x.b)(^y.b))
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  201/1365. ------  

  1. ==[ start ]==> ((^a.b)(^a.(a a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(y y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  202/1386. ------  

  1. ==[ start ]==> (((a a)(^a.a)) b)
  2. ==[ alpha ]==> (((a a)(^x.x)) b)

     REDUCED to normal form.

  ------  203/1401. ------  

  1. ==[ start ]==> ((^a.a)(b a))
  2. ==[ alpha ]==> ((^x.x)(b a))
  3. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  204/1410. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  205/1422. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(a a)))
  3. ==[ beta  ]==> (a (^y.(a a)))
  4. ==[ alpha ]==> (a (^x.(a a)))

     REDUCED to normal form.

  ------  206/1428. ------  

  1. ==[ start ]==> ((^a.(a a))(a b))
  2. ==[ alpha ]==> ((^x.(x x))(a b))
  3. ==[ beta  ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  207/1431. ------  

  1. ==[ start ]==> ((a (a a))(^a.b))
  2. ==[ alpha ]==> ((a (a a))(^x.b))

     REDUCED to normal form.

  ------  208/1449. ------  

  1. ==[ start ]==> (((a a) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  209/1455. ------  

  1. ==[ start ]==> ((^a.b)(a (a a)))
  2. ==[ alpha ]==> ((^x.b)(a (a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  210/1458. ------  

  1. ==[ start ]==> ((a b)(^a.(a a)))
  2. ==[ alpha ]==> ((a b)(^x.(x x)))

     REDUCED to normal form.

  ------  211/1467. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.a))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  212/1476. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  213/1490. ------  

  1. ==[ start ]==> (^a.(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  214/1491. ------  

  1. ==[ start ]==> (a (^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  215/1497. ------  

  1. ==[ start ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  216/1506. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  217/1515. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a)))
  3. ==[ beta  ]==> (a ((^y.y)(a a)))
  4. ==[ alpha ]==> (a ((^x.x)(a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  218/1524. ------  

  1. ==[ start ]==> ((a (a a))(a b))

     REDUCED to normal form.

  ------  219/1533. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  220/1542. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y)))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  221/1551. ------  

  1. ==[ start ]==> ((a b)(a (a a)))

     REDUCED to normal form.

  ------  222/1560. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y) a))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  223/1569. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  224/1584. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a))) a)
  2. ==[ alpha ]==> ((^x.(^y.(^z.z))) a)
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  225/1586. ------  

  1. ==[ start ]==> (^a.(a (^a.(^a.a))))
  2. ==[ alpha ]==> (^x.(x (^y.(^z.z))))

     REDUCED to normal form.

  ------  226/1587. ------  

  1. ==[ start ]==> (a (a (^a.(^a.a))))
  2. ==[ alpha ]==> (a (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  227/1590. ------  

  1. ==[ start ]==> ((^a.a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  228/1617. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(a a)))
  3. ==[ beta  ]==> ((^y.(a a))(^y.(a a)))
  4. ==[ alpha ]==> ((^x.(a a))(^y.(a a)))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  229/1644. ------  

  1. ==[ start ]==> ((^a.b)(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  230/1680. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  231/1683. ------  

  1. ==[ start ]==> ((a (^a.(^a.a))) a)
  2. ==[ alpha ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  232/1689. ------  

  1. ==[ start ]==> ((^a.a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  3. ==[ beta  ]==> (a (^y.(^z.z)))
  4. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  233/1692. ------  

  1. ==[ start ]==> ((a a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  234/1698. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b a))
  2. ==[ alpha ]==> ((^x.(^y.y))(b a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  235/1716. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(a a)))
  3. ==[ beta  ]==> (((^y.y)(a a))((^y.y)(a a)))
  4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a)))
  5. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  6. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  7. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  236/1719. ------  

  1. ==[ start ]==> ((a (a a))(^b.(a a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(a a)))

     REDUCED to normal form.

  ------  237/1728. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.b))
  3. ==[ beta  ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  238/1743. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  239/1746. ------  

  1. ==[ start ]==> ((a b)(^b.(^a.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  240/1755. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(y y)))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  241/1764. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.a))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.a))

     REDUCED to normal form.

  ------  242/1779. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  243/1782. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  244/1787. ------  

  1. ==[ start ]==> (^a.(^b.b))
  2. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  245/1788. ------  

  1. ==[ start ]==> (a (^b.b))
  2. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  246/1794. ------  

  1. ==[ start ]==> ((a a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  247/1803. ------  

  1. ==[ start ]==> ((a (^a.a))(b a))
  2. ==[ alpha ]==> ((a (^x.x))(b a))

     REDUCED to normal form.

  ------  248/1812. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(^y.y)))
  3. ==[ beta  ]==> (a ((a a)(^y.y)))
  4. ==[ alpha ]==> (a ((a a)(^x.x)))

     REDUCED to normal form.

  ------  249/1821. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(a a)))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  250/1830. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  251/1839. ------  

  1. ==[ start ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  252/1848. ------  

  1. ==[ start ]==> ((a b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a b)((^x.x)(^y.y)))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  253/1857. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (a a)))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  254/1866. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  255/1881. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a))) b)
  2. ==[ alpha ]==> ((^x.(^y.(^z.z))) b)
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  256/1884. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  257/1892. ------  

  1. ==[ start ]==> (^a.((^a.a) b))
  2. ==[ alpha ]==> (^x.((^y.y) b))
  3. ==[ beta  ]==> (^x.b)

     REDUCED to normal form.

  ------  258/1893. ------  

  1. ==[ start ]==> (a ((^a.a) b))
  2. ==[ alpha ]==> (a ((^x.x) b))
  3. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  259/1896. ------  

  1. ==[ start ]==> ((^a.a)(^b.b))
  2. ==[ alpha ]==> ((^x.x)(^y.y))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  260/1905. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  261/1950. ------  

  1. ==[ start ]==> ((^a.b)(^c.a))
  2. ==[ alpha ]==> ((^x.b)(^y.a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  262/1986. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  263/1989. ------  

  1. ==[ start ]==> ((a (^a.(^a.a))) b)
  2. ==[ alpha ]==> ((a (^x.(^y.y))) b)

     REDUCED to normal form.

  ------  264/1998. ------  

  1. ==[ start ]==> (((^a.a) b) a)
  2. ==[ alpha ]==> (((^x.x) b) a)
  3. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  265/2004. ------  

  1. ==[ start ]==> ((^a.a)((^a.a) b))
  2. ==[ alpha ]==> ((^x.x)((^y.y) b))
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  266/2007. ------  

  1. ==[ start ]==> ((a a)(^b.b))
  2. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  267/2013. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  268/2016. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  269/2031. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y)))
  3. ==[ beta  ]==> (((a a)(^y.y))((a a)(^y.y)))
  4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  270/2043. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  271/2052. ------  

  1. ==[ start ]==> (((a a) a)(^a.b))
  2. ==[ alpha ]==> (((a a) a)(^x.b))

     REDUCED to normal form.

  ------  272/2058. ------  

  1. ==[ start ]==> ((^a.b)((a a) a))
  2. ==[ alpha ]==> ((^x.b)((a a) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  273/2061. ------  

  1. ==[ start ]==> ((a b)(^c.a))
  2. ==[ alpha ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  274/2070. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  275/2079. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  276/2094. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  277/2097. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  278/2106. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.a))
  2. ==[ alpha ]==> (((^x.x) b)(^y.y))
  3. ==[ beta  ]==> (b (^y.y))
  4. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  279/2118. ------  

  1. ==[ start ]==> ((a a)((^a.a) b))
  2. ==[ alpha ]==> ((a a)((^x.x) b))
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  280/2127. ------  

  1. ==[ start ]==> ((a (^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  281/2136. ------  

  1. ==[ start ]==> (((^a.a) a)(b a))
  2. ==[ alpha ]==> (((^x.x) a)(b a))
  3. ==[ beta  ]==> (a (b a))

     REDUCED to normal form.

  ------  282/2145. ------  

  1. ==[ start ]==> ((a (a a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((a a)(^x.x)))

     REDUCED to normal form.

  ------  283/2154. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  284/2163. ------  

  1. ==[ start ]==> (((a a) a)(a b))

     REDUCED to normal form.

  ------  285/2172. ------  

  1. ==[ start ]==> ((a b)((a a) a))

     REDUCED to normal form.

  ------  286/2181. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  287/2190. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (a a)))

     REDUCED to normal form.

  ------  288/2208. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  289/2217. ------  

  1. ==[ start ]==> (((^a.a) b)(a a))
  2. ==[ alpha ]==> (((^x.x) b)(a a))
  3. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  290/2225. ------  

  1. ==[ start ]==> (^a.((a a)(a a)))
  2. ==[ alpha ]==> (^x.((x x)(x x)))

     REDUCED to normal form.

  ------  291/2226. ------  

  1. ==[ start ]==> (a ((a a)(a a)))

     REDUCED to normal form.

  ------  292/2238. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.b))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  293/2283. ------  

  1. ==[ start ]==> ((^a.b)(^a.b))
  2. ==[ alpha ]==> ((^x.b)(^y.b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  294/2319. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  295/2331. ------  

  1. ==[ start ]==> (((^a.a) b) b)
  2. ==[ alpha ]==> (((^x.x) b) b)
  3. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  296/2340. ------  

  1. ==[ start ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  297/2346. ------  

  1. ==[ start ]==> ((^a.a)((a a)(a a)))
  2. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  298/2355. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  299/2358. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.b))
  2. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  300/2367. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a (^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  301/2373. ------  

  1. ==[ start ]==> ((^a.(a a))(b a))
  2. ==[ alpha ]==> ((^x.(x x))(b a))
  3. ==[ beta  ]==> ((b a)(b a))

     REDUCED to normal form.

  ------  302/2394. ------  

  1. ==[ start ]==> (((a a) a)(^b.(a a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(a a)))

     REDUCED to normal form.

  ------  303/2400. ------  

  1. ==[ start ]==> ((^a.b)(a b))
  2. ==[ alpha ]==> ((^x.b)(a b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  304/2403. ------  

  1. ==[ start ]==> ((a b)(^a.b))
  2. ==[ alpha ]==> ((a b)(^x.b))

     REDUCED to normal form.

  ------  305/2421. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  306/2436. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  307/2439. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  308/2448. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z)))
  3. ==[ beta  ]==> (b (^y.(^z.z)))
  4. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  309/2457. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.a))
  2. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  310/2469. ------  

  1. ==[ start ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  311/2478. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a) b))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y) b))
  3. ==[ beta  ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  312/2487. ------  

  1. ==[ start ]==> (((^a.a) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.z))))
  3. ==[ beta  ]==> (a (a (^y.(^z.z))))
  4. ==[ alpha ]==> (a (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  313/2496. ------  

  1. ==[ start ]==> ((a (a a))(b a))

     REDUCED to normal form.

  ------  314/2505. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  315/2514. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(a a)))
  3. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  316/2523. ------  

  1. ==[ start ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  317/2532. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a) a))
  3. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  318/2541. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  319/2559. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  320/2568. ------  

  1. ==[ start ]==> (((^a.a) b)(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(a (^y.y)))
  3. ==[ beta  ]==> (b (a (^y.y)))
  4. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  321/2577. ------  

  1. ==[ start ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  322/2585. ------  

  1. ==[ start ]==> (^a.(b (^a.a)))
  2. ==[ alpha ]==> (^x.(b (^y.y)))

     REDUCED to normal form.

  ------  323/2586. ------  

  1. ==[ start ]==> (a (b (^a.a)))
  2. ==[ alpha ]==> (a (b (^x.x)))

     REDUCED to normal form.

  ------  324/2616. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  325/2643. ------  

  1. ==[ start ]==> ((^a.b)(^b.(a a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  326/2679. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  327/2691. ------  

  1. ==[ start ]==> (((^a.a) b) c)
  2. ==[ alpha ]==> (((^x.x) b) c)
  3. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  328/2700. ------  

  1. ==[ start ]==> (((a a)(a a)) b)

     REDUCED to normal form.

  ------  329/2715. ------  

  1. ==[ start ]==> ((^a.a)(b (^a.a)))
  2. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  3. ==[ beta  ]==> (b (^y.y))
  4. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  330/2724. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  331/2736. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.b))
  2. ==[ alpha ]==> (((^x.x) a)(^y.y))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  332/2742. ------  

  1. ==[ start ]==> ((^a.(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  333/2745. ------  

  1. ==[ start ]==> ((a (a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  334/2769. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  335/2772. ------  

  1. ==[ start ]==> ((a b)(^b.(a a)))
  2. ==[ alpha ]==> ((a b)(^x.(a a)))

     REDUCED to normal form.

  ------  336/2781. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.b))
  3. ==[ beta  ]==> ((a a)(^y.b))
  4. ==[ alpha ]==> ((a a)(^x.b))

     REDUCED to normal form.

  ------  337/2805. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  338/2808. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z)))

     REDUCED to normal form.

  ------  339/2817. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.a))
  2. ==[ alpha ]==> (((^x.x) b)(^y.a))
  3. ==[ beta  ]==> (b (^y.a))
  4. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  340/2826. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  341/2847. ------  

  1. ==[ start ]==> ((a a)(b (^a.a)))
  2. ==[ alpha ]==> ((a a)(b (^x.x)))

     REDUCED to normal form.

  ------  342/2856. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(a a)))

     REDUCED to normal form.

  ------  343/2865. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a) b))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y) b))
  3. ==[ beta  ]==> (a ((^y.y) b))
  4. ==[ alpha ]==> (a ((^x.x) b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  344/2874. ------  

  1. ==[ start ]==> ((a (a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  345/2883. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  346/2892. ------  

  1. ==[ start ]==> (((a a) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  347/2901. ------  

  1. ==[ start ]==> ((a b)((^a.a)(a a)))
  2. ==[ alpha ]==> ((a b)((^x.x)(a a)))
  3. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  348/2910. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a b))
  2. ==[ alpha ]==> (((^x.x)(a a))(a b))
  3. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  349/2919. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a) a))

     REDUCED to normal form.

  ------  350/2937. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a)))

     REDUCED to normal form.

  ------  351/2946. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a) a))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y) a))
  3. ==[ beta  ]==> (b ((^y.y) a))
  4. ==[ alpha ]==> (b ((^x.x) a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  352/2955. ------  

  1. ==[ start ]==> (((a a)(a a))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))(a (^x.x)))

     REDUCED to normal form.

  ------  353/2972. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a)) a))
  2. ==[ alpha ]==> (^x.((^y.(^z.z)) x))
  3. ==[ eta   ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  354/2973. ------  

  1. ==[ start ]==> (a ((^a.(^a.a)) a))
  2. ==[ alpha ]==> (a ((^x.(^y.y)) a))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  355/3003. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.b))
  2. ==[ alpha ]==> ((^x.(x x))(^y.y))
  3. ==[ beta  ]==> ((^y.y)(^y.y))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  356/3030. ------  

  1. ==[ start ]==> ((^a.b)(^c.(^a.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  357/3066. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  358/3105. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a) a)
  2. ==[ alpha ]==> (((^x.(^y.y)) a) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  359/3111. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((^y.(^z.z)) a)
  4. ==[ alpha ]==> ((^x.(^y.y)) a)
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  360/3120. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  361/3138. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y) b))
  3. ==[ beta  ]==> (((^y.y) b)((^y.y) b))
  4. ==[ alpha ]==> (((^x.x) b)((^y.y) b))
  5. ==[ beta  ]==> (b ((^y.y) b))
  6. ==[ alpha ]==> (b ((^x.x) b))
  7. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  362/3141. ------  

  1. ==[ start ]==> ((a (a a))(^b.b))
  2. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  363/3150. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  364/3165. ------  

  1. ==[ start ]==> ((^a.b)((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((a a)(^y.y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  365/3168. ------  

  1. ==[ start ]==> ((a b)(^c.(^a.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  366/3177. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a)))
  3. ==[ beta  ]==> ((a a)(^y.(a a)))
  4. ==[ alpha ]==> ((a a)(^x.(a a)))

     REDUCED to normal form.

  ------  367/3186. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.b))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.b))

     REDUCED to normal form.

  ------  368/3201. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  369/3204. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  370/3213. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(y y)))
  3. ==[ beta  ]==> (b (^y.(y y)))
  4. ==[ alpha ]==> (b (^x.(x x)))

     REDUCED to normal form.

  ------  371/3222. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.a))
  2. ==[ alpha ]==> (((a a)(a a))(^x.a))

     REDUCED to normal form.

  ------  372/3240. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  373/3245. ------  

  1. ==[ start ]==> (^a.(^a.(a (^a.a))))
  2. ==[ alpha ]==> (^x.(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  374/3246. ------  

  1. ==[ start ]==> (a (^a.(a (^a.a))))
  2. ==[ alpha ]==> (a (^x.(x (^y.y))))

     REDUCED to normal form.

  ------  375/3252. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y)) a))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  376/3261. ------  

  1. ==[ start ]==> ((a (^a.a))(b (^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  377/3270. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(a a)))
  3. ==[ beta  ]==> (a ((a a)(a a)))

     REDUCED to normal form.

  ------  378/3279. ------  

  1. ==[ start ]==> ((a (a a))((^a.a) b))
  2. ==[ alpha ]==> ((a (a a))((^x.x) b))
  3. ==[ beta  ]==> ((a (a a)) b)

     REDUCED to normal form.

  ------  379/3288. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  380/3297. ------  

  1. ==[ start ]==> (((a a) a)(b a))

     REDUCED to normal form.

  ------  381/3306. ------  

  1. ==[ start ]==> ((a b)((a a)(^a.a)))
  2. ==[ alpha ]==> ((a b)((a a)(^x.x)))

     REDUCED to normal form.

  ------  382/3315. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  383/3324. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a b))
  2. ==[ alpha ]==> (((a a)(^x.x))(a b))

     REDUCED to normal form.

  ------  384/3342. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  385/3351. ------  

  1. ==[ start ]==> (((^a.a) b)(a (a a)))
  2. ==[ alpha ]==> (((^x.x) b)(a (a a)))
  3. ==[ beta  ]==> (b (a (a a)))

     REDUCED to normal form.

  ------  386/3360. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x) a))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  387/3378. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  388/3384. ------  

  1. ==[ start ]==> ((^a.(a (^a.a))) a)
  2. ==[ alpha ]==> ((^x.(x (^y.y))) a)
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  389/3386. ------  

  1. ==[ start ]==> (^a.(a (a (^a.a))))
  2. ==[ alpha ]==> (^x.(x (x (^y.y))))

     REDUCED to normal form.

  ------  390/3387. ------  

  1. ==[ start ]==> (a (a (a (^a.a))))
  2. ==[ alpha ]==> (a (a (a (^x.x))))

     REDUCED to normal form.

  ------  391/3390. ------  

  1. ==[ start ]==> ((^a.a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  3. ==[ beta  ]==> (^y.(y (^z.z)))
  4. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  392/3519. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a) b)
  2. ==[ alpha ]==> (((^x.(^y.y)) a) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  393/3525. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  3. ==[ beta  ]==> ((^z.z)(^y.y))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  394/3528. ------  

  1. ==[ start ]==> ((a (a (^a.a))) a)
  2. ==[ alpha ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  395/3534. ------  

  1. ==[ start ]==> ((^a.a)(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  3. ==[ beta  ]==> (a (a (^y.y)))
  4. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  396/3537. ------  

  1. ==[ start ]==> ((a a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  397/3543. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  398/3561. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(a a)))
  3. ==[ beta  ]==> (((a a)(a a))((a a)(a a)))

     REDUCED to normal form.

  ------  399/3573. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  400/3582. ------  

  1. ==[ start ]==> (((a a) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  401/3588. ------  

  1. ==[ start ]==> ((^a.b)(b a))
  2. ==[ alpha ]==> ((^x.b)(b a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  402/3609. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a)))

     REDUCED to normal form.

  ------  403/3624. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  404/3636. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z)))
  3. ==[ beta  ]==> (b (^y.(^z.z)))
  4. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  405/3645. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(x x)))

     REDUCED to normal form.

  ------  406/3663. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  407/3669. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a a))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  408/3672. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.a))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  409/3677. ------  

  1. ==[ start ]==> (^a.(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  410/3678. ------  

  1. ==[ start ]==> (a (^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  411/3684. ------  

  1. ==[ start ]==> ((a a)(a (a (^a.a))))
  2. ==[ alpha ]==> ((a a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  412/3693. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  413/3702. ------  

  1. ==[ start ]==> (((^a.a) a)(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)(b (^y.y)))
  3. ==[ beta  ]==> (a (b (^y.y)))
  4. ==[ alpha ]==> (a (b (^x.x)))

     REDUCED to normal form.

  ------  414/3711. ------  

  1. ==[ start ]==> ((a (a a))((a a)(a a)))

     REDUCED to normal form.

  ------  415/3720. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b))
  3. ==[ beta  ]==> ((^y.y)((^z.z) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  416/3729. ------  

  1. ==[ start ]==> (((a a) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  417/3738. ------  

  1. ==[ start ]==> ((a b)(b a))

     REDUCED to normal form.

  ------  418/3747. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.y)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  419/3756. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(a a))

     REDUCED to normal form.

  ------  420/3774. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a))

     REDUCED to normal form.

  ------  421/3783. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z)))
  3. ==[ beta  ]==> (b ((^y.y)(^z.z)))
  4. ==[ alpha ]==> (b ((^x.x)(^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  422/3792. ------  

  1. ==[ start ]==> (((a a)(a a))(a (a a)))

     REDUCED to normal form.

  ------  423/3810. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  424/3816. ------  

  1. ==[ start ]==> ((^a.(a (^a.a))) b)
  2. ==[ alpha ]==> ((^x.(x (^y.y))) b)
  3. ==[ beta  ]==> (b (^y.y))
  4. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  425/3819. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a a))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a a))

     REDUCED to normal form.

  ------  426/3827. ------  

  1. ==[ start ]==> (^a.((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^x.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  427/3828. ------  

  1. ==[ start ]==> (a ((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> (a (^y.(^z.z)))
  4. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  428/3831. ------  

  1. ==[ start ]==> ((^a.a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  429/3840. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  430/3885. ------  

  1. ==[ start ]==> ((^a.b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  431/3921. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  432/3966. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^z.(^x1.x1))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  433/3969. ------  

  1. ==[ start ]==> ((a (a (^a.a))) b)
  2. ==[ alpha ]==> ((a (a (^x.x))) b)

     REDUCED to normal form.

  ------  434/3978. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a))) a)
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a)
  3. ==[ beta  ]==> ((^y.(^z.z)) a)
  4. ==[ alpha ]==> ((^x.(^y.y)) a)
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  435/3984. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  436/3987. ------  

  1. ==[ start ]==> ((a a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  437/3993. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  438/3996. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  439/4011. ------  

  1. ==[ start ]==> ((^a.(a a))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))(b (^y.y)))
  3. ==[ beta  ]==> ((b (^y.y))(b (^y.y)))
  4. ==[ alpha ]==> ((b (^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  440/4032. ------  

  1. ==[ start ]==> (((a a) a)(^b.b))
  2. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  441/4038. ------  

  1. ==[ start ]==> ((^a.b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(a (^y.(^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  442/4041. ------  

  1. ==[ start ]==> ((a b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  443/4074. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  444/4077. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.b))

     REDUCED to normal form.

  ------  445/4086. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.a))
  2. ==[ alpha ]==> (((^x.x) b)(^y.a))
  3. ==[ beta  ]==> (b (^y.a))
  4. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  446/4095. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  447/4113. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.a))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  448/4119. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.z)))
  3. ==[ beta  ]==> ((a (^z.z))(^y.y))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  449/4122. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  450/4131. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  451/4143. ------  

  1. ==[ start ]==> ((a a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  452/4152. ------  

  1. ==[ start ]==> ((a (^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y))))

     REDUCED to normal form.

  ------  453/4161. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) a))
  3. ==[ beta  ]==> (a ((^y.(^z.z)) a))
  4. ==[ alpha ]==> (a ((^x.(^y.y)) a))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  454/4170. ------  

  1. ==[ start ]==> ((a (a a))(b (^a.a)))
  2. ==[ alpha ]==> ((a (a a))(b (^x.x)))

     REDUCED to normal form.

  ------  455/4179. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  456/4188. ------  

  1. ==[ start ]==> (((a a) a)((^a.a) b))
  2. ==[ alpha ]==> (((a a) a)((^x.x) b))
  3. ==[ beta  ]==> (((a a) a) b)

     REDUCED to normal form.

  ------  457/4197. ------  

  1. ==[ start ]==> ((a b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  458/4206. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b a))
  2. ==[ alpha ]==> (((^x.x)(a a))(b a))
  3. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  459/4215. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  460/4233. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a b))

     REDUCED to normal form.

  ------  461/4242. ------  

  1. ==[ start ]==> (((^a.a) b)((a a) a))
  2. ==[ alpha ]==> (((^x.x) b)((a a) a))
  3. ==[ beta  ]==> (b ((a a) a))

     REDUCED to normal form.

  ------  462/4251. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  463/4269. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z) a))
  3. ==[ beta  ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  464/4278. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  465/4287. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a a))
  3. ==[ beta  ]==> ((^y.(^z.z))(a a))
  4. ==[ alpha ]==> ((^x.(^y.y))(a a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  466/4295. ------  

  1. ==[ start ]==> (^a.((a a) b))
  2. ==[ alpha ]==> (^x.((x x) b))

     REDUCED to normal form.

  ------  467/4296. ------  

  1. ==[ start ]==> (a ((a a) b))

     REDUCED to normal form.

  ------  468/4308. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  469/4353. ------  

  1. ==[ start ]==> ((^a.b)(^b.b))
  2. ==[ alpha ]==> ((^x.b)(^y.y))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  470/4389. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  471/4434. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.a))
  3. ==[ beta  ]==> ((^z.a)(^y.y))
  4. ==[ alpha ]==> ((^x.a)(^y.y))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  472/4446. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a))) b)
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) b)
  3. ==[ beta  ]==> ((^y.(^z.z)) b)
  4. ==[ alpha ]==> ((^x.(^y.y)) b)
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  473/4455. ------  

  1. ==[ start ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  474/4461. ------  

  1. ==[ start ]==> ((^a.a)((a a) b))
  2. ==[ alpha ]==> ((^x.x)((a a) b))
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  475/4470. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  476/4473. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  477/4482. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(y (^z.z))))
  3. ==[ beta  ]==> (a (^y.(y (^z.z))))
  4. ==[ alpha ]==> (a (^x.(x (^y.y))))

     REDUCED to normal form.

  ------  478/4488. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((^y.(^z.z)) a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) a))
  5. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  7. ==[ beta  ]==> ((^y.(^z.z)) a)
  8. ==[ alpha ]==> ((^x.(^y.y)) a)
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  479/4515. ------  

  1. ==[ start ]==> ((^a.b)((^a.a) b))
  2. ==[ alpha ]==> ((^x.b)((^y.y) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  480/4518. ------  

  1. ==[ start ]==> ((a b)(^b.b))
  2. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  481/4527. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  482/4551. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  483/4554. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a a)))

     REDUCED to normal form.

  ------  484/4563. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.b))
  2. ==[ alpha ]==> (((^x.x) b)(^y.b))
  3. ==[ beta  ]==> (b (^y.b))
  4. ==[ alpha ]==> (b (^x.b))

     REDUCED to normal form.

  ------  485/4590. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(z z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  486/4596. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z) a))
  3. ==[ beta  ]==> (((^z.z) a)(^y.y))
  4. ==[ alpha ]==> (((^x.x) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  487/4599. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.a))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  488/4608. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  489/4617. ------  

  1. ==[ start ]==> (((a a) b)(^a.a))
  2. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  490/4629. ------  

  1. ==[ start ]==> ((a a)((a a) b))

     REDUCED to normal form.

  ------  491/4638. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.x))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  492/4647. ------  

  1. ==[ start ]==> (((^a.a) a)(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(a (a (^y.y))))
  3. ==[ beta  ]==> (a (a (a (^y.y))))
  4. ==[ alpha ]==> (a (a (a (^x.x))))

     REDUCED to normal form.

  ------  493/4656. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y)) a))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  494/4665. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  495/4674. ------  

  1. ==[ start ]==> (((a a) a)((a a)(a a)))

     REDUCED to normal form.

  ------  496/4683. ------  

  1. ==[ start ]==> ((a b)((^a.a) b))
  2. ==[ alpha ]==> ((a b)((^x.x) b))
  3. ==[ beta  ]==> ((a b) b)

     REDUCED to normal form.

  ------  497/4692. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  498/4701. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b a))
  2. ==[ alpha ]==> (((a a)(^x.x))(b a))

     REDUCED to normal form.

  ------  499/4719. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  500/4728. ------  

  1. ==[ start ]==> (((^a.a) b)(a b))
  2. ==[ alpha ]==> (((^x.x) b)(a b))
  3. ==[ beta  ]==> (b (a b))

     REDUCED to normal form.

  ------  501/4737. ------  

  1. ==[ start ]==> (((a a)(a a))((a a) a))

     REDUCED to normal form.

  ------  502/4755. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  503/4764. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  504/4773. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  505/4782. ------  

  1. ==[ start ]==> (((a a) b)(a a))

     REDUCED to normal form.

  ------  506/4790. ------  

  1. ==[ start ]==> (^a.(b (a a)))
  2. ==[ alpha ]==> (^x.(b (x x)))

     REDUCED to normal form.

  ------  507/4791. ------  

  1. ==[ start ]==> (a (b (a a)))

     REDUCED to normal form.

  ------  508/4821. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((^y.(y (^z.z)))(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1))))
  5. ==[ beta  ]==> ((^z.(z (^x1.x1)))(^y.y))
  6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  7. ==[ beta  ]==> ((^z.z)(^y.y))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  509/4848. ------  

  1. ==[ start ]==> ((^a.b)(^c.(a a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  510/4929. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z z)))
  3. ==[ beta  ]==> ((^z.(z z))(^y.y))
  4. ==[ alpha ]==> ((^x.(x x))(^y.y))
  5. ==[ beta  ]==> ((^y.y)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  511/4950. ------  

  1. ==[ start ]==> (((a a) b) b)

     REDUCED to normal form.

  ------  512/4965. ------  

  1. ==[ start ]==> ((^a.a)(b (a a)))
  2. ==[ alpha ]==> ((^x.x)(b (a a)))
  3. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  513/4974. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a) b))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  514/4986. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a (^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  515/4992. ------  

  1. ==[ start ]==> ((^a.(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(a (a (^y.y))))
  3. ==[ beta  ]==> ((a (a (^y.y)))(a (a (^y.y))))
  4. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y))))

     REDUCED to normal form.

  ------  516/4995. ------  

  1. ==[ start ]==> ((a (a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  517/5019. ------  

  1. ==[ start ]==> ((^a.b)((a a)(a a)))
  2. ==[ alpha ]==> ((^x.b)((a a)(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  518/5022. ------  

  1. ==[ start ]==> ((a b)(^c.(a a)))
  2. ==[ alpha ]==> ((a b)(^x.(a a)))

     REDUCED to normal form.

  ------  519/5031. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  520/5040. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  521/5055. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  522/5067. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(a a)))
  3. ==[ beta  ]==> (b (^y.(a a)))
  4. ==[ alpha ]==> (b (^x.(a a)))

     REDUCED to normal form.

  ------  523/5076. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.b))
  2. ==[ alpha ]==> (((a a)(a a))(^x.b))

     REDUCED to normal form.

  ------  524/5094. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  525/5100. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (a a)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  526/5103. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y y)))

     REDUCED to normal form.

  ------  527/5112. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.a))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.a))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  528/5121. ------  

  1. ==[ start ]==> (((a a) b)(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  529/5142. ------  

  1. ==[ start ]==> ((a a)(b (a a)))

     REDUCED to normal form.

  ------  530/5151. ------  

  1. ==[ start ]==> ((a (^a.a))((a a) b))
  2. ==[ alpha ]==> ((a (^x.x))((a a) b))

     REDUCED to normal form.

  ------  531/5160. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a ((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  532/5169. ------  

  1. ==[ start ]==> ((a (a a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))(a (a (^x.x))))

     REDUCED to normal form.

  ------  533/5178. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  534/5187. ------  

  1. ==[ start ]==> (((a a) a)(b (^a.a)))
  2. ==[ alpha ]==> (((a a) a)(b (^x.x)))

     REDUCED to normal form.

  ------  535/5196. ------  

  1. ==[ start ]==> ((a b)((a a)(a a)))

     REDUCED to normal form.

  ------  536/5205. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y) b))
  3. ==[ beta  ]==> ((a a)((^y.y) b))
  4. ==[ alpha ]==> ((a a)((^x.x) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  537/5214. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  538/5232. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z)))

     REDUCED to normal form.

  ------  539/5241. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(a a)))
  3. ==[ beta  ]==> (b ((^y.y)(a a)))
  4. ==[ alpha ]==> (b ((^x.x)(a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  540/5250. ------  

  1. ==[ start ]==> (((a a)(a a))(a b))

     REDUCED to normal form.

  ------  541/5268. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  542/5277. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (a a)))

     REDUCED to normal form.

  ------  543/5286. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  544/5295. ------  

  1. ==[ start ]==> (((a a) b)(a (^a.a)))
  2. ==[ alpha ]==> (((a a) b)(a (^x.x)))

     REDUCED to normal form.

  ------  545/5312. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  546/5313. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  547/5343. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  548/5451. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^z.(^x1.x1))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  549/5472. ------  

  1. ==[ start ]==> (((a a) b) c)

     REDUCED to normal form.

  ------  550/5490. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a)) a)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z)) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  551/5496. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  552/5505. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b (a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(b (a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  553/5523. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  5. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1))))
  6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1))))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  554/5526. ------  

  1. ==[ start ]==> ((a (a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  555/5535. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  556/5550. ------  

  1. ==[ start ]==> ((^a.b)(b (^a.a)))
  2. ==[ alpha ]==> ((^x.b)(b (^y.y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  557/5571. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.b))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  558/5586. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  559/5598. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z)))
  3. ==[ beta  ]==> (b (^y.(^z.z)))
  4. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  560/5607. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(a a)))

     REDUCED to normal form.

  ------  561/5631. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((^z.z)(^x1.x1))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  562/5634. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  563/5643. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  564/5652. ------  

  1. ==[ start ]==> (((a a) b)(^b.a))
  2. ==[ alpha ]==> (((a a) b)(^x.a))

     REDUCED to normal form.

  ------  565/5670. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  566/5682. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  567/5691. ------  

  1. ==[ start ]==> ((a (^a.a))(b (a a)))
  2. ==[ alpha ]==> ((a (^x.x))(b (a a)))

     REDUCED to normal form.

  ------  568/5700. ------  

  1. ==[ start ]==> (((^a.a) a)((a a) b))
  2. ==[ alpha ]==> (((^x.x) a)((a a) b))
  3. ==[ beta  ]==> (a ((a a) b))

     REDUCED to normal form.

  ------  569/5709. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  570/5718. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  571/5727. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) a))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  572/5736. ------  

  1. ==[ start ]==> ((a b)(b (^a.a)))
  2. ==[ alpha ]==> ((a b)(b (^x.x)))

     REDUCED to normal form.

  ------  573/5745. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(a a)))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  574/5754. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a) b))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b))
  3. ==[ beta  ]==> (((a a)(^x.x)) b)

     REDUCED to normal form.

  ------  575/5772. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b a))

     REDUCED to normal form.

  ------  576/5781. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((a a)(^y.y)))
  3. ==[ beta  ]==> (b ((a a)(^y.y)))
  4. ==[ alpha ]==> (b ((a a)(^x.x)))

     REDUCED to normal form.

  ------  577/5790. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a)))
  3. ==[ beta  ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  578/5808. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  579/5817. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  580/5826. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  581/5835. ------  

  1. ==[ start ]==> (((a a) b)((^a.a) a))
  2. ==[ alpha ]==> (((a a) b)((^x.x) a))
  3. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  582/5853. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  583/5861. ------  

  1. ==[ start ]==> (^a.((a (^a.a)) a))
  2. ==[ alpha ]==> (^x.((x (^y.y)) x))

     REDUCED to normal form.

  ------  584/5862. ------  

  1. ==[ start ]==> (a ((a (^a.a)) a))
  2. ==[ alpha ]==> (a ((a (^x.x)) a))

     REDUCED to normal form.

  ------  585/5955. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  586/6039. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a)) b)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z)) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  587/6048. ------  

  1. ==[ start ]==> (((a (^a.a)) a) a)
  2. ==[ alpha ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  588/6054. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  3. ==[ beta  ]==> ((a (^y.y)) a)
  4. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  589/6063. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  590/6081. ------  

  1. ==[ start ]==> ((^a.(a a))((a a) b))
  2. ==[ alpha ]==> ((^x.(x x))((a a) b))
  3. ==[ beta  ]==> (((a a) b)((a a) b))

     REDUCED to normal form.

  ------  591/6093. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  592/6102. ------  

  1. ==[ start ]==> (((a a) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  593/6108. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  594/6144. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  595/6147. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  596/6183. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.b))
  3. ==[ beta  ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  597/6189. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a) a))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  598/6201. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  599/6210. ------  

  1. ==[ start ]==> (((a a) b)(^a.(a a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(x x)))

     REDUCED to normal form.

  ------  600/6228. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  601/6237. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.a))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  602/6249. ------  

  1. ==[ start ]==> ((a a)((a (^a.a)) a))
  2. ==[ alpha ]==> ((a a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  603/6258. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  604/6267. ------  

  1. ==[ start ]==> (((^a.a) a)(b (a a)))
  2. ==[ alpha ]==> (((^x.x) a)(b (a a)))
  3. ==[ beta  ]==> (a (b (a a)))

     REDUCED to normal form.

  ------  605/6276. ------  

  1. ==[ start ]==> ((a (a a))((a a) b))

     REDUCED to normal form.

  ------  606/6285. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  607/6294. ------  

  1. ==[ start ]==> (((a a) a)(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  608/6303. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y)) a))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  609/6312. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(b (^y.y)))
  3. ==[ beta  ]==> ((a a)(b (^y.y)))
  4. ==[ alpha ]==> ((a a)(b (^x.x)))

     REDUCED to normal form.

  ------  610/6321. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(a a)))

     REDUCED to normal form.

  ------  611/6339. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  612/6348. ------  

  1. ==[ start ]==> (((^a.a) b)(b a))
  2. ==[ alpha ]==> (((^x.x) b)(b a))
  3. ==[ beta  ]==> (b (b a))

     REDUCED to normal form.

  ------  613/6357. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x)))

     REDUCED to normal form.

  ------  614/6375. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  615/6384. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a) a))

     REDUCED to normal form.

  ------  616/6393. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  617/6402. ------  

  1. ==[ start ]==> (((a a) b)(a (a a)))

     REDUCED to normal form.

  ------  618/6420. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  619/6429. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a a))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a a))

     REDUCED to normal form.

  ------  620/6495. ------  

  1. ==[ start ]==> ((^a.b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(y (^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  621/6531. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  622/6576. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.b))
  3. ==[ beta  ]==> ((^z.b)(^y.y))
  4. ==[ alpha ]==> ((^x.b)(^y.y))
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  623/6624. ------  

  1. ==[ start ]==> (((a (^a.a)) a) b)
  2. ==[ alpha ]==> (((a (^x.x)) a) b)

     REDUCED to normal form.

  ------  624/6648. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  625/6666. ------  

  1. ==[ start ]==> ((^a.(a a))(b (a a)))
  2. ==[ alpha ]==> ((^x.(x x))(b (a a)))
  3. ==[ beta  ]==> ((b (a a))(b (a a)))

     REDUCED to normal form.

  ------  626/6687. ------  

  1. ==[ start ]==> (((a a) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  627/6693. ------  

  1. ==[ start ]==> ((^a.b)(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(a (a (^y.y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  628/6696. ------  

  1. ==[ start ]==> ((a b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  629/6729. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  630/6732. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  631/6741. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b (^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  632/6768. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  633/6774. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a b))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  634/6777. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.b))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.b))

     REDUCED to normal form.

  ------  635/6795. ------  

  1. ==[ start ]==> (((a a) b)(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  636/6813. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.a))
  3. ==[ beta  ]==> ((^y.y)(^x1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  637/6822. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z)))

     REDUCED to normal form.

  ------  638/6836. ------  

  1. ==[ start ]==> (^a.(^b.(a (^a.a))))
  2. ==[ alpha ]==> (^x.(^y.(x (^z.z))))

     REDUCED to normal form.

  ------  639/6837. ------  

  1. ==[ start ]==> (a (^b.(a (^a.a))))
  2. ==[ alpha ]==> (a (^x.(a (^y.y))))

     REDUCED to normal form.

  ------  640/6852. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) a))

     REDUCED to normal form.

  ------  641/6861. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (a ((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  642/6870. ------  

  1. ==[ start ]==> ((a (a a))(b (a a)))

     REDUCED to normal form.

  ------  643/6879. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  644/6888. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  645/6897. ------  

  1. ==[ start ]==> ((a b)(a (a (^a.a))))
  2. ==[ alpha ]==> ((a b)(a (a (^x.x))))

     REDUCED to normal form.

  ------  646/6906. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  647/6915. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  648/6933. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) b)

     REDUCED to normal form.

  ------  649/6942. ------  

  1. ==[ start ]==> (((^a.a) b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.z))))
  3. ==[ beta  ]==> (b (a (^y.(^z.z))))
  4. ==[ alpha ]==> (b (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  650/6951. ------  

  1. ==[ start ]==> (((a a)(a a))(b a))

     REDUCED to normal form.

  ------  651/6969. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  652/6978. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a b))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a b))

     REDUCED to normal form.

  ------  653/6987. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  654/6996. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.y)))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  655/7014. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  656/7023. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y)))

     REDUCED to normal form.

  ------  657/7040. ------  

  1. ==[ start ]==> (^a.((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (^x.((^y.y)(x (^z.z))))
  3. ==[ beta  ]==> (^x.(x (^z.z)))
  4. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  658/7041. ------  

  1. ==[ start ]==> (a ((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (a ((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> (a (a (^y.y)))
  4. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  659/7044. ------  

  1. ==[ start ]==> ((^a.a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  3. ==[ beta  ]==> (^y.(a (^z.z)))
  4. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  660/7098. ------  

  1. ==[ start ]==> ((^a.b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  661/7179. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(a a)))
  3. ==[ beta  ]==> ((^z.(a a))(^y.y))
  4. ==[ alpha ]==> ((^x.(a a))(^y.y))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  662/7245. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a))) a)
  2. ==[ alpha ]==> (((^x.x)(a (^y.y))) a)
  3. ==[ beta  ]==> ((a (^y.y)) a)
  4. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  663/7251. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  664/7254. ------  

  1. ==[ start ]==> ((a a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  665/7278. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1)))
  5. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1)))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  7. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  8. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  666/7305. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  667/7308. ------  

  1. ==[ start ]==> ((a b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  668/7317. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  669/7341. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  670/7353. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.b))
  2. ==[ alpha ]==> (((^x.x) b)(^y.y))
  3. ==[ beta  ]==> (b (^y.y))
  4. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  671/7362. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  672/7386. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(a a)))
  3. ==[ beta  ]==> (((^z.z)(a a))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(a a))(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  673/7389. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a a)))

     REDUCED to normal form.

  ------  674/7398. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.b))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.b))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  675/7407. ------  

  1. ==[ start ]==> (((a a) b)(^c.a))
  2. ==[ alpha ]==> (((a a) b)(^x.a))

     REDUCED to normal form.

  ------  676/7425. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  677/7434. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.a))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.a))

     REDUCED to normal form.

  ------  678/7452. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z))
  3. ==[ beta  ]==> ((a (^y.y))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  679/7464. ------  

  1. ==[ start ]==> ((a a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  680/7482. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y)) a))
  3. ==[ beta  ]==> (a ((a (^y.y)) a))
  4. ==[ alpha ]==> (a ((a (^x.x)) a))

     REDUCED to normal form.

  ------  681/7491. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  682/7500. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  683/7509. ------  

  1. ==[ start ]==> (((a a) a)((a a) b))

     REDUCED to normal form.

  ------  684/7518. ------  

  1. ==[ start ]==> ((a b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a b)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  685/7527. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  686/7536. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  687/7554. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a a)))

     REDUCED to normal form.

  ------  688/7563. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a) b))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y) b))
  3. ==[ beta  ]==> (b ((^y.y) b))
  4. ==[ alpha ]==> (b ((^x.x) b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  689/7572. ------  

  1. ==[ start ]==> (((a a)(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  690/7590. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  691/7599. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a a))

     REDUCED to normal form.

  ------  692/7608. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a b))
  3. ==[ beta  ]==> ((^y.(^z.z))(a b))
  4. ==[ alpha ]==> ((^x.(^y.y))(a b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  693/7617. ------  

  1. ==[ start ]==> (((a a) b)((a a) a))

     REDUCED to normal form.

  ------  694/7635. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  695/7644. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) a))
  3. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  696/7662. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a a))
  3. ==[ beta  ]==> ((a (^y.y))(a a))
  4. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  697/7670. ------  

  1. ==[ start ]==> (^a.((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.((x x)(^y.(^z.z))))

     REDUCED to normal form.

  ------  698/7671. ------  

  1. ==[ start ]==> (a ((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (a ((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  699/7683. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  700/7728. ------  

  1. ==[ start ]==> ((^a.b)(^c.b))
  2. ==[ alpha ]==> ((^x.b)(^y.b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  701/7875. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a))) b)
  2. ==[ alpha ]==> (((^x.x)(a (^y.y))) b)
  3. ==[ beta  ]==> ((a (^y.y)) b)
  4. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  702/7884. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a))) a)
  2. ==[ alpha ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  703/7890. ------  

  1. ==[ start ]==> ((^a.a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  704/7899. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  705/7902. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  706/7917. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y)) a))
  3. ==[ beta  ]==> (((a (^y.y)) a)((a (^y.y)) a))
  4. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y)) a))

     REDUCED to normal form.

  ------  707/7944. ------  

  1. ==[ start ]==> ((^a.b)((a a) b))
  2. ==[ alpha ]==> ((^x.b)((a a) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  708/7947. ------  

  1. ==[ start ]==> ((a b)(^c.b))
  2. ==[ alpha ]==> ((a b)(^x.b))

     REDUCED to normal form.

  ------  709/7956. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  710/7965. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  711/7980. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  712/7992. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.(a a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(a a)))
  3. ==[ beta  ]==> (b (^y.(a a)))
  4. ==[ alpha ]==> (b (^x.(a a)))

     REDUCED to normal form.

  ------  713/8001. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.b))
  2. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  714/8025. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^z.z))(^y.y))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  715/8037. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  716/8046. ------  

  1. ==[ start ]==> (((a a) b)(^a.b))
  2. ==[ alpha ]==> (((a a) b)(^x.b))

     REDUCED to normal form.

  ------  717/8064. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  718/8073. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y y)))

     REDUCED to normal form.

  ------  719/8091. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  720/8100. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  721/8112. ------  

  1. ==[ start ]==> ((a a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  722/8121. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  723/8139. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x)) a))

     REDUCED to normal form.

  ------  724/8148. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  725/8157. ------  

  1. ==[ start ]==> (((a a) a)(b (a a)))

     REDUCED to normal form.

  ------  726/8166. ------  

  1. ==[ start ]==> ((a b)((a a) b))

     REDUCED to normal form.

  ------  727/8175. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  728/8184. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.y))))

     REDUCED to normal form.

  ------  729/8202. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z)))

     REDUCED to normal form.

  ------  730/8211. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x) b)((a a)(a a)))
  3. ==[ beta  ]==> (b ((a a)(a a)))

     REDUCED to normal form.

  ------  731/8220. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a) b))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x) b))
  3. ==[ beta  ]==> (((a a)(a a)) b)

     REDUCED to normal form.

  ------  732/8238. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  733/8247. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.y)))

     REDUCED to normal form.

  ------  734/8256. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  735/8265. ------  

  1. ==[ start ]==> (((a a) b)(a b))

     REDUCED to normal form.

  ------  736/8283. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  737/8292. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (a a)))

     REDUCED to normal form.

  ------  738/8310. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  739/8319. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  740/8327. ------  

  1. ==[ start ]==> (^a.(b b))
  2. ==[ alpha ]==> (^x.(b b))

     REDUCED to normal form.

  ------  741/8328. ------  

  1. ==[ start ]==> (a (b b))

     REDUCED to normal form.

  ------  742/8541. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a))) b)
  2. ==[ alpha ]==> (((a a)(^x.(^y.y))) b)

     REDUCED to normal form.

  ------  743/8556. ------  

  1. ==[ start ]==> ((^a.a)(b b))
  2. ==[ alpha ]==> ((^x.x)(b b))
  3. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  744/8565. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  745/8577. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(a (^z.z))))
  3. ==[ beta  ]==> (a (^y.(a (^z.z))))
  4. ==[ alpha ]==> (a (^x.(a (^y.y))))

     REDUCED to normal form.

  ------  746/8610. ------  

  1. ==[ start ]==> ((^a.b)(b (a a)))
  2. ==[ alpha ]==> ((^x.b)(b (a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  747/8631. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  748/8646. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  749/8685. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  750/8691. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b a))
  3. ==[ beta  ]==> ((b a)(^y.y))
  4. ==[ alpha ]==> ((b a)(^x.x))

     REDUCED to normal form.

  ------  751/8712. ------  

  1. ==[ start ]==> (((a a) b)(^b.(a a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(a a)))

     REDUCED to normal form.

  ------  752/8739. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z)))

     REDUCED to normal form.

  ------  753/8757. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.a))
  3. ==[ beta  ]==> ((a (^y.y))(^z.a))
  4. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  754/8766. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  755/8787. ------  

  1. ==[ start ]==> ((a a)(b b))

     REDUCED to normal form.

  ------  756/8796. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  757/8805. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (a ((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> (a ((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  758/8823. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  759/8832. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  760/8841. ------  

  1. ==[ start ]==> ((a b)(b (a a)))

     REDUCED to normal form.

  ------  761/8850. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a) b))
  3. ==[ beta  ]==> ((a a)((a a) b))

     REDUCED to normal form.

  ------  762/8859. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  763/8877. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  764/8886. ------  

  1. ==[ start ]==> (((^a.a) b)(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(b (^y.y)))
  3. ==[ beta  ]==> (b (b (^y.y)))
  4. ==[ alpha ]==> (b (b (^x.x)))

     REDUCED to normal form.

  ------  765/8895. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)(a a)))

     REDUCED to normal form.

  ------  766/8913. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  767/8922. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b a))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b a))

     REDUCED to normal form.

  ------  768/8931. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  769/8940. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(a a)))
  3. ==[ beta  ]==> (((a a) b)(a a))

     REDUCED to normal form.

  ------  770/8958. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  771/8967. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  772/8985. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y) a))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  773/8994. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  774/9011. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))(x x)))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  775/9012. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (a ((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  776/9042. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((^y.(a (^z.z)))(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((^x.(a (^y.y)))(^z.(a (^x1.x1))))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  777/9105. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 (^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  778/9150. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^z.(^x1.(^y1.y1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  779/9243. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a)) a)
  2. ==[ alpha ]==> (((^x.(^y.y))(a a)) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  780/9249. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(a a))
  4. ==[ alpha ]==> ((^x.(^y.y))(a a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  781/9258. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b b))
  2. ==[ alpha ]==> ((^x.(^y.y))(b b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  782/9276. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((^y.y)(a (^z.z)))((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a (^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))((^z.z)(a (^x1.x1))))
  6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z))))
  7. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  8. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  783/9279. ------  

  1. ==[ start ]==> ((a (a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  784/9303. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  785/9339. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  786/9342. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (^x1.x1))))

     REDUCED to normal form.

  ------  787/9378. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  788/9384. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^z.(^x1.x1)))(^y.y))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  789/9387. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  790/9405. ------  

  1. ==[ start ]==> (((a a) b)(^c.(^a.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  791/9423. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.b))
  3. ==[ beta  ]==> ((^y.y)(^x1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  792/9450. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(z z)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(z z)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  793/9459. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  794/9477. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  795/9489. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  796/9498. ------  

  1. ==[ start ]==> ((a (^a.a))(b b))
  2. ==[ alpha ]==> ((a (^x.x))(b b))

     REDUCED to normal form.

  ------  797/9507. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> (a ((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> (a ((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  798/9516. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> ((a (a a))(a (^y.y)))
  4. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  799/9534. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  800/9543. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  801/9552. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(b (a a)))
  3. ==[ beta  ]==> ((a a)(b (a a)))

     REDUCED to normal form.

  ------  802/9561. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a) b))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a) b))

     REDUCED to normal form.

  ------  803/9579. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (^z.z))))

     REDUCED to normal form.

  ------  804/9588. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) a))
  3. ==[ beta  ]==> (b ((^y.(^z.z)) a))
  4. ==[ alpha ]==> (b ((^x.(^y.y)) a))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  805/9597. ------  

  1. ==[ start ]==> (((a a)(a a))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))(b (^x.x)))

     REDUCED to normal form.

  ------  806/9615. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z) b))
  3. ==[ beta  ]==> ((^y.y)((^z.z) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  807/9624. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  808/9633. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b a))
  3. ==[ beta  ]==> ((^y.(^z.z))(b a))
  4. ==[ alpha ]==> ((^x.(^y.y))(b a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  809/9642. ------  

  1. ==[ start ]==> (((a a) b)((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a) b)((a a)(^x.x)))

     REDUCED to normal form.

  ------  810/9660. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  811/9669. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a) a))

     REDUCED to normal form.

  ------  812/9687. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (a a)))
  3. ==[ beta  ]==> ((a (^y.y))(a (a a)))
  4. ==[ alpha ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  813/9696. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) a))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  814/9714. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  815/9722. ------  

  1. ==[ start ]==> (^a.((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (^x.((x (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  816/9723. ------  

  1. ==[ start ]==> (a ((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (a ((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  817/9816. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  818/9861. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  3. ==[ beta  ]==> ((^z.z)(^y.y))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  819/9954. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a)) b)
  2. ==[ alpha ]==> (((^x.(^y.y))(a a)) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  820/9963. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a)) a)
  2. ==[ alpha ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  821/9969. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  822/9978. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  823/9996. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a)(^y.(^z.z)))((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  824/10008. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  825/10023. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y)) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  826/10059. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  827/10062. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  828/10071. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(y (^z.z))))
  3. ==[ beta  ]==> (b (^y.(y (^z.z))))
  4. ==[ alpha ]==> (b (^x.(x (^y.y))))

     REDUCED to normal form.

  ------  829/10104. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z) b))
  3. ==[ beta  ]==> (((^z.z) b)(^y.y))
  4. ==[ alpha ]==> (((^x.x) b)(^y.y))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  830/10107. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.b))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  831/10116. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  832/10143. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  833/10152. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.b))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.b))

     REDUCED to normal form.

  ------  834/10170. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  835/10179. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z z)))

     REDUCED to normal form.

  ------  836/10197. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  837/10206. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  838/10218. ------  

  1. ==[ start ]==> ((a a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  839/10227. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  840/10236. ------  

  1. ==[ start ]==> (((^a.a) a)(b b))
  2. ==[ alpha ]==> (((^x.x) a)(b b))
  3. ==[ beta  ]==> (a (b b))

     REDUCED to normal form.

  ------  841/10245. ------  

  1. ==[ start ]==> ((a (a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  842/10254. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  843/10272. ------  

  1. ==[ start ]==> ((a b)((a (^a.a)) a))
  2. ==[ alpha ]==> ((a b)((a (^x.x)) a))

     REDUCED to normal form.

  ------  844/10281. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  845/10290. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b (a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(b (a a)))

     REDUCED to normal form.

  ------  846/10308. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  847/10317. ------  

  1. ==[ start ]==> (((^a.a) b)(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(a (a (^y.y))))
  3. ==[ beta  ]==> (b (a (a (^y.y))))
  4. ==[ alpha ]==> (b (a (a (^x.x))))

     REDUCED to normal form.

  ------  848/10326. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) a))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  849/10344. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  850/10353. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) b))
  3. ==[ beta  ]==> ((a (a (^x.x))) b)

     REDUCED to normal form.

  ------  851/10362. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  852/10371. ------  

  1. ==[ start ]==> (((a a) b)(b a))

     REDUCED to normal form.

  ------  853/10389. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  854/10398. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a b))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a b))

     REDUCED to normal form.

  ------  855/10416. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  856/10425. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a a)))

     REDUCED to normal form.

  ------  857/10443. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  858/10452. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a a))

     REDUCED to normal form.

  ------  859/10518. ------  

  1. ==[ start ]==> ((^a.b)(^a.c))
  2. ==[ alpha ]==> ((^x.b)(^y.c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  860/10701. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a)) b)
  2. ==[ alpha ]==> (((a (^x.x))(^y.y)) b)

     REDUCED to normal form.

  ------  861/10725. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  862/10743. ------  

  1. ==[ start ]==> ((^a.(a a))(b b))
  2. ==[ alpha ]==> ((^x.(x x))(b b))
  3. ==[ beta  ]==> ((b b)(b b))

     REDUCED to normal form.

  ------  863/10764. ------  

  1. ==[ start ]==> (((a a) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  864/10770. ------  

  1. ==[ start ]==> ((^a.b)(a c))
  2. ==[ alpha ]==> ((^x.b)(a c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  865/10773. ------  

  1. ==[ start ]==> ((a b)(^a.c))
  2. ==[ alpha ]==> ((a b)(^x.c))

     REDUCED to normal form.

  ------  866/10806. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  867/10818. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b (^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  868/10827. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  869/10851. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(a a)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  870/10863. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  871/10872. ------  

  1. ==[ start ]==> (((a a) b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  872/10899. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(a a)))

     REDUCED to normal form.

  ------  873/10926. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  874/10944. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.a))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  875/10953. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  876/10967. ------  

  1. ==[ start ]==> (^a.(^a.(^b.a)))
  2. ==[ alpha ]==> (^x.(^y.(^z.y)))

     REDUCED to normal form.

  ------  877/10968. ------  

  1. ==[ start ]==> (a (^a.(^b.a)))
  2. ==[ alpha ]==> (a (^x.(^y.x)))

     REDUCED to normal form.

  ------  878/10983. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  879/10992. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (a ((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> (a ((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  880/11001. ------  

  1. ==[ start ]==> ((a (a a))(b b))

     REDUCED to normal form.

  ------  881/11010. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  882/11019. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> (((a a) a)(a (^y.y)))
  4. ==[ alpha ]==> (((a a) a)(a (^x.x)))

     REDUCED to normal form.

  ------  883/11028. ------  

  1. ==[ start ]==> ((a b)(a c))

     REDUCED to normal form.

  ------  884/11037. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y)) a))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) a))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  885/11046. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  886/11064. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) b))

     REDUCED to normal form.

  ------  887/11073. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b ((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  888/11082. ------  

  1. ==[ start ]==> (((a a)(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(a (a (^x.x))))

     REDUCED to normal form.

  ------  889/11100. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  890/11109. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(a a)))

     REDUCED to normal form.

  ------  891/11118. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) b))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1) b))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  892/11127. ------  

  1. ==[ start ]==> (((a a) b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  893/11145. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  894/11154. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a a))

     REDUCED to normal form.

  ------  895/11172. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a) a))
  3. ==[ beta  ]==> ((a (^y.y))((a a) a))
  4. ==[ alpha ]==> ((a (^x.x))((a a) a))

     REDUCED to normal form.

  ------  896/11181. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  897/11199. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z) a))
  3. ==[ beta  ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  898/11208. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z)))

     REDUCED to normal form.

  ------  899/11223. ------  

  1. ==[ start ]==> ((^a.(^b.a)) a)
  2. ==[ alpha ]==> ((^x.(^y.x)) a)
  3. ==[ beta  ]==> (^y.a)
  4. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  900/11225. ------  

  1. ==[ start ]==> (^a.(a (^b.a)))
  2. ==[ alpha ]==> (^x.(x (^y.x)))

     REDUCED to normal form.

  ------  901/11226. ------  

  1. ==[ start ]==> (a (a (^b.a)))
  2. ==[ alpha ]==> (a (a (^x.a)))

     REDUCED to normal form.

  ------  902/11229. ------  

  1. ==[ start ]==> ((^a.a)(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  3. ==[ beta  ]==> (^y.(^z.y))
  4. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  903/11283. ------  

  1. ==[ start ]==> ((^a.b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(a (^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  904/11481. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.a))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.z))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  905/11484. ------  

  1. ==[ start ]==> ((a (^b.a)) a)
  2. ==[ alpha ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  906/11490. ------  

  1. ==[ start ]==> ((^a.a)(a (^b.a)))
  2. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  3. ==[ beta  ]==> (a (^y.a))
  4. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  907/11493. ------  

  1. ==[ start ]==> ((a a)(^a.(^b.a)))
  2. ==[ alpha ]==> ((a a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  908/11517. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((^y.(^z.z))(a a))((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(a a)))
  5. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  7. ==[ beta  ]==> ((^y.(^z.z))(a a))
  8. ==[ alpha ]==> ((^x.(^y.y))(a a))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  909/11544. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  910/11547. ------  

  1. ==[ start ]==> ((a b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  911/11580. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  912/11592. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.b))
  2. ==[ alpha ]==> (((^x.x) b)(^y.b))
  3. ==[ beta  ]==> (b (^y.b))
  4. ==[ alpha ]==> (b (^x.b))

     REDUCED to normal form.

  ------  913/11601. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  914/11625. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.z)))
  3. ==[ beta  ]==> ((b (^z.z))(^y.y))
  4. ==[ alpha ]==> ((b (^x.x))(^y.y))

     REDUCED to normal form.

  ------  915/11646. ------  

  1. ==[ start ]==> (((a a) b)(^b.b))
  2. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  916/11691. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.b))
  3. ==[ beta  ]==> ((a (^y.y))(^z.b))
  4. ==[ alpha ]==> ((a (^x.x))(^y.b))

     REDUCED to normal form.

  ------  917/11718. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(z z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  918/11727. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.a))

     REDUCED to normal form.

  ------  919/11742. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a a))
  2. ==[ alpha ]==> ((^x.(^y.x))(a a))
  3. ==[ beta  ]==> (^y.(a a))
  4. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  920/11745. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.a))
  2. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  921/11750. ------  

  1. ==[ start ]==> (^a.(^b.c))
  2. ==[ alpha ]==> (^x.(^y.c))

     REDUCED to normal form.

  ------  922/11751. ------  

  1. ==[ start ]==> (a (^b.c))
  2. ==[ alpha ]==> (a (^x.c))

     REDUCED to normal form.

  ------  923/11757. ------  

  1. ==[ start ]==> ((a a)(a (^b.a)))
  2. ==[ alpha ]==> ((a a)(a (^x.a)))

     REDUCED to normal form.

  ------  924/11775. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> (a ((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> (a ((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  925/11784. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  926/11793. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  927/11802. ------  

  1. ==[ start ]==> (((a a) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  928/11811. ------  

  1. ==[ start ]==> ((a b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a b)((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> ((a b)(a (^y.y)))
  4. ==[ alpha ]==> ((a b)(a (^x.x)))

     REDUCED to normal form.

  ------  929/11829. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) a))

     REDUCED to normal form.

  ------  930/11847. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a a)))

     REDUCED to normal form.

  ------  931/11856. ------  

  1. ==[ start ]==> (((^a.a) b)((a a) b))
  2. ==[ alpha ]==> (((^x.x) b)((a a) b))
  3. ==[ beta  ]==> (b ((a a) b))

     REDUCED to normal form.

  ------  932/11865. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a)(a a))(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  933/11883. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  934/11892. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y)))

     REDUCED to normal form.

  ------  935/11901. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  936/11910. ------  

  1. ==[ start ]==> (((a a) b)((^a.a) b))
  2. ==[ alpha ]==> (((a a) b)((^x.x) b))
  3. ==[ beta  ]==> (((a a) b) b)

     REDUCED to normal form.

  ------  937/11928. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  938/11937. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.y)))

     REDUCED to normal form.

  ------  939/11955. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a b))
  3. ==[ beta  ]==> ((a (^y.y))(a b))
  4. ==[ alpha ]==> ((a (^x.x))(a b))

     REDUCED to normal form.

  ------  940/11964. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a) a))

     REDUCED to normal form.

  ------  941/11982. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  942/11991. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  943/12006. ------  

  1. ==[ start ]==> ((^a.(^b.a)) b)
  2. ==[ alpha ]==> ((^x.(^y.x)) b)
  3. ==[ beta  ]==> (^y.b)
  4. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  944/12009. ------  

  1. ==[ start ]==> ((a (^b.a))(a a))
  2. ==[ alpha ]==> ((a (^x.a))(a a))

     REDUCED to normal form.

  ------  945/12021. ------  

  1. ==[ start ]==> ((^a.a)(^b.c))
  2. ==[ alpha ]==> ((^x.x)(^y.c))
  3. ==[ beta  ]==> (^y.c)
  4. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  946/12030. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  947/12075. ------  

  1. ==[ start ]==> ((^a.b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  948/12273. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  949/12276. ------  

  1. ==[ start ]==> ((a (^b.a)) b)
  2. ==[ alpha ]==> ((a (^x.a)) b)

     REDUCED to normal form.

  ------  950/12294. ------  

  1. ==[ start ]==> ((a a)(^b.c))
  2. ==[ alpha ]==> ((a a)(^x.c))

     REDUCED to normal form.

  ------  951/12300. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  952/12303. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y)))

     REDUCED to normal form.

  ------  953/12318. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> (((a (^y.y))(^z.z))((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1)))

     REDUCED to normal form.

  ------  954/12345. ------  

  1. ==[ start ]==> ((^a.b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  955/12348. ------  

  1. ==[ start ]==> ((a b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  956/12357. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  957/12381. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  958/12420. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  959/12426. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (((^z.(^x1.x1)) a)(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  960/12447. ------  

  1. ==[ start ]==> (((a a) b)(^c.(a a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(a a)))

     REDUCED to normal form.

  ------  961/12465. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  962/12492. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(a a)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(a a)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(a a)))

     REDUCED to normal form.

  ------  963/12501. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.b))

     REDUCED to normal form.

  ------  964/12519. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  965/12528. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z z)))

     REDUCED to normal form.

  ------  966/12543. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.z)))
  3. ==[ beta  ]==> (^y.(a (^z.z)))
  4. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  967/12546. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  968/12576. ------  

  1. ==[ start ]==> ((a (^a.a))(a (^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))(a (^y.a)))

     REDUCED to normal form.

  ------  969/12594. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  970/12603. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  971/12612. ------  

  1. ==[ start ]==> (((a a) a)(b b))

     REDUCED to normal form.

  ------  972/12621. ------  

  1. ==[ start ]==> ((a b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  973/12630. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a a)((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  974/12657. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  975/12666. ------  

  1. ==[ start ]==> (((^a.a) b)(b (a a)))
  2. ==[ alpha ]==> (((^x.x) b)(b (a a)))
  3. ==[ beta  ]==> (b (b (a a)))

     REDUCED to normal form.

  ------  976/12675. ------  

  1. ==[ start ]==> (((a a)(a a))((a a) b))

     REDUCED to normal form.

  ------  977/12693. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  978/12702. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  979/12711. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(b (^x1.x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  980/12720. ------  

  1. ==[ start ]==> (((a a) b)((a a)(a a)))

     REDUCED to normal form.

  ------  981/12738. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  982/12747. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b a))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b a))

     REDUCED to normal form.

  ------  983/12765. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a)))
  5. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  984/12774. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a b))

     REDUCED to normal form.

  ------  985/12792. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  986/12801. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a a)))

     REDUCED to normal form.

  ------  987/12816. ------  

  1. ==[ start ]==> ((^a.(^b.a)) c)
  2. ==[ alpha ]==> ((^x.(^y.x)) c)
  3. ==[ beta  ]==> (^y.c)
  4. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  988/12819. ------  

  1. ==[ start ]==> ((a (^b.a))(a (^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(a (^y.y)))

     REDUCED to normal form.

  ------  989/12836. ------  

  1. ==[ start ]==> (^a.((a a)(a (^a.a))))
  2. ==[ alpha ]==> (^x.((x x)(x (^y.y))))

     REDUCED to normal form.

  ------  990/12837. ------  

  1. ==[ start ]==> (a ((a a)(a (^a.a))))
  2. ==[ alpha ]==> (a ((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  991/12849. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.c))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.c))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  992/12975. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^z.(z (^x1.x1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  5. ==[ beta  ]==> ((^z.z)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  993/13092. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.a))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.a))
  3. ==[ beta  ]==> (^y.(^z.a))
  4. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  994/13095. ------  

  1. ==[ start ]==> ((a (^b.a)) c)
  2. ==[ alpha ]==> ((a (^x.a)) c)

     REDUCED to normal form.

  ------  995/13113. ------  

  1. ==[ start ]==> (((a a)(a (^a.a))) a)
  2. ==[ alpha ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  996/13119. ------  

  1. ==[ start ]==> ((^a.a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  997/13131. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.c))
  2. ==[ alpha ]==> ((a (^x.x))(^y.c))

     REDUCED to normal form.

  ------  998/13140. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.y)))
  3. ==[ beta  ]==> (a (^y.(^z.y)))
  4. ==[ alpha ]==> (a (^x.(^y.x)))

     REDUCED to normal form.

  ------  999/13173. ------  

  1. ==[ start ]==> ((^a.b)(b b))
  2. ==[ alpha ]==> ((^x.b)(b b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1000/13194. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1001/13209. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1)) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1002/13248. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1003/13254. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (a (^z.z))))
  3. ==[ beta  ]==> ((a (a (^z.z)))(^y.y))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1004/13257. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1005/13293. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1006/13302. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1007/13329. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a a)))

     REDUCED to normal form.

  ------  1008/13356. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  1009/13371. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z) a))
  3. ==[ beta  ]==> (^y.((^z.z) a))
  4. ==[ alpha ]==> (^x.((^y.y) a))
  5. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  1010/13374. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.a))
  2. ==[ alpha ]==> ((a (^x.a))(^y.a))

     REDUCED to normal form.

  ------  1011/13392. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1012/13404. ------  

  1. ==[ start ]==> ((a a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1013/13422. ------  

  1. ==[ start ]==> (((^a.a) a)(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)(a (^y.a)))
  3. ==[ beta  ]==> (a (a (^y.a)))
  4. ==[ alpha ]==> (a (a (^x.a)))

     REDUCED to normal form.

  ------  1014/13440. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1015/13449. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  1016/13458. ------  

  1. ==[ start ]==> ((a b)(b b))

     REDUCED to normal form.

  ------  1017/13467. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  1018/13476. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a a)(^x.x))(a (^z.z)))
  4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  1019/13494. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) a))

     REDUCED to normal form.

  ------  1020/13503. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (b ((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1021/13512. ------  

  1. ==[ start ]==> (((a a)(a a))(b (a a)))

     REDUCED to normal form.

  ------  1022/13530. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1023/13539. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y))))

     REDUCED to normal form.

  ------  1024/13548. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1025/13557. ------  

  1. ==[ start ]==> (((a a) b)(b (^a.a)))
  2. ==[ alpha ]==> (((a a) b)(b (^x.x)))

     REDUCED to normal form.

  ------  1026/13575. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1027/13584. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1028/13602. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  1029/13611. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  1030/13629. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1031/13638. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  1032/13656. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a) a))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y) a))
  3. ==[ beta  ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  1033/13674. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a a))

     REDUCED to normal form.

  ------  1034/13682. ------  

  1. ==[ start ]==> (^a.(b (^a.(^a.a))))
  2. ==[ alpha ]==> (^x.(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  1035/13683. ------  

  1. ==[ start ]==> (a (b (^a.(^a.a))))
  2. ==[ alpha ]==> (a (b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1036/13713. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.y)))
  3. ==[ beta  ]==> ((^y.(^z.y))(^y.(^z.y)))
  4. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.z)))
  5. ==[ beta  ]==> (^y.(^z.(^x1.z)))
  6. ==[ alpha ]==> (^x.(^y.(^z.y)))

     REDUCED to normal form.

  ------  1037/13821. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^z.(^x1.(^y1.y1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1038/13938. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(z z)))
  3. ==[ beta  ]==> (^y.(^z.(z z)))
  4. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  1039/13959. ------  

  1. ==[ start ]==> (((a a)(a (^a.a))) b)
  2. ==[ alpha ]==> (((a a)(a (^x.x))) b)

     REDUCED to normal form.

  ------  1040/13974. ------  

  1. ==[ start ]==> ((^a.a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  3. ==[ beta  ]==> (b (^y.(^z.z)))
  4. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  1041/13983. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1042/13995. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.c))
  2. ==[ alpha ]==> (((^x.x) a)(^y.c))
  3. ==[ beta  ]==> (a (^y.c))
  4. ==[ alpha ]==> (a (^x.c))

     REDUCED to normal form.

  ------  1043/14001. ------  

  1. ==[ start ]==> ((^a.(a a))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))(a (^y.a)))
  3. ==[ beta  ]==> ((a (^y.a))(a (^y.a)))
  4. ==[ alpha ]==> ((a (^x.a))(a (^y.a)))

     REDUCED to normal form.

  ------  1044/14004. ------  

  1. ==[ start ]==> ((a (a a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.x)))

     REDUCED to normal form.

  ------  1045/14028. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1046/14109. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^z.z)(^x1.(^y1.y1)))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1047/14112. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1048/14121. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1049/14157. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.b))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  1050/14202. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.b))
  3. ==[ beta  ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  1051/14226. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (a a)))
  3. ==[ beta  ]==> (^y.(a (a a)))
  4. ==[ alpha ]==> (^x.(a (a a)))

     REDUCED to normal form.

  ------  1052/14229. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(a a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(y y)))

     REDUCED to normal form.

  ------  1053/14247. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1054/14268. ------  

  1. ==[ start ]==> ((a a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1055/14277. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  1056/14295. ------  

  1. ==[ start ]==> ((a (a a))(a (^b.a)))
  2. ==[ alpha ]==> ((a (a a))(a (^x.a)))

     REDUCED to normal form.

  ------  1057/14313. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1058/14322. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  1059/14331. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b b))
  2. ==[ alpha ]==> (((^x.x)(a a))(b b))
  3. ==[ beta  ]==> ((a a)(b b))

     REDUCED to normal form.

  ------  1060/14340. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  1061/14367. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) a))
  3. ==[ beta  ]==> (b ((a (^y.y)) a))
  4. ==[ alpha ]==> (b ((a (^x.x)) a))

     REDUCED to normal form.

  ------  1062/14376. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  1063/14394. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1064/14403. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1065/14412. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1066/14421. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) a))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  1067/14439. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1068/14448. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) b))
  3. ==[ beta  ]==> (((a (^x.x)) a) b)

     REDUCED to normal form.

  ------  1069/14466. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b a))
  3. ==[ beta  ]==> ((a (^y.y))(b a))
  4. ==[ alpha ]==> ((a (^x.x))(b a))

     REDUCED to normal form.

  ------  1070/14475. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.z)))

     REDUCED to normal form.

  ------  1071/14493. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  1072/14502. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a) a))

     REDUCED to normal form.

  ------  1073/14520. ------  

  1. ==[ start ]==> ((a (^b.a))(a (a a)))
  2. ==[ alpha ]==> ((a (^x.a))(a (a a)))

     REDUCED to normal form.

  ------  1074/14538. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  1075/14555. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a)) b))
  2. ==[ alpha ]==> (^x.((^y.(^z.z)) b))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1076/14556. ------  

  1. ==[ start ]==> (a ((^a.(^a.a)) b))
  2. ==[ alpha ]==> (a ((^x.(^y.y)) b))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1077/14586. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.c))
  2. ==[ alpha ]==> ((^x.(x x))(^y.c))
  3. ==[ beta  ]==> ((^y.c)(^y.c))
  4. ==[ alpha ]==> ((^x.c)(^y.c))
  5. ==[ beta  ]==> c

     REDUCED to normal form.

  ------  1078/14649. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1079/14811. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1080/14850. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b) a)
  2. ==[ alpha ]==> (((^x.(^y.y)) b) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1081/14856. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((^y.(^z.z)) b)
  4. ==[ alpha ]==> ((^x.(^y.y)) b)
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1082/14865. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1083/14886. ------  

  1. ==[ start ]==> ((a (a a))(^b.c))
  2. ==[ alpha ]==> ((a (a a))(^x.c))

     REDUCED to normal form.

  ------  1084/14895. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  1085/14910. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1086/14946. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a (^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1087/14949. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (^x1.x1))))

     REDUCED to normal form.

  ------  1088/14958. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.c))
  2. ==[ alpha ]==> (((^x.x) b)(^y.c))
  3. ==[ beta  ]==> (b (^y.c))
  4. ==[ alpha ]==> (b (^x.c))

     REDUCED to normal form.

  ------  1089/14991. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a) b))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  1090/15003. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1091/15012. ------  

  1. ==[ start ]==> (((a a) b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  1092/15057. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1093/15084. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1094/15093. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.b))

     REDUCED to normal form.

  ------  1095/15108. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (^y.((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> (^x.((^y.y)(^z.z)))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1096/15111. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1097/15129. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  1098/15147. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1099/15159. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y)) b))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1100/15168. ------  

  1. ==[ start ]==> ((a (^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  1101/15177. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(a (^y.y))))
  3. ==[ beta  ]==> (a ((a a)(a (^y.y))))
  4. ==[ alpha ]==> (a ((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1102/15195. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1103/15213. ------  

  1. ==[ start ]==> ((a b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a b)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1104/15222. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1105/15231. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b b))
  2. ==[ alpha ]==> (((a a)(^x.x))(b b))

     REDUCED to normal form.

  ------  1106/15249. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a (^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  1107/15258. ------  

  1. ==[ start ]==> (((^a.a) b)(a c))
  2. ==[ alpha ]==> (((^x.x) b)(a c))
  3. ==[ beta  ]==> (b (a c))

     REDUCED to normal form.

  ------  1108/15267. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x)) a))

     REDUCED to normal form.

  ------  1109/15285. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  1110/15294. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a) b))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a) b))

     REDUCED to normal form.

  ------  1111/15303. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1112/15312. ------  

  1. ==[ start ]==> (((a a) b)(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)(a (a (^x.x))))

     REDUCED to normal form.

  ------  1113/15330. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1114/15339. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(a a)))

     REDUCED to normal form.

  ------  1115/15357. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1116/15366. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b a))

     REDUCED to normal form.

  ------  1117/15384. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1118/15393. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a b))

     REDUCED to normal form.

  ------  1119/15411. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  1120/15429. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) a))
  3. ==[ beta  ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  1121/15447. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1122/15455. ------  

  1. ==[ start ]==> (^a.((a (^a.a))(a a)))
  2. ==[ alpha ]==> (^x.((x (^y.y))(x x)))

     REDUCED to normal form.

  ------  1123/15456. ------  

  1. ==[ start ]==> (a ((a (^a.a))(a a)))
  2. ==[ alpha ]==> (a ((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1124/15711. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.a))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.a))
  3. ==[ beta  ]==> (^y.(^z.a))
  4. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  1125/15750. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b) b)
  2. ==[ alpha ]==> (((^x.(^y.y)) b) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1126/15759. ------  

  1. ==[ start ]==> (((a (^a.a))(a a)) a)
  2. ==[ alpha ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  1127/15765. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  3. ==[ beta  ]==> ((a (^y.y))(a a))
  4. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  1128/15774. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1129/15792. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(a (^y.y))))
  3. ==[ beta  ]==> (((a a)(a (^y.y)))((a a)(a (^y.y))))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  1130/15804. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.c))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.c))
  3. ==[ beta  ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  1131/15813. ------  

  1. ==[ start ]==> (((a a) a)(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  1132/15819. ------  

  1. ==[ start ]==> ((^a.b)(c a))
  2. ==[ alpha ]==> ((^x.b)(c a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1133/15855. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1134/15867. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.z))))
  3. ==[ beta  ]==> (b (^y.(a (^z.z))))
  4. ==[ alpha ]==> (b (^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1135/15900. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (a a)))
  3. ==[ beta  ]==> ((b (a a))(^y.y))
  4. ==[ alpha ]==> ((b (a a))(^x.x))

     REDUCED to normal form.

  ------  1136/15921. ------  

  1. ==[ start ]==> (((a a) b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  1137/15966. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z))
  3. ==[ beta  ]==> ((a (^y.y))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1138/15975. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  1139/16002. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a a)))

     REDUCED to normal form.

  ------  1140/16017. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a) a))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a) a))
  3. ==[ beta  ]==> (^y.((a a) a))
  4. ==[ alpha ]==> (^x.((a a) a))

     REDUCED to normal form.

  ------  1141/16020. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.a))
  2. ==[ alpha ]==> ((a (^x.a))(^y.a))

     REDUCED to normal form.

  ------  1142/16038. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(y y)))

     REDUCED to normal form.

  ------  1143/16056. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1144/16065. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  1145/16077. ------  

  1. ==[ start ]==> ((a a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a a)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1146/16086. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1147/16095. ------  

  1. ==[ start ]==> (((^a.a) a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(b (^y.(^z.z))))
  3. ==[ beta  ]==> (a (b (^y.(^z.z))))
  4. ==[ alpha ]==> (a (b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1148/16104. ------  

  1. ==[ start ]==> ((a (a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1149/16122. ------  

  1. ==[ start ]==> (((a a) a)(a (^b.a)))
  2. ==[ alpha ]==> (((a a) a)(a (^x.a)))

     REDUCED to normal form.

  ------  1150/16131. ------  

  1. ==[ start ]==> ((a b)(c a))

     REDUCED to normal form.

  ------  1151/16140. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1152/16149. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  1153/16167. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1154/16176. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (b ((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> (b ((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  1155/16203. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1156/16212. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b (a a)))

     REDUCED to normal form.

  ------  1157/16221. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a) b))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a) b))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a) b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1158/16230. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) b)(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a) b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1159/16248. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1160/16257. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y)))

     REDUCED to normal form.

  ------  1161/16275. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z) b))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z) b))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y) b))
  5. ==[ beta  ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  1162/16284. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1163/16302. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1164/16311. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(a a))

     REDUCED to normal form.

  ------  1165/16329. ------  

  1. ==[ start ]==> ((a (^b.a))((a a) a))
  2. ==[ alpha ]==> ((a (^x.a))((a a) a))

     REDUCED to normal form.

  ------  1166/16347. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (a a)))

     REDUCED to normal form.

  ------  1167/16365. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1168/16374. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a a))

     REDUCED to normal form.

  ------  1169/16440. ------  

  1. ==[ start ]==> ((^a.b)(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1170/16638. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.b))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.b))
  3. ==[ beta  ]==> (^y.(^z.b))
  4. ==[ alpha ]==> (^x.(^y.b))

     REDUCED to normal form.

  ------  1171/16677. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b) c)
  2. ==[ alpha ]==> (((^x.(^y.y)) b) c)
  3. ==[ beta  ]==> ((^y.y) c)
  4. ==[ alpha ]==> ((^x.x) c)
  5. ==[ beta  ]==> c

     REDUCED to normal form.

  ------  1172/16686. ------  

  1. ==[ start ]==> (((a (^a.a))(a a)) b)
  2. ==[ alpha ]==> (((a (^x.x))(a a)) b)

     REDUCED to normal form.

  ------  1173/16710. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1174/16728. ------  

  1. ==[ start ]==> ((^a.(a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(b (^y.(^z.z))))
  3. ==[ beta  ]==> ((b (^y.(^z.z)))(b (^y.(^z.z))))
  4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1175/16749. ------  

  1. ==[ start ]==> (((a a) a)(^b.c))
  2. ==[ alpha ]==> (((a a) a)(^x.c))

     REDUCED to normal form.

  ------  1176/16755. ------  

  1. ==[ start ]==> ((^a.b)(a (^b.a)))
  2. ==[ alpha ]==> ((^x.b)(a (^y.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1177/16758. ------  

  1. ==[ start ]==> ((a b)(^a.(^b.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.x)))

     REDUCED to normal form.

  ------  1178/16791. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1179/16803. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b (^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  1180/16812. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1181/16836. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (((^z.(^x1.x1))(^y1.y1))(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1))
  5. ==[ beta  ]==> ((^y.y)(^x1.x1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1182/16857. ------  

  1. ==[ start ]==> (((a a) b)(^c.b))
  2. ==[ alpha ]==> (((a a) b)(^x.b))

     REDUCED to normal form.

  ------  1183/16875. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(x1 (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  1184/16911. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1185/16953. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a b))
  2. ==[ alpha ]==> ((^x.(^y.x))(a b))
  3. ==[ beta  ]==> (^y.(a b))
  4. ==[ alpha ]==> (^x.(a b))

     REDUCED to normal form.

  ------  1186/16956. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.b))
  2. ==[ alpha ]==> ((a (^x.a))(^y.b))

     REDUCED to normal form.

  ------  1187/16974. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1188/16992. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.a))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1189/17001. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1190/17031. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  1191/17040. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) b))
  3. ==[ beta  ]==> (a ((^y.(^z.z)) b))
  4. ==[ alpha ]==> (a ((^x.(^y.y)) b))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1192/17049. ------  

  1. ==[ start ]==> ((a (a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1193/17058. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  1194/17076. ------  

  1. ==[ start ]==> ((a b)(a (^b.a)))
  2. ==[ alpha ]==> ((a b)(a (^x.a)))

     REDUCED to normal form.

  ------  1195/17094. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  1196/17112. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b b))

     REDUCED to normal form.

  ------  1197/17121. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> (b ((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> (b ((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  1198/17130. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> (((a a)(a a))(a (^y.y)))
  4. ==[ alpha ]==> (((a a)(a a))(a (^x.x)))

     REDUCED to normal form.

  ------  1199/17148. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1200/17157. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1201/17166. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(b (a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(b (a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1202/17175. ------  

  1. ==[ start ]==> (((a a) b)((a a) b))

     REDUCED to normal form.

  ------  1203/17193. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  1204/17202. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  1205/17220. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(a a)))

     REDUCED to normal form.

  ------  1206/17229. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) b))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) b)

     REDUCED to normal form.

  ------  1207/17247. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  1208/17256. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z)))

     REDUCED to normal form.

  ------  1209/17274. ------  

  1. ==[ start ]==> ((a (^b.a))(a b))
  2. ==[ alpha ]==> ((a (^x.a))(a b))

     REDUCED to normal form.

  ------  1210/17292. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1211/17310. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z) a))
  3. ==[ beta  ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1212/17319. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y)))

     REDUCED to normal form.

  ------  1213/17336. ------  

  1. ==[ start ]==> (^a.((^b.a) a))
  2. ==[ alpha ]==> (^x.((^y.x) x))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  1214/17337. ------  

  1. ==[ start ]==> (a ((^b.a) a))
  2. ==[ alpha ]==> (a ((^x.a) a))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1215/17394. ------  

  1. ==[ start ]==> ((^a.b)(^b.c))
  2. ==[ alpha ]==> ((^x.b)(^y.c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1216/17592. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(a a)))
  3. ==[ beta  ]==> (^y.(^z.(a a)))
  4. ==[ alpha ]==> (^x.(^y.(a a)))

     REDUCED to normal form.

  ------  1217/17664. ------  

  1. ==[ start ]==> ((^a.a)((^b.a) a))
  2. ==[ alpha ]==> ((^x.x)((^y.a) a))
  3. ==[ beta  ]==> ((^y.a) a)
  4. ==[ alpha ]==> ((^x.a) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1218/17691. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((^y.(^z.z)) b)((^y.(^z.z)) b))
  4. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1)) b))
  5. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) b))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  7. ==[ beta  ]==> ((^y.(^z.z)) b)
  8. ==[ alpha ]==> ((^x.(^y.y)) b)
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1219/17718. ------  

  1. ==[ start ]==> ((^a.b)((^a.a) c))
  2. ==[ alpha ]==> ((^x.b)((^y.y) c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1220/17721. ------  

  1. ==[ start ]==> ((a b)(^b.c))
  2. ==[ alpha ]==> ((a b)(^x.c))

     REDUCED to normal form.

  ------  1221/17730. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.y)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.y)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  1222/17754. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1223/17799. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z)) a))
  3. ==[ beta  ]==> (((a (^z.z)) a)(^y.y))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  1224/17838. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1225/17847. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1226/17892. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1227/17916. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(a a)))
  3. ==[ beta  ]==> (^y.((^z.z)(a a)))
  4. ==[ alpha ]==> (^x.((^y.y)(a a)))
  5. ==[ beta  ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1228/17919. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.(a a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(a a)))

     REDUCED to normal form.

  ------  1229/17955. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(z z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  1230/17964. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.a))

     REDUCED to normal form.

  ------  1231/17987. ------  

  1. ==[ start ]==> (^a.(^a.((^a.a) a)))
  2. ==[ alpha ]==> (^x.(^y.((^z.z) y)))
  3. ==[ eta   ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1232/17988. ------  

  1. ==[ start ]==> (a (^a.((^a.a) a)))
  2. ==[ alpha ]==> (a (^x.((^y.y) x)))
  3. ==[ eta   ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1233/17994. ------  

  1. ==[ start ]==> ((a a)((^b.a) a))
  2. ==[ alpha ]==> ((a a)((^x.a) a))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1234/18012. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a a)))
  3. ==[ beta  ]==> (a ((a (^y.y))(a a)))
  4. ==[ alpha ]==> (a ((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1235/18021. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y)) b))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  1236/18030. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  1237/18039. ------  

  1. ==[ start ]==> (((a a) a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1238/18048. ------  

  1. ==[ start ]==> ((a b)((^a.a) c))
  2. ==[ alpha ]==> ((a b)((^x.x) c))
  3. ==[ beta  ]==> ((a b) c)

     REDUCED to normal form.

  ------  1239/18057. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (^y.a)))
  3. ==[ beta  ]==> ((a a)(a (^y.a)))
  4. ==[ alpha ]==> ((a a)(a (^x.a)))

     REDUCED to normal form.

  ------  1240/18084. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1241/18093. ------  

  1. ==[ start ]==> (((^a.a) b)(b b))
  2. ==[ alpha ]==> (((^x.x) b)(b b))
  3. ==[ beta  ]==> (b (b b))

     REDUCED to normal form.

  ------  1242/18102. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  1243/18129. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y)) a))

     REDUCED to normal form.

  ------  1244/18138. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1245/18147. ------  

  1. ==[ start ]==> (((a a) b)(b (a a)))

     REDUCED to normal form.

  ------  1246/18165. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1247/18174. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (a (^y.y))))

     REDUCED to normal form.

  ------  1248/18192. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))(b (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  1249/18201. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(a a)))

     REDUCED to normal form.

  ------  1250/18219. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  1251/18228. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b a))

     REDUCED to normal form.

  ------  1252/18246. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (^x.a))(a a))

     REDUCED to normal form.

  ------  1253/18264. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a) a))

     REDUCED to normal form.

  ------  1254/18282. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1255/18291. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) a))
  3. ==[ beta  ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  1256/18315. ------  

  1. ==[ start ]==> ((^a.((^a.a) a)) a)
  2. ==[ alpha ]==> ((^x.((^y.y) x)) a)
  3. ==[ eta   ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1257/18317. ------  

  1. ==[ start ]==> (^a.(a ((^a.a) a)))
  2. ==[ alpha ]==> (^x.(x ((^y.y) x)))
  3. ==[ beta  ]==> (^x.(x x))

     REDUCED to normal form.

  ------  1258/18318. ------  

  1. ==[ start ]==> (a (a ((^a.a) a)))
  2. ==[ alpha ]==> (a (a ((^x.x) a)))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1259/18321. ------  

  1. ==[ start ]==> ((^a.a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((^x.x)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1260/18375. ------  

  1. ==[ start ]==> ((^a.b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(a (^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1261/18573. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  4. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1262/18645. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.z))
  3. ==[ eta   ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1263/18648. ------  

  1. ==[ start ]==> ((a ((^a.a) a)) a)
  2. ==[ alpha ]==> ((a ((^x.x) a)) a)
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1264/18654. ------  

  1. ==[ start ]==> ((^a.a)(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  3. ==[ beta  ]==> (a ((^y.y) a))
  4. ==[ alpha ]==> (a ((^x.x) a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1265/18657. ------  

  1. ==[ start ]==> ((a a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a a)(^x.((^y.y) x)))
  3. ==[ eta   ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1266/18663. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1267/18681. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(a a)))
  3. ==[ beta  ]==> (((a (^y.y))(a a))((a (^y.y))(a a)))
  4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  1268/18708. ------  

  1. ==[ start ]==> ((^a.b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)((a a)(a (^y.y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1269/18711. ------  

  1. ==[ start ]==> ((a b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> ((a b)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1270/18720. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.c))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.c))
  3. ==[ beta  ]==> ((a a)(^y.c))
  4. ==[ alpha ]==> ((a a)(^x.c))

     REDUCED to normal form.

  ------  1271/18729. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.y)))

     REDUCED to normal form.

  ------  1272/18744. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1273/18783. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  1274/18837. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1275/18882. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1276/18891. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  1277/18906. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)(^z.z)))
  3. ==[ beta  ]==> (^y.((a a)(^z.z)))
  4. ==[ alpha ]==> (^x.((a a)(^y.y)))

     REDUCED to normal form.

  ------  1278/18909. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1279/18927. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.b))

     REDUCED to normal form.

  ------  1280/18945. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1281/18954. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(y y)))

     REDUCED to normal form.

  ------  1282/18978. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a a))
  3. ==[ eta   ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1283/18981. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.a))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1284/18986. ------  

  1. ==[ start ]==> (^a.(^b.(^b.a)))
  2. ==[ alpha ]==> (^x.(^y.(^z.x)))

     REDUCED to normal form.

  ------  1285/18987. ------  

  1. ==[ start ]==> (a (^b.(^b.a)))
  2. ==[ alpha ]==> (a (^x.(^y.a)))

     REDUCED to normal form.

  ------  1286/18993. ------  

  1. ==[ start ]==> ((a a)(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a a)(a ((^x.x) a)))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1287/19002. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a) a))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a) a))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1288/19020. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1289/19029. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1290/19038. ------  

  1. ==[ start ]==> (((a a) a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1291/19047. ------  

  1. ==[ start ]==> ((a b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a b)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1292/19065. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.a)))

     REDUCED to normal form.

  ------  1293/19083. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1)))

     REDUCED to normal form.

  ------  1294/19092. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (b ((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> (b ((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1295/19101. ------  

  1. ==[ start ]==> (((a a)(a a))(b b))

     REDUCED to normal form.

  ------  1296/19119. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1297/19137. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1298/19146. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  1299/19164. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1300/19173. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z)))

     REDUCED to normal form.

  ------  1301/19191. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1302/19200. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z)))

     REDUCED to normal form.

  ------  1303/19218. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z) b))
  3. ==[ beta  ]==> ((^y.y)((^z.z) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1304/19227. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1305/19245. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))((a a)(^y.y)))

     REDUCED to normal form.

  ------  1306/19263. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a b))

     REDUCED to normal form.

  ------  1307/19281. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1308/19290. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (a a)))

     REDUCED to normal form.

  ------  1309/19314. ------  

  1. ==[ start ]==> ((^a.((^a.a) a)) b)
  2. ==[ alpha ]==> ((^x.((^y.y) x)) b)
  3. ==[ eta   ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1310/19317. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a a))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1311/19325. ------  

  1. ==[ start ]==> (^a.((^a.a)(^b.a)))
  2. ==[ alpha ]==> (^x.((^y.y)(^z.x)))
  3. ==[ beta  ]==> (^x.(^z.x))
  4. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  1312/19326. ------  

  1. ==[ start ]==> (a ((^a.a)(^b.a)))
  2. ==[ alpha ]==> (a ((^x.x)(^y.a)))
  3. ==[ beta  ]==> (a (^y.a))
  4. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1313/19329. ------  

  1. ==[ start ]==> ((^a.a)(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  3. ==[ beta  ]==> (^y.(^z.a))
  4. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  1314/19338. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((^x.(^y.y))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1315/19464. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^z.(a (^x1.x1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(a (^y.y)))(^z.z))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1316/19653. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1317/19656. ------  

  1. ==[ start ]==> ((a ((^a.a) a)) b)
  2. ==[ alpha ]==> ((a ((^x.x) a)) b)
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1318/19665. ------  

  1. ==[ start ]==> (((^a.a)(^b.a)) a)
  2. ==[ alpha ]==> (((^x.x)(^y.a)) a)
  3. ==[ beta  ]==> ((^y.a) a)
  4. ==[ alpha ]==> ((^x.a) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1319/19671. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1320/19674. ------  

  1. ==[ start ]==> ((a a)(^b.(^b.a)))
  2. ==[ alpha ]==> ((a a)(^x.(^y.a)))

     REDUCED to normal form.

  ------  1321/19680. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1322/19683. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1323/19725. ------  

  1. ==[ start ]==> ((^a.b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(b (^y.(^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1324/19746. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.c))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.c))

     REDUCED to normal form.

  ------  1325/19806. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (((^z.z)(a (^x1.x1)))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1326/19809. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1327/19872. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1328/19908. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  1329/19923. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b a))
  2. ==[ alpha ]==> ((^x.(^y.x))(b a))
  3. ==[ beta  ]==> (^y.(b a))
  4. ==[ alpha ]==> (^x.(b a))

     REDUCED to normal form.

  ------  1330/19944. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(a a)))

     REDUCED to normal form.

  ------  1331/19962. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.a))
  3. ==[ beta  ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1332/19971. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1333/19995. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.z)))
  3. ==[ eta   ]==> ((^y.y)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1334/19998. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1335/20007. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z))
  3. ==[ beta  ]==> ((^y.a)(^z.z))
  4. ==[ alpha ]==> ((^x.a)(^y.y))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1336/20019. ------  

  1. ==[ start ]==> ((a a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a a)((^x.x)(^y.a)))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1337/20028. ------  

  1. ==[ start ]==> ((a (^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  1338/20037. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a) a))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a) a))
  3. ==[ beta  ]==> (a ((^y.a) a))
  4. ==[ alpha ]==> (a ((^x.a) a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1339/20055. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  1340/20064. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) b))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  1341/20073. ------  

  1. ==[ start ]==> ((a b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1342/20082. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(a (^y.y))))
  3. ==[ beta  ]==> ((a a)((a a)(a (^y.y))))
  4. ==[ alpha ]==> ((a a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1343/20118. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> (b ((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> (b ((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1344/20127. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  1345/20145. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1346/20154. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a (^z.z)))
  4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  1347/20172. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x)) a))

     REDUCED to normal form.

  ------  1348/20190. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  1349/20199. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a) b))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a) b))

     REDUCED to normal form.

  ------  1350/20217. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))(a (a (^z.z))))
  4. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y))))

     REDUCED to normal form.

  ------  1351/20226. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1352/20244. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1353/20253. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) b))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) b)

     REDUCED to normal form.

  ------  1354/20271. ------  

  1. ==[ start ]==> ((a (^b.a))(b a))
  2. ==[ alpha ]==> ((a (^x.a))(b a))

     REDUCED to normal form.

  ------  1355/20289. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(a a))

     REDUCED to normal form.

  ------  1356/20307. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1357/20316. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  1358/20343. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a (^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.y)))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  1359/20352. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a a))
  3. ==[ beta  ]==> ((^y.a)(a a))
  4. ==[ alpha ]==> ((^x.a)(a a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1360/20373. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1361/20454. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.x1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1362/20616. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1363/20688. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.a))
  3. ==[ eta   ]==> ((^y.y)(^z.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1364/20700. ------  

  1. ==[ start ]==> (((^a.a)(^b.a)) b)
  2. ==[ alpha ]==> (((^x.x)(^y.a)) b)
  3. ==[ beta  ]==> ((^y.a) b)
  4. ==[ alpha ]==> ((^x.a) b)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1365/20724. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1366/20727. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.a)))

     REDUCED to normal form.

  ------  1367/20736. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((^x.x) a)(^z.z))
  4. ==[ alpha ]==> (((^x.x) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1368/20742. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a) a))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a) a))
  3. ==[ beta  ]==> (((^y.a) a)((^y.a) a))
  4. ==[ alpha ]==> (((^x.a) a)((^y.a) a))
  5. ==[ beta  ]==> (a ((^y.a) a))
  6. ==[ alpha ]==> (a ((^x.a) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1369/20769. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1370/20805. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1371/20808. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.z)))

     REDUCED to normal form.

  ------  1372/20850. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^z.(^x1.x1)))(^y.y))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1373/20862. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1374/20871. ------  

  1. ==[ start ]==> (((a a) b)(^a.c))
  2. ==[ alpha ]==> (((a a) b)(^x.c))

     REDUCED to normal form.

  ------  1375/20916. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1376/20925. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (^x1.x1))))

     REDUCED to normal form.

  ------  1377/20967. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> (^x.(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1378/20970. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1379/21006. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.b))
  3. ==[ beta  ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  1380/21039. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z) a))
  3. ==[ eta   ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1381/21042. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.a))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.a))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1382/21051. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1383/21081. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.a))
  4. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  1384/21090. ------  

  1. ==[ start ]==> (((^a.a) a)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)(a ((^y.y) a)))
  3. ==[ beta  ]==> (a (a ((^y.y) a)))
  4. ==[ alpha ]==> (a (a ((^x.x) a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1385/21099. ------  

  1. ==[ start ]==> ((a (a a))((^b.a) a))
  2. ==[ alpha ]==> ((a (a a))((^x.a) a))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  1386/21117. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1387/21126. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y)) b))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  1388/21135. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(b (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1389/21144. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  1390/21162. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.a)))

     REDUCED to normal form.

  ------  1391/21171. ------  

  1. ==[ start ]==> (((^a.a) b)(c a))
  2. ==[ alpha ]==> (((^x.x) b)(c a))
  3. ==[ beta  ]==> (b (c a))

     REDUCED to normal form.

  ------  1392/21180. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1393/21198. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  1394/21207. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  1395/21216. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1396/21225. ------  

  1. ==[ start ]==> (((a a) b)(a c))

     REDUCED to normal form.

  ------  1397/21243. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1398/21252. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b (a a)))

     REDUCED to normal form.

  ------  1399/21270. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^x.x))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1400/21279. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.z))))

     REDUCED to normal form.

  ------  1401/21297. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1402/21306. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a a)))

     REDUCED to normal form.

  ------  1403/21324. ------  

  1. ==[ start ]==> ((a (^b.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1404/21342. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.y)))

     REDUCED to normal form.

  ------  1405/21360. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  1406/21369. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a) a))

     REDUCED to normal form.

  ------  1407/21396. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y) a))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1408/21405. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.z)))
  3. ==[ beta  ]==> ((^y.a)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.a)(a (^y.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1409/21422. ------  

  1. ==[ start ]==> (^a.(b (a (^a.a))))
  2. ==[ alpha ]==> (^x.(b (x (^y.y))))

     REDUCED to normal form.

  ------  1410/21423. ------  

  1. ==[ start ]==> (a (b (a (^a.a))))
  2. ==[ alpha ]==> (a (b (a (^x.x))))

     REDUCED to normal form.

  ------  1411/21453. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((^x.(x x))(^z.z))
  4. ==[ alpha ]==> ((^x.(x x))(^y.y))
  5. ==[ beta  ]==> ((^y.y)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1412/21516. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.c))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1413/21678. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.b))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.z))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1414/21750. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(z z)))
  3. ==[ eta   ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  1415/21762. ------  

  1. ==[ start ]==> (((^a.a)(^b.a)) c)
  2. ==[ alpha ]==> (((^x.x)(^y.a)) c)
  3. ==[ beta  ]==> ((^y.a) c)
  4. ==[ alpha ]==> ((^x.a) c)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1416/21786. ------  

  1. ==[ start ]==> ((^a.a)(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  3. ==[ beta  ]==> (b (a (^y.y)))
  4. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  1417/21807. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.a)))
  3. ==[ beta  ]==> (a (^y.(^z.a)))
  4. ==[ alpha ]==> (a (^x.(^y.a)))

     REDUCED to normal form.

  ------  1418/21813. ------  

  1. ==[ start ]==> ((^a.(a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a ((^y.y) a))(a ((^y.y) a)))
  4. ==[ alpha ]==> ((a ((^x.x) a))(a ((^y.y) a)))
  5. ==[ beta  ]==> ((a a)(a ((^y.y) a)))
  6. ==[ alpha ]==> ((a a)(a ((^x.x) a)))
  7. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1419/21816. ------  

  1. ==[ start ]==> ((a (a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))(^x.((^y.y) x)))
  3. ==[ eta   ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  1420/21840. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y))(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1421/21879. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.c))

     REDUCED to normal form.

  ------  1422/21888. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.y)))
  3. ==[ beta  ]==> (b (^y.(^z.y)))
  4. ==[ alpha ]==> (b (^x.(^y.x)))

     REDUCED to normal form.

  ------  1423/21921. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b b))
  3. ==[ beta  ]==> ((b b)(^y.y))
  4. ==[ alpha ]==> ((b b)(^x.x))

     REDUCED to normal form.

  ------  1424/21942. ------  

  1. ==[ start ]==> (((a a) b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1425/21996. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  1426/22038. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z) b))
  3. ==[ beta  ]==> (^y.((^z.z) b))
  4. ==[ alpha ]==> (^x.((^y.y) b))
  5. ==[ beta  ]==> (^x.b)

     REDUCED to normal form.

  ------  1427/22041. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.b))
  2. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  1428/22077. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1429/22086. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.b))

     REDUCED to normal form.

  ------  1430/22110. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a (a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a (a a)))
  3. ==[ eta   ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1431/22113. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(y y)))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  1432/22122. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.a))
  3. ==[ beta  ]==> ((^y.a)(^z.a))
  4. ==[ alpha ]==> ((^x.a)(^y.a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1433/22152. ------  

  1. ==[ start ]==> ((a a)(b (a (^a.a))))
  2. ==[ alpha ]==> ((a a)(b (a (^x.x))))

     REDUCED to normal form.

  ------  1434/22170. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.a)))
  3. ==[ beta  ]==> (a ((^y.y)(^z.a)))
  4. ==[ alpha ]==> (a ((^x.x)(^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1435/22179. ------  

  1. ==[ start ]==> ((a (a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))(a ((^x.x) a)))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  1436/22188. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) a))
  3. ==[ beta  ]==> ((^y.y)((^z.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1437/22206. ------  

  1. ==[ start ]==> ((a b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a b)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1438/22215. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) b))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) b))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1439/22224. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  1440/22251. ------  

  1. ==[ start ]==> (((^a.a) b)(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)(a (^y.a)))
  3. ==[ beta  ]==> (b (a (^y.a)))
  4. ==[ alpha ]==> (b (a (^x.a)))

     REDUCED to normal form.

  ------  1441/22278. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1442/22287. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b b))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b b))

     REDUCED to normal form.

  ------  1443/22296. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1444/22305. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> (((a a) b)(a (^y.y)))
  4. ==[ alpha ]==> (((a a) b)(a (^x.x)))

     REDUCED to normal form.

  ------  1445/22323. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1446/22332. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  1447/22350. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a) b))
  3. ==[ beta  ]==> ((a (^y.y))((a a) b))
  4. ==[ alpha ]==> ((a (^x.x))((a a) b))

     REDUCED to normal form.

  ------  1448/22359. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  1449/22377. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1450/22386. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z)))

     REDUCED to normal form.

  ------  1451/22404. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a) b))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y) b))
  3. ==[ beta  ]==> ((a (^x.a)) b)

     REDUCED to normal form.

  ------  1452/22422. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b a))

     REDUCED to normal form.

  ------  1453/22440. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1454/22449. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a b))

     REDUCED to normal form.

  ------  1455/22476. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a (a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a (a a)))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  1456/22485. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z) a))
  3. ==[ beta  ]==> ((^y.a)((^z.z) a))
  4. ==[ alpha ]==> ((^x.a)((^y.y) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1457/22511. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1458/22512. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1459/22542. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.a)))
  3. ==[ beta  ]==> ((^y.(^z.a))(^y.(^z.a)))
  4. ==[ alpha ]==> ((^x.(^y.a))(^z.(^x1.a)))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1460/22767. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(a a)))
  3. ==[ beta  ]==> (^y.(^z.(a a)))
  4. ==[ alpha ]==> (^x.(^y.(a a)))

     REDUCED to normal form.

  ------  1461/22839. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1462/22878. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a))) a)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1463/22884. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1464/22893. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1465/22911. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((^y.y)(^z.a))((^y.y)(^z.a)))
  4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.a)))
  5. ==[ beta  ]==> ((^y.a)((^z.z)(^x1.a)))
  6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.a)))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1466/22914. ------  

  1. ==[ start ]==> ((a (a a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.a)))

     REDUCED to normal form.

  ------  1467/22923. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.x)(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1468/22938. ------  

  1. ==[ start ]==> ((^a.b)(c (^a.a)))
  2. ==[ alpha ]==> ((^x.b)(c (^y.y)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1469/22974. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1470/22986. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.c))
  2. ==[ alpha ]==> (((^x.x) b)(^y.c))
  3. ==[ beta  ]==> (b (^y.c))
  4. ==[ alpha ]==> (b (^x.c))

     REDUCED to normal form.

  ------  1471/22995. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.x)))

     REDUCED to normal form.

  ------  1472/23019. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (((^z.(^x1.x1))(a a))(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1473/23040. ------  

  1. ==[ start ]==> (((a a) b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  1474/23112. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  1475/23136. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)(a a)))
  3. ==[ beta  ]==> (^y.((a a)(a a)))
  4. ==[ alpha ]==> (^x.((a a)(a a)))

     REDUCED to normal form.

  ------  1476/23139. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.(a a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(a a)))

     REDUCED to normal form.

  ------  1477/23157. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1478/23175. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1479/23184. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(a a)))

     REDUCED to normal form.

  ------  1480/23208. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1481/23211. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1482/23220. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(z z)))
  3. ==[ beta  ]==> ((^y.a)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.a)(^y.(y y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1483/23247. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1))
  3. ==[ beta  ]==> ((^y.y)(^y1.y1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1484/23259. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1485/23268. ------  

  1. ==[ start ]==> ((a (^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(b (a (^y.y))))

     REDUCED to normal form.

  ------  1486/23286. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a)))
  3. ==[ beta  ]==> ((a (a a))(^y.a))
  4. ==[ alpha ]==> ((a (a a))(^x.a))

     REDUCED to normal form.

  ------  1487/23295. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1488/23304. ------  

  1. ==[ start ]==> (((a a) a)((^b.a) a))
  2. ==[ alpha ]==> (((a a) a)((^x.a) a))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  1489/23313. ------  

  1. ==[ start ]==> ((a b)(c (^a.a)))
  2. ==[ alpha ]==> ((a b)(c (^x.x)))

     REDUCED to normal form.

  ------  1490/23322. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(a a)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(a a)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1491/23331. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  1492/23349. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (^z.z))))

     REDUCED to normal form.

  ------  1493/23358. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a) c))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y) c))
  3. ==[ beta  ]==> (b ((^y.y) c))
  4. ==[ alpha ]==> (b ((^x.x) c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  1494/23367. ------  

  1. ==[ start ]==> (((a a)(a a))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))(a (^x.a)))

     REDUCED to normal form.

  ------  1495/23385. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1496/23394. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1497/23403. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b b))
  3. ==[ beta  ]==> ((^y.(^z.z))(b b))
  4. ==[ alpha ]==> ((^x.(^y.y))(b b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1498/23412. ------  

  1. ==[ start ]==> (((a a) b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  1499/23439. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y)) a))

     REDUCED to normal form.

  ------  1500/23457. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (a a)))
  3. ==[ beta  ]==> ((a (^y.y))(b (a a)))
  4. ==[ alpha ]==> ((a (^x.x))(b (a a)))

     REDUCED to normal form.

  ------  1501/23466. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a) b))

     REDUCED to normal form.

  ------  1502/23484. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  1503/23493. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  1504/23511. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)(a a)))
  2. ==[ alpha ]==> ((a (^x.a))((a a)(a a)))

     REDUCED to normal form.

  ------  1505/23529. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1506/23547. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1507/23556. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(a a))

     REDUCED to normal form.

  ------  1508/23583. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1509/23592. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a (a a)))
  3. ==[ beta  ]==> ((^y.a)(a (a a)))
  4. ==[ alpha ]==> ((^x.a)(a (a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1510/23619. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1511/23627. ------  

  1. ==[ start ]==> (^a.((a (^a.a)) b))
  2. ==[ alpha ]==> (^x.((x (^y.y)) b))

     REDUCED to normal form.

  ------  1512/23628. ------  

  1. ==[ start ]==> (a ((a (^a.a)) b))
  2. ==[ alpha ]==> (a ((a (^x.x)) b))

     REDUCED to normal form.

  ------  1513/23994. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a))) b)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1514/24003. ------  

  1. ==[ start ]==> (((a (^a.a)) b) a)
  2. ==[ alpha ]==> (((a (^x.x)) b) a)

     REDUCED to normal form.

  ------  1515/24009. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  3. ==[ beta  ]==> ((a (^y.y)) b)
  4. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  1516/24018. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1517/24048. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  1518/24057. ------  

  1. ==[ start ]==> (((a a) a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)(^x.((^y.y) x)))
  3. ==[ eta   ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  1519/24063. ------  

  1. ==[ start ]==> ((^a.b)((^b.a) a))
  2. ==[ alpha ]==> ((^x.b)((^y.a) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1520/24099. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1521/24111. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.z))))
  3. ==[ beta  ]==> (b (^y.(a (^z.z))))
  4. ==[ alpha ]==> (b (^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1522/24120. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.c))
  2. ==[ alpha ]==> (((a a)(a a))(^x.c))

     REDUCED to normal form.

  ------  1523/24144. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a (^z.z))(^x1.x1))(^y.y))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  1524/24183. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  1525/24237. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1526/24246. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (^x1.x1))))

     REDUCED to normal form.

  ------  1527/24261. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(b (^z.z)))
  3. ==[ beta  ]==> (^y.(b (^z.z)))
  4. ==[ alpha ]==> (^x.(b (^y.y)))

     REDUCED to normal form.

  ------  1528/24282. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1529/24333. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a) a))
  3. ==[ eta   ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1530/24345. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1531/24372. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1532/24381. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  1533/24393. ------  

  1. ==[ start ]==> ((a a)((a (^a.a)) b))
  2. ==[ alpha ]==> ((a a)((a (^x.x)) b))

     REDUCED to normal form.

  ------  1534/24402. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1535/24411. ------  

  1. ==[ start ]==> (((^a.a) a)(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(b (a (^y.y))))
  3. ==[ beta  ]==> (a (b (a (^y.y))))
  4. ==[ alpha ]==> (a (b (a (^x.x))))

     REDUCED to normal form.

  ------  1536/24429. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1537/24438. ------  

  1. ==[ start ]==> (((a a) a)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)(a ((^x.x) a)))
  3. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  1538/24447. ------  

  1. ==[ start ]==> ((a b)((^b.a) a))
  2. ==[ alpha ]==> ((a b)((^x.a) a))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  1539/24465. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  1540/24483. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1541/24492. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((a a)(a (^y.y))))
  3. ==[ beta  ]==> (b ((a a)(a (^y.y))))
  4. ==[ alpha ]==> (b ((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1542/24528. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  1543/24537. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1544/24546. ------  

  1. ==[ start ]==> (((a a) b)(b b))

     REDUCED to normal form.

  ------  1545/24564. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1546/24591. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1547/24600. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a a)))

     REDUCED to normal form.

  ------  1548/24618. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1549/24627. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (^z.z))))

     REDUCED to normal form.

  ------  1550/24645. ------  

  1. ==[ start ]==> ((a (^b.a))(b (^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(b (^y.y)))

     REDUCED to normal form.

  ------  1551/24663. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) b))
  3. ==[ beta  ]==> (((a a)(a (^x.x))) b)

     REDUCED to normal form.

  ------  1552/24681. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  1553/24690. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.y)))

     REDUCED to normal form.

  ------  1554/24717. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a) a))
  3. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  1555/24726. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1556/24753. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(a (^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1557/24762. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a a))

     REDUCED to normal form.

  ------  1558/24828. ------  

  1. ==[ start ]==> ((^a.b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((^x.b)(^z.z))
  4. ==[ alpha ]==> ((^x.b)(^y.y))
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1559/25098. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.b))
  3. ==[ eta   ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  1560/25146. ------  

  1. ==[ start ]==> (((a (^a.a)) b) b)
  2. ==[ alpha ]==> (((a (^x.x)) b) b)

     REDUCED to normal form.

  ------  1561/25170. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1562/25188. ------  

  1. ==[ start ]==> ((^a.(a a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(b (a (^y.y))))
  3. ==[ beta  ]==> ((b (a (^y.y)))(b (a (^y.y))))
  4. ==[ alpha ]==> ((b (a (^x.x)))(b (a (^y.y))))

     REDUCED to normal form.

  ------  1563/25209. ------  

  1. ==[ start ]==> (((a a) a)(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.a)))

     REDUCED to normal form.

  ------  1564/25215. ------  

  1. ==[ start ]==> ((^a.b)(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)(a ((^y.y) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1565/25218. ------  

  1. ==[ start ]==> ((a b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a b)(^x.((^y.y) x)))
  3. ==[ eta   ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  1566/25251. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1567/25290. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  1568/25344. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1569/25398. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  1570/25413. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> (^x.((^y.(^z.z)) a))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1571/25452. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1572/25485. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a b))
  3. ==[ eta   ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  1573/25488. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.b))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.b))
  3. ==[ beta  ]==> ((a a)(^y.b))
  4. ==[ alpha ]==> ((a a)(^x.b))

     REDUCED to normal form.

  ------  1574/25497. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.a))
  3. ==[ beta  ]==> ((^y.a)(^z.a))
  4. ==[ alpha ]==> ((^x.a)(^y.a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1575/25524. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.a))
  3. ==[ beta  ]==> ((^y.y)(^y1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  1576/25533. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z)))

     REDUCED to normal form.

  ------  1577/25563. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) b))

     REDUCED to normal form.

  ------  1578/25572. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (a ((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1579/25581. ------  

  1. ==[ start ]==> ((a (a a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))(b (a (^x.x))))

     REDUCED to normal form.

  ------  1580/25599. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.a)))
  3. ==[ beta  ]==> (((a a) a)(^y.a))
  4. ==[ alpha ]==> (((a a) a)(^x.a))

     REDUCED to normal form.

  ------  1581/25608. ------  

  1. ==[ start ]==> ((a b)(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a b)(a ((^x.x) a)))
  3. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  1582/25617. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.a) a))
  3. ==[ beta  ]==> ((a a)((^y.a) a))
  4. ==[ alpha ]==> ((a a)((^x.a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1583/25644. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1584/25653. ------  

  1. ==[ start ]==> (((^a.a) b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(b (^y.(^z.z))))
  3. ==[ beta  ]==> (b (b (^y.(^z.z))))
  4. ==[ alpha ]==> (b (b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1585/25662. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1586/25680. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1587/25698. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1588/25707. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a a)))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  1589/25725. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1590/25734. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a (^z.z)))
  4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y)))

     REDUCED to normal form.

  ------  1591/25752. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z)) a))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z)) a))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) a))

     REDUCED to normal form.

  ------  1592/25761. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1593/25779. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1594/25788. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  1595/25806. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  1596/25824. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(a a)))

     REDUCED to normal form.

  ------  1597/25842. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  1598/25851. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b a))

     REDUCED to normal form.

  ------  1599/25878. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a b))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a b))
  3. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  1600/25887. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a) a))
  3. ==[ beta  ]==> ((^y.a)((a a) a))
  4. ==[ alpha ]==> ((^x.a)((a a) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1601/25914. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1) a))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1602/25923. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.y)))

     REDUCED to normal form.

  ------  1603/25940. ------  

  1. ==[ start ]==> (^a.((^b.a)(^a.a)))
  2. ==[ alpha ]==> (^x.((^y.x)(^z.z)))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  1604/25941. ------  

  1. ==[ start ]==> (a ((^b.a)(^a.a)))
  2. ==[ alpha ]==> (a ((^x.a)(^y.y)))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1605/25998. ------  

  1. ==[ start ]==> ((^a.b)(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1606/26079. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^z.(^x1.z))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.x))(^z.z))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1607/26196. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> (^x.(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1608/26268. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(a a)))
  3. ==[ eta   ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1609/26316. ------  

  1. ==[ start ]==> (((a (^a.a)) b) c)
  2. ==[ alpha ]==> (((a (^x.x)) b) c)

     REDUCED to normal form.

  ------  1610/26340. ------  

  1. ==[ start ]==> ((^a.a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((^y.a)(^z.z))
  4. ==[ alpha ]==> ((^x.a)(^y.y))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1611/26367. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^y.(^z.z))(^x1.(^y1.y1)))((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2))))
  5. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  7. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1612/26394. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1613/26397. ------  

  1. ==[ start ]==> ((a b)(^b.(^b.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.a)))

     REDUCED to normal form.

  ------  1614/26406. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((^x.x)(a a))(^z.z))
  4. ==[ alpha ]==> (((^x.x)(a a))(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1615/26430. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1616/26469. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.c))
  3. ==[ beta  ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  1617/26475. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.a)))
  3. ==[ beta  ]==> ((a (^z.a))(^y.y))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  1618/26478. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.y)))

     REDUCED to normal form.

  ------  1619/26592. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (a (^z.z))))
  3. ==[ beta  ]==> (^y.(a (a (^z.z))))
  4. ==[ alpha ]==> (^x.(a (a (^y.y))))

     REDUCED to normal form.

  ------  1620/26595. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1621/26631. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1622/26640. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1623/26664. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(a a)))
  3. ==[ eta   ]==> ((^y.y)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1624/26667. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(a a)))
  3. ==[ beta  ]==> ((a a)(^y.(a a)))
  4. ==[ alpha ]==> ((a a)(^x.(a a)))

     REDUCED to normal form.

  ------  1625/26676. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.b))
  3. ==[ beta  ]==> ((^y.a)(^z.b))
  4. ==[ alpha ]==> ((^x.a)(^y.b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1626/26703. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 y1)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(y1 y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  1627/26712. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.a))

     REDUCED to normal form.

  ------  1628/26742. ------  

  1. ==[ start ]==> ((a a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a a)((^x.a)(^y.y)))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1629/26760. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y)) b))
  3. ==[ beta  ]==> (a ((a (^y.y)) b))
  4. ==[ alpha ]==> (a ((a (^x.x)) b))

     REDUCED to normal form.

  ------  1630/26769. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  1631/26778. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  1632/26796. ------  

  1. ==[ start ]==> ((a b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a b)((^x.x)(^y.a)))
  3. ==[ beta  ]==> ((a b)(^y.a))
  4. ==[ alpha ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  1633/26805. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a a)(a ((^y.y) a)))
  4. ==[ alpha ]==> ((a a)(a ((^x.x) a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1634/26814. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^b.a) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.a) a))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  1635/26832. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a a)))

     REDUCED to normal form.

  ------  1636/26841. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) b))
  3. ==[ beta  ]==> (b ((^y.(^z.z)) b))
  4. ==[ alpha ]==> (b ((^x.(^y.y)) b))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1637/26850. ------  

  1. ==[ start ]==> (((a a)(a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1638/26877. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.a)))

     REDUCED to normal form.

  ------  1639/26895. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  1640/26913. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  1641/26922. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  1642/26949. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z)) a))

     REDUCED to normal form.

  ------  1643/26967. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  1644/26976. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a) b))

     REDUCED to normal form.

  ------  1645/26994. ------  

  1. ==[ start ]==> ((a (^b.a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(a (a (^y.y))))

     REDUCED to normal form.

  ------  1646/27012. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.y)))

     REDUCED to normal form.

  ------  1647/27030. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z) b))
  3. ==[ beta  ]==> ((^y.y)((^z.z) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1648/27039. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  1649/27066. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1650/27075. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a b))
  3. ==[ beta  ]==> ((^y.a)(a b))
  4. ==[ alpha ]==> ((^x.a)(a b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1651/27102. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1652/27111. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) a))
  3. ==[ beta  ]==> (((a (^x.x)) b) a)

     REDUCED to normal form.

  ------  1653/27137. ------  

  1. ==[ start ]==> (^a.(((^a.a) a) a))
  2. ==[ alpha ]==> (^x.(((^y.y) x) x))
  3. ==[ beta  ]==> (^x.(x x))

     REDUCED to normal form.

  ------  1654/27138. ------  

  1. ==[ start ]==> (a (((^a.a) a) a))
  2. ==[ alpha ]==> (a (((^x.x) a) a))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1655/27195. ------  

  1. ==[ start ]==> ((^a.b)(^c.c))
  2. ==[ alpha ]==> ((^x.b)(^y.y))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1656/27276. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.c))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.c))
  3. ==[ beta  ]==> ((^z.c)(^y.y))
  4. ==[ alpha ]==> ((^x.c)(^y.y))
  5. ==[ beta  ]==> c

     REDUCED to normal form.

  ------  1657/27393. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1658/27540. ------  

  1. ==[ start ]==> ((((^a.a) a) a) a)
  2. ==[ alpha ]==> ((((^x.x) a) a) a)
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1659/27546. ------  

  1. ==[ start ]==> ((^a.a)(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  3. ==[ beta  ]==> (((^y.y) a) a)
  4. ==[ alpha ]==> (((^x.x) a) a)
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1660/27555. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1661/27573. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y)) b))
  3. ==[ beta  ]==> (((a (^y.y)) b)((a (^y.y)) b))
  4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y)) b))

     REDUCED to normal form.

  ------  1662/27600. ------  

  1. ==[ start ]==> ((^a.b)((a a) c))
  2. ==[ alpha ]==> ((^x.b)((a a) c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1663/27603. ------  

  1. ==[ start ]==> ((a b)(^c.c))
  2. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  1664/27612. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.a)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.a)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.a)))

     REDUCED to normal form.

  ------  1665/27621. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  1666/27684. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.c))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.c))

     REDUCED to normal form.

  ------  1667/27693. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.x1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1668/27747. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1669/27798. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^x.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1670/27801. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1671/27837. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1672/27846. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  1673/27870. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(^z.z)))
  3. ==[ eta   ]==> ((^y.y)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1674/27882. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a a)))
  3. ==[ beta  ]==> ((^y.a)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.a)(^y.(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1675/27909. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1676/27918. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(y y)))

     REDUCED to normal form.

  ------  1677/27945. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.a))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1678/27957. ------  

  1. ==[ start ]==> ((a a)(((^a.a) a) a))
  2. ==[ alpha ]==> ((a a)(((^x.x) a) a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1679/27966. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1680/27984. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x)) b))

     REDUCED to normal form.

  ------  1681/27993. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1682/28002. ------  

  1. ==[ start ]==> (((a a) a)(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)(b (a (^x.x))))

     REDUCED to normal form.

  ------  1683/28011. ------  

  1. ==[ start ]==> ((a b)((a a) c))

     REDUCED to normal form.

  ------  1684/28020. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1685/28029. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(a a))

     REDUCED to normal form.

  ------  1686/28056. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a a)))
  3. ==[ beta  ]==> (b ((a (^y.y))(a a)))
  4. ==[ alpha ]==> (b ((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1687/28065. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) b))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  1688/28083. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  1689/28101. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1690/28110. ------  

  1. ==[ start ]==> (((a a) b)(c a))

     REDUCED to normal form.

  ------  1691/28128. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1692/28137. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b b))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b b))

     REDUCED to normal form.

  ------  1693/28155. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  1694/28182. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1695/28191. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (a a)))

     REDUCED to normal form.

  ------  1696/28209. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.a))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1697/28227. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1698/28245. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1699/28254. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) b))
  3. ==[ beta  ]==> (((a (^x.x))(a a)) b)

     REDUCED to normal form.

  ------  1700/28281. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(^y.y)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.y)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  1701/28290. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.a)((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.a)((^y.y)(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1702/28317. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1703/28326. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a (a a)))

     REDUCED to normal form.

  ------  1704/28353. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a a))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1705/28617. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.b))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.b))
  3. ==[ beta  ]==> (^y.(^z.b))
  4. ==[ alpha ]==> (^x.(^y.b))

     REDUCED to normal form.

  ------  1706/28764. ------  

  1. ==[ start ]==> ((((^a.a) a) a) b)
  2. ==[ alpha ]==> ((((^x.x) a) a) b)
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1707/28788. ------  

  1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1708/28833. ------  

  1. ==[ start ]==> ((^a.b)(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(b (a (^y.y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1709/28854. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.a)))

     REDUCED to normal form.

  ------  1710/28869. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1711/28914. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(a (^z.z))))
  3. ==[ beta  ]==> (((a a)(a (^z.z)))(^y.y))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1712/28926. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.c))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.c))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.c))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1713/28935. ------  

  1. ==[ start ]==> (((a a) b)(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.x)))

     REDUCED to normal form.

  ------  1714/28989. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (^x1.x1))))

     REDUCED to normal form.

  ------  1715/29031. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a) b))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a) b))
  3. ==[ beta  ]==> (^y.((a a) b))
  4. ==[ alpha ]==> (^x.((a a) b))

     REDUCED to normal form.

  ------  1716/29034. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.b))
  2. ==[ alpha ]==> ((a (^x.a))(^y.b))

     REDUCED to normal form.

  ------  1717/29052. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1718/29103. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b a))
  3. ==[ eta   ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  1719/29115. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1720/29151. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z)))

     REDUCED to normal form.

  ------  1721/29178. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1722/29192. ------  

  1. ==[ start ]==> (^a.(^b.((^a.a) a)))
  2. ==[ alpha ]==> (^x.(^y.((^z.z) x)))
  3. ==[ beta  ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  1723/29193. ------  

  1. ==[ start ]==> (a (^b.((^a.a) a)))
  2. ==[ alpha ]==> (a (^x.((^y.y) a)))
  3. ==[ beta  ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1724/29208. ------  

  1. ==[ start ]==> ((a (^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a) a))
  3. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  1725/29217. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.z)))
  3. ==[ beta  ]==> (a ((^y.a)(^z.z)))
  4. ==[ alpha ]==> (a ((^x.a)(^y.y)))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1726/29235. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  1727/29244. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  1728/29253. ------  

  1. ==[ start ]==> ((a b)(b (a (^a.a))))
  2. ==[ alpha ]==> ((a b)(b (a (^x.x))))

     REDUCED to normal form.

  ------  1729/29271. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.a))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.a))

     REDUCED to normal form.

  ------  1730/29289. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) a))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  1731/29298. ------  

  1. ==[ start ]==> (((^a.a) b)(c (^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(c (^y.y)))
  3. ==[ beta  ]==> (b (c (^y.y)))
  4. ==[ alpha ]==> (b (c (^x.x)))

     REDUCED to normal form.

  ------  1732/29307. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1733/29325. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  1734/29334. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  1735/29352. ------  

  1. ==[ start ]==> (((a a) b)(a (^b.a)))
  2. ==[ alpha ]==> (((a a) b)(a (^x.a)))

     REDUCED to normal form.

  ------  1736/29370. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1737/29379. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  1738/29397. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  1739/29406. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a (^x1.x1)))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  1740/29424. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1741/29433. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  1742/29451. ------  

  1. ==[ start ]==> ((a (^b.a))((a a) b))
  2. ==[ alpha ]==> ((a (^x.a))((a a) b))

     REDUCED to normal form.

  ------  1743/29469. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (a (^y.y))))

     REDUCED to normal form.

  ------  1744/29487. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1745/29496. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(a a)))

     REDUCED to normal form.

  ------  1746/29523. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b a))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b a))
  3. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  1747/29532. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.a)((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.a)((a a)(^y.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1748/29559. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1749/29568. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  1750/29595. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a (^y.y)))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  1751/29612. ------  

  1. ==[ start ]==> (^a.((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (^x.((^y.y)((^z.z) x)))
  3. ==[ beta  ]==> (^x.((^z.z) x))
  4. ==[ alpha ]==> (^x.((^y.y) x))
  5. ==[ eta   ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1752/29613. ------  

  1. ==[ start ]==> (a ((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (a ((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> (a ((^y.y) a))
  4. ==[ alpha ]==> (a ((^x.x) a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1753/29616. ------  

  1. ==[ start ]==> ((^a.a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (^y.((^z.z) a))
  4. ==[ alpha ]==> (^x.((^y.y) a))
  5. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  1754/29706. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1) x1)))
  3. ==[ eta   ]==> ((^x.(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1755/29940. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(^y1.y1))))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1756/30033. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a)) a)
  2. ==[ alpha ]==> (((^x.x)((^y.y) a)) a)
  3. ==[ beta  ]==> (((^y.y) a) a)
  4. ==[ alpha ]==> (((^x.x) a) a)
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1757/30039. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1758/30042. ------  

  1. ==[ start ]==> ((a a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a a)(^x.((^y.y) a)))
  3. ==[ beta  ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1759/30066. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((^y.a)(^z.z))((^y.a)(^z.z)))
  4. ==[ alpha ]==> (((^x.a)(^y.y))((^z.a)(^x1.x1)))
  5. ==[ beta  ]==> (a ((^z.a)(^x1.x1)))
  6. ==[ alpha ]==> (a ((^x.a)(^y.y)))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1760/30093. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1761/30129. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1762/30132. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1763/30174. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((b (^z.(^x1.x1)))(^y.y))
  4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1764/30195. ------  

  1. ==[ start ]==> (((a a) b)(^b.c))
  2. ==[ alpha ]==> (((a a) b)(^x.c))

     REDUCED to normal form.

  ------  1765/30291. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b (a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(b (a a)))
  3. ==[ beta  ]==> (^y.(b (a a)))
  4. ==[ alpha ]==> (^x.(b (a a)))

     REDUCED to normal form.

  ------  1766/30312. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1767/30363. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.(^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  1768/30366. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  1769/30402. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.b))
  3. ==[ beta  ]==> ((^y.y)(^y1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  1770/30411. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.a))

     REDUCED to normal form.

  ------  1771/30438. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.a))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.a))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1772/30456. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.z))
  3. ==[ beta  ]==> (((^y.y) a)(^z.z))
  4. ==[ alpha ]==> (((^x.x) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1773/30468. ------  

  1. ==[ start ]==> ((a a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1774/30486. ------  

  1. ==[ start ]==> (((^a.a) a)(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a) a))
  3. ==[ beta  ]==> (a (((^y.y) a) a))
  4. ==[ alpha ]==> (a (((^x.x) a) a))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1775/30495. ------  

  1. ==[ start ]==> ((a (a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.a)(^y.y)))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  1776/30513. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x)) b))

     REDUCED to normal form.

  ------  1777/30522. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  1778/30531. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(b (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(b (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(b (a (^x.x))))

     REDUCED to normal form.

  ------  1779/30558. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  1780/30567. ------  

  1. ==[ start ]==> (((^a.a) b)((^b.a) a))
  2. ==[ alpha ]==> (((^x.x) b)((^y.a) a))
  3. ==[ beta  ]==> (b ((^y.a) a))
  4. ==[ alpha ]==> (b ((^x.a) a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  1781/30594. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1782/30603. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  1783/30612. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.z))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1784/30621. ------  

  1. ==[ start ]==> (((a a) b)((^a.a) c))
  2. ==[ alpha ]==> (((a a) b)((^x.x) c))
  3. ==[ beta  ]==> (((a a) b) c)

     REDUCED to normal form.

  ------  1785/30648. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  1786/30666. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b b))
  3. ==[ beta  ]==> ((a (^y.y))(b b))
  4. ==[ alpha ]==> ((a (^x.x))(b b))

     REDUCED to normal form.

  ------  1787/30675. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1788/30702. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z)) a))

     REDUCED to normal form.

  ------  1789/30720. ------  

  1. ==[ start ]==> ((a (^b.a))(b (a a)))
  2. ==[ alpha ]==> ((a (^x.a))(b (a a)))

     REDUCED to normal form.

  ------  1790/30738. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1791/30756. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1792/30765. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.y)))

     REDUCED to normal form.

  ------  1793/30792. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  1794/30801. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b a))
  3. ==[ beta  ]==> ((^y.a)(b a))
  4. ==[ alpha ]==> ((^x.a)(b a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1795/30828. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  1796/30837. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a) a))

     REDUCED to normal form.

  ------  1797/30864. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y) a))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1798/30882. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a a))
  3. ==[ beta  ]==> (((^y.y) a)(a a))
  4. ==[ alpha ]==> (((^x.x) a)(a a))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  1799/30890. ------  

  1. ==[ start ]==> (^a.((a a)(^b.a)))
  2. ==[ alpha ]==> (^x.((x x)(^y.x)))

     REDUCED to normal form.

  ------  1800/30891. ------  

  1. ==[ start ]==> (a ((a a)(^b.a)))
  2. ==[ alpha ]==> (a ((a a)(^x.a)))

     REDUCED to normal form.

  ------  1801/30903. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1802/30984. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1803/31218. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.z))
  3. ==[ eta   ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1804/31311. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a)) b)
  2. ==[ alpha ]==> (((^x.x)((^y.y) a)) b)
  3. ==[ beta  ]==> (((^y.y) a) b)
  4. ==[ alpha ]==> (((^x.x) a) b)
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  1805/31320. ------  

  1. ==[ start ]==> (((a a)(^b.a)) a)
  2. ==[ alpha ]==> (((a a)(^x.a)) a)

     REDUCED to normal form.

  ------  1806/31326. ------  

  1. ==[ start ]==> ((^a.a)((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  1807/31335. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1808/31338. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  1809/31353. ------  

  1. ==[ start ]==> ((^a.(a a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a) a))
  3. ==[ beta  ]==> ((((^y.y) a) a)(((^y.y) a) a))
  4. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) a) a))
  5. ==[ beta  ]==> ((a a)(((^y.y) a) a))
  6. ==[ alpha ]==> ((a a)(((^x.x) a) a))
  7. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1810/31380. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y)) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1811/31416. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1812/31419. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.a)))

     REDUCED to normal form.

  ------  1813/31428. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((^x.x) b)(^z.z))
  4. ==[ alpha ]==> (((^x.x) b)(^y.y))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1814/31461. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (((^z.(^x1.x1)) b)(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1815/31482. ------  

  1. ==[ start ]==> (((a a) b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  1816/31500. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  1817/31554. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  1818/31578. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1819/31617. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  1820/31650. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a) b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z) b))
  3. ==[ eta   ]==> ((^y.y)((^z.z) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1821/31653. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.b))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1822/31662. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1823/31689. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  1824/31698. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.b))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.b))

     REDUCED to normal form.

  ------  1825/31725. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(y y)))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  1826/31743. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z)))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  1827/31752. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.a))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  1828/31764. ------  

  1. ==[ start ]==> ((a a)((a a)(^b.a)))
  2. ==[ alpha ]==> ((a a)((a a)(^x.a)))

     REDUCED to normal form.

  ------  1829/31773. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.x))((^z.z) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y) a))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  1830/31791. ------  

  1. ==[ start ]==> ((a (a a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a (a a))(((^x.x) a) a))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  1831/31800. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1832/31818. ------  

  1. ==[ start ]==> ((a b)((a (^a.a)) b))
  2. ==[ alpha ]==> ((a b)((a (^x.x)) b))

     REDUCED to normal form.

  ------  1833/31827. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1834/31836. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(b (a (^y.y))))

     REDUCED to normal form.

  ------  1835/31854. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.a))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  1836/31863. ------  

  1. ==[ start ]==> (((^a.a) b)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)(a ((^y.y) a)))
  3. ==[ beta  ]==> (b (a ((^y.y) a)))
  4. ==[ alpha ]==> (b (a ((^x.x) a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  1837/31872. ------  

  1. ==[ start ]==> (((a a)(a a))((^b.a) a))
  2. ==[ alpha ]==> (((a a)(a a))((^x.a) a))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  1838/31890. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  1839/31899. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1840/31908. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(b (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1841/31917. ------  

  1. ==[ start ]==> (((a a) b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  1842/31935. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1843/31962. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1844/31971. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b b))

     REDUCED to normal form.

  ------  1845/31989. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1846/32016. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  1847/32034. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a) b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a) b))

     REDUCED to normal form.

  ------  1848/32052. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  1849/32061. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  1850/32088. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a) b))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y) b))
  3. ==[ beta  ]==> ((a a)((^y.y) b))
  4. ==[ alpha ]==> ((a a)((^x.x) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1851/32097. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1852/32124. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1853/32133. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a b))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a b))

     REDUCED to normal form.

  ------  1854/32160. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a (a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a (a a)))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  1855/32178. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (^z.z)))
  3. ==[ beta  ]==> (((^y.y) a)(a (^z.z)))
  4. ==[ alpha ]==> (((^x.x) a)(a (^y.y)))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  1856/32187. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a a))
  2. ==[ alpha ]==> (((a a)(^x.a))(a a))

     REDUCED to normal form.

  ------  1857/32195. ------  

  1. ==[ start ]==> (^a.(b c))
  2. ==[ alpha ]==> (^x.(b c))

     REDUCED to normal form.

  ------  1858/32196. ------  

  1. ==[ start ]==> (a (b c))

     REDUCED to normal form.

  ------  1859/32625. ------  

  1. ==[ start ]==> (((a a)(^b.a)) b)
  2. ==[ alpha ]==> (((a a)(^x.a)) b)

     REDUCED to normal form.

  ------  1860/32640. ------  

  1. ==[ start ]==> ((^a.a)(b c))
  2. ==[ alpha ]==> ((^x.x)(b c))
  3. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  1861/32649. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1862/32661. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (a (^y.((^z.z) a)))
  4. ==[ alpha ]==> (a (^x.((^y.y) a)))
  5. ==[ beta  ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1863/32694. ------  

  1. ==[ start ]==> ((^a.b)(c (a a)))
  2. ==[ alpha ]==> ((^x.b)(c (a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1864/32742. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a)))
  3. ==[ beta  ]==> (b (^y.(^z.a)))
  4. ==[ alpha ]==> (b (^x.(^y.a)))

     REDUCED to normal form.

  ------  1865/32751. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y) x)))
  3. ==[ eta   ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  1866/32775. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(a a)))
  3. ==[ beta  ]==> (((a (^z.z))(a a))(^y.y))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  1867/32814. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.c))
  3. ==[ beta  ]==> ((^y.y)(^x1.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  1868/32823. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.y)))

     REDUCED to normal form.

  ------  1869/32877. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a (^x1.x1))))

     REDUCED to normal form.

  ------  1870/32892. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z)) a))
  3. ==[ beta  ]==> (^y.((a (^z.z)) a))
  4. ==[ alpha ]==> (^x.((a (^y.y)) a))

     REDUCED to normal form.

  ------  1871/32931. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1872/32940. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  1873/32964. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(a a)))
  3. ==[ eta   ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  1874/32976. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z))
  3. ==[ beta  ]==> ((^y.a)(^z.z))
  4. ==[ alpha ]==> ((^x.a)(^y.y))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1875/33012. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a a)))

     REDUCED to normal form.

  ------  1876/33039. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1877/33057. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.a))
  3. ==[ beta  ]==> (((^y.y) a)(^z.a))
  4. ==[ alpha ]==> (((^x.x) a)(^y.a))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  1878/33066. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1879/33087. ------  

  1. ==[ start ]==> ((a a)(b c))

     REDUCED to normal form.

  ------  1880/33096. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.a)))

     REDUCED to normal form.

  ------  1881/33105. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (a ((^y.y)((^z.z) a)))
  4. ==[ alpha ]==> (a ((^x.x)((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1882/33123. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1883/33132. ------  

  1. ==[ start ]==> (((a a) a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.a)(^y.y)))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  1884/33141. ------  

  1. ==[ start ]==> ((a b)(c (a a)))

     REDUCED to normal form.

  ------  1885/33150. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y)) b))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) b))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) b))

     REDUCED to normal form.

  ------  1886/33159. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  1887/33186. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.a)))
  3. ==[ beta  ]==> (b ((^y.y)(^z.a)))
  4. ==[ alpha ]==> (b ((^x.x)(^y.a)))
  5. ==[ beta  ]==> (b (^y.a))
  6. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  1888/33195. ------  

  1. ==[ start ]==> (((a a)(a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) a)))
  3. ==[ beta  ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  1889/33222. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  1890/33231. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) b))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1)) b))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1891/33240. ------  

  1. ==[ start ]==> (((a a) b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  1892/33267. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.a)))

     REDUCED to normal form.

  ------  1893/33285. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  1894/33294. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1895/33312. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  1896/33321. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(a (^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z)))

     REDUCED to normal form.

  ------  1897/33339. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y)) a))

     REDUCED to normal form.

  ------  1898/33357. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (a a)))

     REDUCED to normal form.

  ------  1899/33375. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1900/33384. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (a (^y.y))))

     REDUCED to normal form.

  ------  1901/33411. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a)(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(a a)))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  1902/33420. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z) b))
  3. ==[ beta  ]==> ((^y.a)((^z.z) b))
  4. ==[ alpha ]==> ((^x.a)((^y.y) b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1903/33447. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1904/33456. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(a a))

     REDUCED to normal form.

  ------  1905/33483. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1906/33501. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z) a))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z) a))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y) a))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1907/33510. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(a (^y.y)))

     REDUCED to normal form.

  ------  1908/33527. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))(x (^x1.x1))))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1909/33528. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1910/33558. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((^y.((^z.z) a))(^y.((^z.z) a)))
  4. ==[ alpha ]==> ((^x.((^y.y) a))(^z.((^x1.x1) a)))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1911/33783. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.c))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.c))
  3. ==[ beta  ]==> (^y.(^z.c))
  4. ==[ alpha ]==> (^x.(^y.c))

     REDUCED to normal form.

  ------  1912/33957. ------  

  1. ==[ start ]==> (((a a)(^b.a)) c)
  2. ==[ alpha ]==> (((a a)(^x.a)) c)

     REDUCED to normal form.

  ------  1913/33975. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a))) a)
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z))) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1914/33981. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1915/33990. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b c))
  2. ==[ alpha ]==> ((^x.(^y.y))(b c))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1916/34008. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((^y.y)((^z.z) a))((^y.y)((^z.z) a)))
  4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.x1) a)))
  5. ==[ beta  ]==> (((^y.y) a)((^z.z)((^x1.x1) a)))
  6. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z) a)))
  7. ==[ beta  ]==> (a ((^y.y)((^z.z) a)))
  8. ==[ alpha ]==> (a ((^x.x)((^y.y) a)))
  9. ==[ beta  ]==> (a ((^y.y) a))
 10. ==[ alpha ]==> (a ((^x.x) a))
 11. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1917/34011. ------  

  1. ==[ start ]==> ((a (a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))(^x.((^y.y) a)))
  3. ==[ beta  ]==> ((a (a a))(^x.a))

     REDUCED to normal form.

  ------  1918/34035. ------  

  1. ==[ start ]==> ((^a.b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.a)(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1919/34071. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1920/34083. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.c))
  2. ==[ alpha ]==> (((^x.x) b)(^y.y))
  3. ==[ beta  ]==> (b (^y.y))
  4. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1921/34092. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.a)))

     REDUCED to normal form.

  ------  1922/34164. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.c))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.c))

     REDUCED to normal form.

  ------  1923/34233. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a c))
  2. ==[ alpha ]==> ((^x.(^y.x))(a c))
  3. ==[ beta  ]==> (^y.(a c))
  4. ==[ alpha ]==> (^x.(a c))

     REDUCED to normal form.

  ------  1924/34236. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.c))
  2. ==[ alpha ]==> ((a (^x.a))(^y.c))

     REDUCED to normal form.

  ------  1925/34272. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.b))
  3. ==[ beta  ]==> ((^y.y)(^z.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  1926/34281. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1927/34305. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b (^z.z)))
  3. ==[ eta   ]==> ((^y.y)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  1928/34317. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a a)))
  3. ==[ beta  ]==> ((^y.a)(^z.(a a)))
  4. ==[ alpha ]==> ((^x.a)(^y.(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1929/34353. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z)))

     REDUCED to normal form.

  ------  1930/34398. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(z z)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(z z)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(y y)))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  1931/34407. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.a))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.a))

     REDUCED to normal form.

  ------  1932/34425. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1933/34437. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  1934/34446. ------  

  1. ==[ start ]==> ((a (^a.a))(b c))
  2. ==[ alpha ]==> ((a (^x.x))(b c))

     REDUCED to normal form.

  ------  1935/34455. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(^y.a)))
  3. ==[ beta  ]==> (a ((a a)(^y.a)))
  4. ==[ alpha ]==> (a ((a a)(^x.a)))

     REDUCED to normal form.

  ------  1936/34464. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> ((a (a a))((^y.y) a))
  4. ==[ alpha ]==> ((a (a a))((^x.x) a))
  5. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  1937/34482. ------  

  1. ==[ start ]==> (((a a) a)(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a) a)(((^x.x) a) a))
  3. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  1938/34491. ------  

  1. ==[ start ]==> ((a b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a b)((^x.a)(^y.y)))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  1939/34509. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) b))

     REDUCED to normal form.

  ------  1940/34527. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (^z.z))))

     REDUCED to normal form.

  ------  1941/34536. ------  

  1. ==[ start ]==> (((^a.a) b)((a a) c))
  2. ==[ alpha ]==> (((^x.x) b)((a a) c))
  3. ==[ beta  ]==> (b ((a a) c))

     REDUCED to normal form.

  ------  1942/34545. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.a))
  4. ==[ alpha ]==> (((a a)(a a))(^x.a))

     REDUCED to normal form.

  ------  1943/34563. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a) a))
  3. ==[ beta  ]==> ((^y.y)((^z.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1944/34581. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1945/34590. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) b))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  1946/34608. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  1947/34644. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.x1)))

     REDUCED to normal form.

  ------  1948/34662. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  1949/34671. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1950/34689. ------  

  1. ==[ start ]==> ((a (^b.a))(a c))
  2. ==[ alpha ]==> ((a (^x.a))(a c))

     REDUCED to normal form.

  ------  1951/34707. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  1952/34725. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  1953/34734. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1954/34761. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b (^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.y)))
  3. ==[ beta  ]==> ((a a)(b (^y.y)))
  4. ==[ alpha ]==> ((a a)(b (^x.x)))

     REDUCED to normal form.

  ------  1955/34770. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.a)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.a)((a a)(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1956/34797. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  1957/34806. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.y)))

     REDUCED to normal form.

  ------  1958/34833. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a) a))
  3. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  1959/34851. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (a a)))
  3. ==[ beta  ]==> (((^y.y) a)(a (a a)))
  4. ==[ alpha ]==> (((^x.x) a)(a (a a)))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  1960/34860. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y) a))
  3. ==[ beta  ]==> (((a a)(^x.a)) a)

     REDUCED to normal form.

  ------  1961/34878. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1962/34886. ------  

  1. ==[ start ]==> (^a.((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.((x (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  1963/34887. ------  

  1. ==[ start ]==> (a ((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (a ((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  1964/35142. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> (^x.(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1965/35334. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a))) b)
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z))) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1966/35343. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a))) a)
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z))) a)

     REDUCED to normal form.

  ------  1967/35349. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  1968/35358. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1969/35376. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(^y.a)))
  3. ==[ beta  ]==> (((a a)(^y.a))((a a)(^y.a)))
  4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.a)))

     REDUCED to normal form.

  ------  1970/35388. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  1971/35403. ------  

  1. ==[ start ]==> ((^a.b)(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.b)(((^y.y) a) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  1972/35439. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1973/35478. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.(^y.y)) a)(^x1.x1))
  4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1974/35484. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a) a))
  3. ==[ beta  ]==> (((^z.a) a)(^y.y))
  4. ==[ alpha ]==> (((^x.a) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  1975/35550. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.z)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y)))

     REDUCED to normal form.

  ------  1976/35601. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> (^x.((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> (^x.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  1977/35604. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  1978/35673. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1)) a))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  1979/35712. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.(^x2.x2))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  1980/35748. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.b))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.b))
  3. ==[ beta  ]==> ((a a)(^y.b))
  4. ==[ alpha ]==> ((a a)(^x.b))

     REDUCED to normal form.

  ------  1981/35766. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z)))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  1982/35775. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(y y)))

     REDUCED to normal form.

  ------  1983/35793. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  1984/35802. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  1985/35814. ------  

  1. ==[ start ]==> ((a a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  1986/35823. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  1987/35832. ------  

  1. ==[ start ]==> (((^a.a) a)(b c))
  2. ==[ alpha ]==> (((^x.x) a)(b c))
  3. ==[ beta  ]==> (a (b c))

     REDUCED to normal form.

  ------  1988/35841. ------  

  1. ==[ start ]==> ((a (a a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a (a a))((a a)(^x.a)))

     REDUCED to normal form.

  ------  1989/35850. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  1990/35868. ------  

  1. ==[ start ]==> ((a b)(((^a.a) a) a))
  2. ==[ alpha ]==> ((a b)(((^x.x) a) a))
  3. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  1991/35877. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.a)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.a)(^y.y)))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  1992/35904. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  1993/35913. ------  

  1. ==[ start ]==> (((^a.a) b)(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(b (a (^y.y))))
  3. ==[ beta  ]==> (b (b (a (^y.y))))
  4. ==[ alpha ]==> (b (b (a (^x.x))))

     REDUCED to normal form.

  ------  1994/35940. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  1995/35949. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^b.a) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a) a))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  1996/35967. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  1997/35985. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  1998/35994. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  1999/36012. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.a)))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.a)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.a)))

     REDUCED to normal form.

  ------  2000/36039. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2001/36048. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b b))

     REDUCED to normal form.

  ------  2002/36066. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^x.a))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.a))(a (^y.y)))

     REDUCED to normal form.

  ------  2003/36084. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y)) a))

     REDUCED to normal form.

  ------  2004/36102. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  2005/36111. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a) b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a) b))

     REDUCED to normal form.

  ------  2006/36138. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2007/36147. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b (^z.z)))
  3. ==[ beta  ]==> ((^y.a)(b (^z.z)))
  4. ==[ alpha ]==> ((^x.a)(b (^y.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2008/36174. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(a (^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  2009/36183. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b a))

     REDUCED to normal form.

  ------  2010/36210. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a b))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a b))
  3. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  2011/36228. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z)))
  5. ==[ beta  ]==> (a ((^y.y)(^z.z)))
  6. ==[ alpha ]==> (a ((^x.x)(^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2012/36237. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a (a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(a (a a)))

     REDUCED to normal form.

  ------  2013/36255. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2014/36264. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a a))

     REDUCED to normal form.

  ------  2015/36411. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((^x.(x (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  5. ==[ beta  ]==> ((^z.z)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2016/36528. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2017/36600. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(z (^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  2018/36729. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a))) b)
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z))) b)

     REDUCED to normal form.

  ------  2019/36753. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2020/36771. ------  

  1. ==[ start ]==> ((^a.(a a))(b c))
  2. ==[ alpha ]==> ((^x.(x x))(b c))
  3. ==[ beta  ]==> ((b c)(b c))

     REDUCED to normal form.

  ------  2021/36792. ------  

  1. ==[ start ]==> (((a a) a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)(^x.((^y.y) a)))
  3. ==[ beta  ]==> (((a a) a)(^x.a))

     REDUCED to normal form.

  ------  2022/36834. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1)) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2023/36873. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  2024/36879. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((a ((^z.z) a))(^y.y))
  4. ==[ alpha ]==> ((a ((^x.x) a))(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2025/36882. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2026/36945. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.c))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.c))
  3. ==[ beta  ]==> ((a (^y.y))(^z.c))
  4. ==[ alpha ]==> ((a (^x.x))(^y.c))

     REDUCED to normal form.

  ------  2027/36954. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.z)))

     REDUCED to normal form.

  ------  2028/36996. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (^x.((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  2029/36999. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2030/37068. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a (a (^z.z))))
  3. ==[ eta   ]==> ((^y.y)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  2031/37071. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  2032/37107. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1))
  3. ==[ beta  ]==> ((^y.y)(^y1.y1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2033/37116. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2034/37143. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(a a)))
  3. ==[ beta  ]==> ((a a)(^y.(a a)))
  4. ==[ alpha ]==> ((a a)(^x.(a a)))

     REDUCED to normal form.

  ------  2035/37170. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2036/37188. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.a))
  3. ==[ beta  ]==> ((^y.y)(^x1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  2037/37197. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1)))

     REDUCED to normal form.

  ------  2038/37227. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2039/37236. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (a ((^y.(^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.z))))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2040/37245. ------  

  1. ==[ start ]==> ((a (a a))(b c))

     REDUCED to normal form.

  ------  2041/37254. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  2042/37263. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> (((a a) a)((^y.y) a))
  4. ==[ alpha ]==> (((a a) a)((^x.x) a))
  5. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  2043/37281. ------  

  1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a) a))
  3. ==[ beta  ]==> ((a a)(((^y.y) a) a))
  4. ==[ alpha ]==> ((a a)(((^x.x) a) a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2044/37290. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  2045/37308. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) b))

     REDUCED to normal form.

  ------  2046/37317. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (b ((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  2047/37326. ------  

  1. ==[ start ]==> (((a a)(a a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))(b (a (^x.x))))

     REDUCED to normal form.

  ------  2048/37344. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  2049/37353. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a a))

     REDUCED to normal form.

  ------  2050/37362. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.a) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2051/37371. ------  

  1. ==[ start ]==> (((a a) b)(c (^a.a)))
  2. ==[ alpha ]==> (((a a) b)(c (^x.x)))

     REDUCED to normal form.

  ------  2052/37389. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1)) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2053/37398. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2054/37425. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.a)))

     REDUCED to normal form.

  ------  2055/37443. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2056/37452. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  2057/37470. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  2058/37506. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2059/37515. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b (a a)))

     REDUCED to normal form.

  ------  2060/37542. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  2061/37551. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z)) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2062/37578. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1) b))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2063/37587. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  2064/37614. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2065/37632. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a) a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a) a))
  3. ==[ beta  ]==> (((^y.y) a)((a a) a))
  4. ==[ alpha ]==> (((^x.x) a)((a a) a))
  5. ==[ beta  ]==> (a ((a a) a))

     REDUCED to normal form.

  ------  2066/37641. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  2067/37659. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2068/37668. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1)))

     REDUCED to normal form.

  ------  2069/37685. ------  

  1. ==[ start ]==> (^a.((^b.a)(a a)))
  2. ==[ alpha ]==> (^x.((^y.x)(x x)))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  2070/37686. ------  

  1. ==[ start ]==> (a ((^b.a)(a a)))
  2. ==[ alpha ]==> (a ((^x.a)(a a)))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2071/37743. ------  

  1. ==[ start ]==> ((^a.b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)(^y.((^z.z) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2072/37824. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^z.(^x1.a))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.a))(^z.z))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  2073/38013. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(^y1.y1))))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  2074/38166. ------  

  1. ==[ start ]==> ((^a.a)((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  3. ==[ beta  ]==> ((^y.a)(a a))
  4. ==[ alpha ]==> ((^x.a)(a a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2075/38193. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((^y.(^z.z))(a (^x1.x1)))((^y.(^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1))))
  5. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1))))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  7. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  8. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2076/38220. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2077/38223. ------  

  1. ==[ start ]==> ((a b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a b)(^x.((^y.y) a)))
  3. ==[ beta  ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  2078/38301. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (((^z.z)(^x1.a))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2079/38304. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.a)))

     REDUCED to normal form.

  ------  2080/38313. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1) x1)))
  3. ==[ eta   ]==> (((^x.x)(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2081/38376. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.c))

     REDUCED to normal form.

  ------  2082/38418. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b b))
  2. ==[ alpha ]==> ((^x.(^y.x))(b b))
  3. ==[ beta  ]==> (^y.(b b))
  4. ==[ alpha ]==> (^x.(b b))

     REDUCED to normal form.

  ------  2083/38439. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  2084/38490. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(^x1.(^y1.y1))))
  3. ==[ eta   ]==> ((^y.y)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2085/38493. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2086/38502. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(y (^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2087/38538. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.b))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  2088/38583. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.b))
  3. ==[ beta  ]==> (((^y.y) a)(^z.b))
  4. ==[ alpha ]==> (((^x.x) a)(^y.b))
  5. ==[ beta  ]==> (a (^y.b))
  6. ==[ alpha ]==> (a (^x.b))

     REDUCED to normal form.

  ------  2089/38592. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.a))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.a))

     REDUCED to normal form.

  ------  2090/38610. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2091/38619. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.a))

     REDUCED to normal form.

  ------  2092/38649. ------  

  1. ==[ start ]==> ((a a)((^b.a)(a a)))
  2. ==[ alpha ]==> ((a a)((^x.a)(a a)))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2093/38667. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a ((a (^y.y))(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a ((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2094/38676. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  2095/38685. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b c))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  2096/38694. ------  

  1. ==[ start ]==> (((a a) a)((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a) a)((a a)(^x.a)))

     REDUCED to normal form.

  ------  2097/38703. ------  

  1. ==[ start ]==> ((a b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a b)((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> ((a b)((^y.y) a))
  4. ==[ alpha ]==> ((a b)((^x.x) a))
  5. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  2098/38721. ------  

  1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a) a))
  3. ==[ beta  ]==> (((a a)(^x.x))(a a))

     REDUCED to normal form.

  ------  2099/38748. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) b))
  3. ==[ beta  ]==> (b ((a (^y.y)) b))
  4. ==[ alpha ]==> (b ((a (^x.x)) b))

     REDUCED to normal form.

  ------  2100/38757. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  2101/38784. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.a))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  2102/38793. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(a ((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2103/38802. ------  

  1. ==[ start ]==> (((a a) b)((^b.a) a))
  2. ==[ alpha ]==> (((a a) b)((^x.a) a))
  3. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  2104/38820. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2105/38829. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  2106/38847. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  2107/38883. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1)))

     REDUCED to normal form.

  ------  2108/38901. ------  

  1. ==[ start ]==> ((a (^b.a))(b b))
  2. ==[ alpha ]==> ((a (^x.a))(b b))

     REDUCED to normal form.

  ------  2109/38919. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(a (^z.z)))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  2110/38937. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2111/38946. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  2112/38973. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2113/38982. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.a)(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.a)(a (a (^y.y))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2114/39009. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2115/39018. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) b))
  3. ==[ beta  ]==> (((a (^x.x)) b) b)

     REDUCED to normal form.

  ------  2116/39045. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(^y.y)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.y)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  2117/39063. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a b))
  3. ==[ beta  ]==> (((^y.y) a)(a b))
  4. ==[ alpha ]==> (((^x.x) a)(a b))
  5. ==[ beta  ]==> (a (a b))

     REDUCED to normal form.

  ------  2118/39072. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a) a))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a) a))

     REDUCED to normal form.

  ------  2119/39090. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2120/39099. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z))) a)

     REDUCED to normal form.

  ------  2121/39125. ------  

  1. ==[ start ]==> (^a.(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (^x.(((^y.y) x)(^z.z)))
  3. ==[ beta  ]==> (^x.(x (^z.z)))
  4. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  2122/39126. ------  

  1. ==[ start ]==> (a (((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (a (((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> (a (a (^y.y)))
  4. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  2123/39183. ------  

  1. ==[ start ]==> ((^a.b)(^c.(^b.a)))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2124/39609. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a)) a)
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y)) a)
  3. ==[ beta  ]==> ((a (^y.y)) a)
  4. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2125/39615. ------  

  1. ==[ start ]==> ((^a.a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.z))
  4. ==[ alpha ]==> (((^x.x) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2126/39624. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2127/39642. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a (^y.y))(^z.(^x1.x1)))((a (^y.y))(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1))))

     REDUCED to normal form.

  ------  2128/39669. ------  

  1. ==[ start ]==> ((^a.b)((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.b)((a a)(^y.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2129/39672. ------  

  1. ==[ start ]==> ((a b)(^c.(^b.a)))
  2. ==[ alpha ]==> ((a b)(^x.(^y.a)))

     REDUCED to normal form.

  ------  2130/39681. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a a)(^y.((^z.z) a)))
  4. ==[ alpha ]==> ((a a)(^x.((^y.y) a)))
  5. ==[ beta  ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  2131/39705. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2132/39762. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2133/39771. ------  

  1. ==[ start ]==> (((a a) b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)(^x.((^y.y) x)))
  3. ==[ eta   ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  2134/39843. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  2135/39867. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> (^x.((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2136/39906. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.c))
  3. ==[ beta  ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  2137/39939. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a) b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a) b))
  3. ==[ eta   ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  2138/39951. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2139/39987. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a a)))

     REDUCED to normal form.

  ------  2140/40032. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(a a)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(a a)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(a a)))
  5. ==[ beta  ]==> (a (^y.(a a)))
  6. ==[ alpha ]==> (a (^x.(a a)))

     REDUCED to normal form.

  ------  2141/40041. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.b))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.b))

     REDUCED to normal form.

  ------  2142/40059. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2143/40068. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 x1)))

     REDUCED to normal form.

  ------  2144/40095. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.z))
  3. ==[ beta  ]==> ((a (^y.y))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2145/40107. ------  

  1. ==[ start ]==> ((a a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2146/40116. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a)(a a)))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2147/40134. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2148/40143. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2149/40152. ------  

  1. ==[ start ]==> (((a a) a)(b c))

     REDUCED to normal form.

  ------  2150/40161. ------  

  1. ==[ start ]==> ((a b)((a a)(^b.a)))
  2. ==[ alpha ]==> ((a b)((a a)(^x.a)))

     REDUCED to normal form.

  ------  2151/40170. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((a a)((^y.y)((^z.z) a)))
  4. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2152/40197. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  2153/40206. ------  

  1. ==[ start ]==> (((^a.a) b)(c (a a)))
  2. ==[ alpha ]==> (((^x.x) b)(c (a a)))
  3. ==[ beta  ]==> (b (c (a a)))

     REDUCED to normal form.

  ------  2154/40215. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x)) b))

     REDUCED to normal form.

  ------  2155/40233. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  2156/40251. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2157/40260. ------  

  1. ==[ start ]==> (((a a) b)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)(a ((^x.x) a)))
  3. ==[ beta  ]==> (((a a) b)(a a))

     REDUCED to normal form.

  ------  2158/40287. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2159/40305. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2160/40314. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(a (^z.z))))

     REDUCED to normal form.

  ------  2161/40332. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  2162/40359. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  2163/40377. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  2164/40395. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a c))
  3. ==[ beta  ]==> ((^y.y)(a c))
  4. ==[ alpha ]==> ((^x.x)(a c))
  5. ==[ beta  ]==> (a c)

     REDUCED to normal form.

  ------  2165/40404. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y)) a))

     REDUCED to normal form.

  ------  2166/40431. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a) b))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a) b))
  3. ==[ beta  ]==> ((a a)((a a) b))

     REDUCED to normal form.

  ------  2167/40440. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2168/40467. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(b (^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  2169/40476. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(a a)))

     REDUCED to normal form.

  ------  2170/40503. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b a))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b a))
  3. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  2171/40521. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(a a)))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z)(a a)))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a)))
  5. ==[ beta  ]==> (a ((^y.y)(a a)))
  6. ==[ alpha ]==> (a ((^x.x)(a a)))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2172/40530. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a b))
  2. ==[ alpha ]==> (((a a)(^x.a))(a b))

     REDUCED to normal form.

  ------  2173/40548. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2174/40557. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (a a)))

     REDUCED to normal form.

  ------  2175/40584. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a a))
  3. ==[ beta  ]==> ((a (^y.y))(a a))
  4. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2176/41076. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a)) b)
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y)) b)
  3. ==[ beta  ]==> ((a (^y.y)) b)
  4. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  2177/41100. ------  

  1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2178/41145. ------  

  1. ==[ start ]==> ((^a.b)(b c))
  2. ==[ alpha ]==> ((^x.b)(b c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2179/41166. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^y.a))

     REDUCED to normal form.

  ------  2180/41181. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2181/41226. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (a (^z.z))))
  3. ==[ beta  ]==> ((b (a (^z.z)))(^y.y))
  4. ==[ alpha ]==> ((b (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2182/41247. ------  

  1. ==[ start ]==> (((a a) b)(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.a)))

     REDUCED to normal form.

  ------  2183/41319. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.c))
  3. ==[ beta  ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  2184/41328. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.z)))

     REDUCED to normal form.

  ------  2185/41343. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (^y.((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (^x.((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  2186/41382. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  2187/41415. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b (a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b (a a)))
  3. ==[ eta   ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  2188/41427. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.b))
  3. ==[ beta  ]==> ((^y.a)(^z.b))
  4. ==[ alpha ]==> ((^x.a)(^y.b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2189/41490. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2190/41517. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a a)))

     REDUCED to normal form.

  ------  2191/41544. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1)))

     REDUCED to normal form.

  ------  2192/41571. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2193/41585. ------  

  1. ==[ start ]==> (^a.(^a.(^a.(a a))))
  2. ==[ alpha ]==> (^x.(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  2194/41586. ------  

  1. ==[ start ]==> (a (^a.(^a.(a a))))
  2. ==[ alpha ]==> (a (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2195/41601. ------  

  1. ==[ start ]==> ((a (^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2196/41610. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a)(a a)))
  3. ==[ beta  ]==> (a ((^y.a)(a a)))
  4. ==[ alpha ]==> (a ((^x.a)(a a)))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2197/41628. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2198/41637. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  2199/41646. ------  

  1. ==[ start ]==> ((a b)(b c))

     REDUCED to normal form.

  ------  2200/41655. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.a)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.a)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.a)))

     REDUCED to normal form.

  ------  2201/41664. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(^x.x))((^z.z) a))
  4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a))
  5. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  2202/41682. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a) a))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  2203/41691. ------  

  1. ==[ start ]==> (((^a.a) b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.z)))
  3. ==[ beta  ]==> (b ((^y.a)(^z.z)))
  4. ==[ alpha ]==> (b ((^x.a)(^y.y)))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  2204/41718. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2205/41727. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b (a (^y.y))))

     REDUCED to normal form.

  ------  2206/41745. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.a)))
  3. ==[ beta  ]==> (((a a) b)(^y.a))
  4. ==[ alpha ]==> (((a a) b)(^x.a))

     REDUCED to normal form.

  ------  2207/41763. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2208/41790. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2209/41799. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2210/41826. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.a)))

     REDUCED to normal form.

  ------  2211/41844. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  2212/41862. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b b))

     REDUCED to normal form.

  ------  2213/41880. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2214/41916. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b (a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b (a a)))
  3. ==[ beta  ]==> ((a a)(b (a a)))

     REDUCED to normal form.

  ------  2215/41925. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a) b))
  3. ==[ beta  ]==> ((^y.a)((a a) b))
  4. ==[ alpha ]==> ((^x.a)((a a) b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2216/41952. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1)) a))
  3. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2217/41961. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.y)))

     REDUCED to normal form.

  ------  2218/41988. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  2219/42006. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(^z.z)))
  3. ==[ beta  ]==> (((^y.y) a)((a a)(^z.z)))
  4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.y)))
  5. ==[ beta  ]==> (a ((a a)(^y.y)))
  6. ==[ alpha ]==> (a ((a a)(^x.x)))

     REDUCED to normal form.

  ------  2220/42015. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.a))(a a))

     REDUCED to normal form.

  ------  2221/42033. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2222/42042. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  2223/42069. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2224/42084. ------  

  1. ==[ start ]==> ((^a.(^a.(a a))) a)
  2. ==[ alpha ]==> ((^x.(^y.(y y))) a)
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2225/42086. ------  

  1. ==[ start ]==> (^a.(a (^a.(a a))))
  2. ==[ alpha ]==> (^x.(x (^y.(y y))))

     REDUCED to normal form.

  ------  2226/42087. ------  

  1. ==[ start ]==> (a (a (^a.(a a))))
  2. ==[ alpha ]==> (a (a (^x.(x x))))

     REDUCED to normal form.

  ------  2227/42090. ------  

  1. ==[ start ]==> ((^a.a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (^y.(^z.(z z)))
  4. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  2228/42585. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2229/42588. ------  

  1. ==[ start ]==> ((a (^a.(a a))) a)
  2. ==[ alpha ]==> ((a (^x.(x x))) a)

     REDUCED to normal form.

  ------  2230/42594. ------  

  1. ==[ start ]==> ((^a.a)(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  3. ==[ beta  ]==> (a (^y.(y y)))
  4. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  2231/42597. ------  

  1. ==[ start ]==> ((a a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2232/42621. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a)(a a)))
  3. ==[ beta  ]==> (((^y.a)(a a))((^y.a)(a a)))
  4. ==[ alpha ]==> (((^x.a)(a a))((^y.a)(a a)))
  5. ==[ beta  ]==> (a ((^y.a)(a a)))
  6. ==[ alpha ]==> (a ((^x.a)(a a)))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2233/42648. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2234/42729. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (((^z.(^x1.x1))(^y1.(^z1.z1)))(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1))
  5. ==[ beta  ]==> ((^y.y)(^y1.y1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2235/42750. ------  

  1. ==[ start ]==> (((a a) b)(^c.c))
  2. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  2236/42768. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.((^y1.y1) x1)))
  3. ==[ eta   ]==> (((^x.(^y.y))(^z.z))(^y1.y1))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1))
  5. ==[ beta  ]==> ((^y.y)(^x1.x1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2237/42831. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.c))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.c))

     REDUCED to normal form.

  ------  2238/42846. ------  

  1. ==[ start ]==> ((^a.(^b.a))(c a))
  2. ==[ alpha ]==> ((^x.(^y.x))(c a))
  3. ==[ beta  ]==> (^y.(c a))
  4. ==[ alpha ]==> (^x.(c a))

     REDUCED to normal form.

  ------  2239/42885. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  2240/42894. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  2241/42918. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2242/42957. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 (^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^y1.(y1 (^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  2243/42993. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.b))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2244/43020. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2245/43038. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.b))
  3. ==[ beta  ]==> ((^y.y)(^x1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  2246/43074. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.a))
  3. ==[ beta  ]==> ((a (^y.y))(^z.a))
  4. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  2247/43089. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2248/43092. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.a))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  2249/43104. ------  

  1. ==[ start ]==> ((a a)(a (^a.(a a))))
  2. ==[ alpha ]==> ((a a)(a (^x.(x x))))

     REDUCED to normal form.

  ------  2250/43122. ------  

  1. ==[ start ]==> (((^a.a) a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (a (((^y.y) a)(^z.z)))
  4. ==[ alpha ]==> (a (((^x.x) a)(^y.y)))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  2251/43131. ------  

  1. ==[ start ]==> ((a (a a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a (a a))((^x.a)(a a)))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  2252/43149. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2253/43158. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  2254/43167. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b c))
  2. ==[ alpha ]==> (((^x.x)(a a))(b c))
  3. ==[ beta  ]==> ((a a)(b c))

     REDUCED to normal form.

  ------  2255/43176. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.a)))

     REDUCED to normal form.

  ------  2256/43203. ------  

  1. ==[ start ]==> (((^a.a) b)(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) a))
  3. ==[ beta  ]==> (b (((^y.y) a) a))
  4. ==[ alpha ]==> (b (((^x.x) a) a))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  2257/43212. ------  

  1. ==[ start ]==> (((a a)(a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.y)))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  2258/43230. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  2259/43239. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2260/43248. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(b (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2261/43257. ------  

  1. ==[ start ]==> (((a a) b)((a a) c))

     REDUCED to normal form.

  ------  2262/43275. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a ((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2263/43284. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^b.a) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.a) a))
  3. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  2264/43302. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2265/43311. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2266/43329. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2267/43356. ------  

  1. ==[ start ]==> ((a (^b.a))(c a))
  2. ==[ alpha ]==> ((a (^x.a))(c a))

     REDUCED to normal form.

  ------  2268/43374. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2269/43392. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2270/43401. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(a (^z.z)))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y)))

     REDUCED to normal form.

  ------  2271/43428. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2272/43437. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b (a a)))
  3. ==[ beta  ]==> ((^y.a)(b (a a)))
  4. ==[ alpha ]==> ((^x.a)(b (a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2273/43464. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  2274/43473. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  2275/43500. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a) b))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y) b))
  3. ==[ beta  ]==> ((a a)((^y.y) b))
  4. ==[ alpha ]==> ((a a)((^x.x) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  2276/43518. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b a))
  3. ==[ beta  ]==> (((^y.y) a)(b a))
  4. ==[ alpha ]==> (((^x.x) a)(b a))
  5. ==[ beta  ]==> (a (b a))

     REDUCED to normal form.

  ------  2277/43527. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.y)))

     REDUCED to normal form.

  ------  2278/43545. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  2279/43554. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a) a))

     REDUCED to normal form.

  ------  2280/43581. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y) a))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2281/43596. ------  

  1. ==[ start ]==> ((^a.(^a.(a a))) b)
  2. ==[ alpha ]==> ((^x.(^y.(y y))) b)
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2282/43599. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a a))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a a))

     REDUCED to normal form.

  ------  2283/43620. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2284/43701. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1) a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2285/43863. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.z)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.z)))
  4. ==[ alpha ]==> (^x.(^y.(^z.y)))

     REDUCED to normal form.

  ------  2286/44106. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2287/44109. ------  

  1. ==[ start ]==> ((a (^a.(a a))) b)
  2. ==[ alpha ]==> ((a (^x.(x x))) b)

     REDUCED to normal form.

  ------  2288/44133. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2289/44136. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  2290/44151. ------  

  1. ==[ start ]==> ((^a.(a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> ((((^y.y) a)(^z.z))(((^y.y) a)(^z.z)))
  4. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1)))
  5. ==[ beta  ]==> ((a (^y.y))(((^z.z) a)(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z)))
  7. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  8. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2291/44178. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2292/44214. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1) a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2293/44217. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  2294/44259. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z)) b))
  3. ==[ beta  ]==> (((a (^z.z)) b)(^y.y))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  2295/44298. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  2296/44307. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  2297/44376. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.a)))
  3. ==[ beta  ]==> (^y.(a (^z.a)))
  4. ==[ alpha ]==> (^x.(a (^y.a)))

     REDUCED to normal form.

  ------  2298/44379. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.y)))

     REDUCED to normal form.

  ------  2299/44448. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z)) a))
  3. ==[ eta   ]==> ((^y.y)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2300/44487. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.(^x2.x2))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  2301/44496. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  2302/44541. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (a (^y.(^z.(^x1.x1))))
  6. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2303/44568. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  2304/44577. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.b))

     REDUCED to normal form.

  ------  2305/44604. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(z z)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(z z)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  2306/44619. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (^z.z)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2307/44622. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2308/44652. ------  

  1. ==[ start ]==> ((a (^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y))))

     REDUCED to normal form.

  ------  2309/44670. ------  

  1. ==[ start ]==> ((a (a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> ((a (a a))(a (^y.y)))
  4. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  2310/44679. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2311/44697. ------  

  1. ==[ start ]==> ((a b)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2312/44706. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2313/44715. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b c))
  2. ==[ alpha ]==> (((a a)(^x.x))(b c))

     REDUCED to normal form.

  ------  2314/44733. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))((^x1.x1) a))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a))
  5. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  2315/44751. ------  

  1. ==[ start ]==> (((a a)(a a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a) a))
  3. ==[ beta  ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  2316/44778. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y)) b))

     REDUCED to normal form.

  ------  2317/44787. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2))))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2318/44796. ------  

  1. ==[ start ]==> (((a a) b)(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)(b (a (^x.x))))

     REDUCED to normal form.

  ------  2319/44814. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  2320/44823. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a a))

     REDUCED to normal form.

  ------  2321/44850. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(a a)))

     REDUCED to normal form.

  ------  2322/44868. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  2323/44877. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a (^z.z))))

     REDUCED to normal form.

  ------  2324/44895. ------  

  1. ==[ start ]==> ((a (^b.a))(a (^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))(a (^y.a)))

     REDUCED to normal form.

  ------  2325/44913. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  2326/44931. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  2327/44940. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  2328/44967. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y)) a))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) a))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  2329/44976. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2330/45003. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2))))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)(^z1.(^x2.x2))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2331/45012. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a (a (^y.y))))

     REDUCED to normal form.

  ------  2332/45039. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(a a)))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  2333/45057. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (a (^y.(^z.z))))
  6. ==[ alpha ]==> (a (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  2334/45066. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b a))
  2. ==[ alpha ]==> (((a a)(^x.a))(b a))

     REDUCED to normal form.

  ------  2335/45084. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2336/45093. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a b))

     REDUCED to normal form.

  ------  2337/45120. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (a a)))
  3. ==[ beta  ]==> ((a (^y.y))(a (a a)))
  4. ==[ alpha ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  2338/45138. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a (^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y)))

     REDUCED to normal form.

  ------  2339/45155. ------  

  1. ==[ start ]==> (^a.((a a)((^a.a) a)))
  2. ==[ alpha ]==> (^x.((x x)((^y.y) x)))
  3. ==[ beta  ]==> (^x.((x x) x))

     REDUCED to normal form.

  ------  2340/45156. ------  

  1. ==[ start ]==> (a ((a a)((^a.a) a)))
  2. ==[ alpha ]==> (a ((a a)((^x.x) a)))
  3. ==[ beta  ]==> (a ((a a) a))

     REDUCED to normal form.

  ------  2341/45411. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.c))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.c))
  3. ==[ beta  ]==> (^y.(^z.c))
  4. ==[ alpha ]==> (^x.(^y.c))

     REDUCED to normal form.

  ------  2342/45654. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2343/45675. ------  

  1. ==[ start ]==> (((a a)((^a.a) a)) a)
  2. ==[ alpha ]==> (((a a)((^x.x) a)) a)
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  2344/45681. ------  

  1. ==[ start ]==> ((^a.a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a)))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2345/45702. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (a (^y.(^z.(z z))))
  4. ==[ alpha ]==> (a (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2346/45735. ------  

  1. ==[ start ]==> ((^a.b)(c b))
  2. ==[ alpha ]==> ((^x.b)(c b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2347/45771. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2348/45783. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (b (^y.((^z.z) a)))
  4. ==[ alpha ]==> (b (^x.((^y.y) a)))
  5. ==[ beta  ]==> (b (^x.a))

     REDUCED to normal form.

  ------  2349/45864. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.a)))

     REDUCED to normal form.

  ------  2350/45933. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a) c))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z) c))
  3. ==[ beta  ]==> (^y.((^z.z) c))
  4. ==[ alpha ]==> (^x.((^y.y) c))
  5. ==[ beta  ]==> (^x.c)

     REDUCED to normal form.

  ------  2351/45936. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.c))
  2. ==[ alpha ]==> ((a (^x.a))(^y.c))

     REDUCED to normal form.

  ------  2352/46053. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2353/46098. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.z))
  3. ==[ beta  ]==> (((^y.y) a)(^z.z))
  4. ==[ alpha ]==> (((^x.x) a)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2354/46107. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2355/46134. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(a a)))

     REDUCED to normal form.

  ------  2356/46161. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2357/46176. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z) a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2358/46179. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.a))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.a))

     REDUCED to normal form.

  ------  2359/46197. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.y))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  2360/46209. ------  

  1. ==[ start ]==> ((a a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a a)((a a)((^x.x) a)))
  3. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  2361/46227. ------  

  1. ==[ start ]==> (((^a.a) a)(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) a)(a (^y.(y y))))
  3. ==[ beta  ]==> (a (a (^y.(y y))))
  4. ==[ alpha ]==> (a (a (^x.(x x))))

     REDUCED to normal form.

  ------  2362/46245. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2363/46254. ------  

  1. ==[ start ]==> (((a a) a)((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a) a)((^x.a)(a a)))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  2364/46263. ------  

  1. ==[ start ]==> ((a b)(c b))

     REDUCED to normal form.

  ------  2365/46272. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2366/46281. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  2367/46299. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.a)))

     REDUCED to normal form.

  ------  2368/46308. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (b ((^y.y)((^z.z) a)))
  4. ==[ alpha ]==> (b ((^x.x)((^y.y) a)))
  5. ==[ beta  ]==> (b ((^y.y) a))
  6. ==[ alpha ]==> (b ((^x.x) a))
  7. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  2369/46335. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2370/46353. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2371/46362. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  2372/46389. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.a))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.a))

     REDUCED to normal form.

  ------  2373/46407. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.a) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.a) a))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2374/46434. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2375/46443. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2376/46461. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a) c))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y) c))
  3. ==[ beta  ]==> ((a (^x.a)) c)

     REDUCED to normal form.

  ------  2377/46497. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2378/46506. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b b))

     REDUCED to normal form.

  ------  2379/46542. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.a)((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.a)((a (^y.y)) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2380/46569. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  2381/46578. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z)))

     REDUCED to normal form.

  ------  2382/46605. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b (^y.y)))
  3. ==[ beta  ]==> ((a a)(b (^y.y)))
  4. ==[ alpha ]==> ((a a)(b (^x.x)))

     REDUCED to normal form.

  ------  2383/46623. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z) b))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z) b))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y) b))
  5. ==[ beta  ]==> (a ((^y.y) b))
  6. ==[ alpha ]==> (a ((^x.x) b))
  7. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  2384/46632. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  2385/46650. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2386/46659. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(a a))

     REDUCED to normal form.

  ------  2387/46686. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2388/46704. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a) a))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) a))
  3. ==[ beta  ]==> ((a (^x.(x x))) a)

     REDUCED to normal form.

  ------  2389/46722. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a a))
  3. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  2390/46730. ------  

  1. ==[ start ]==> (^a.(b (^b.a)))
  2. ==[ alpha ]==> (^x.(b (^y.x)))

     REDUCED to normal form.

  ------  2391/46731. ------  

  1. ==[ start ]==> (a (b (^b.a)))
  2. ==[ alpha ]==> (a (b (^x.a)))

     REDUCED to normal form.

  ------  2392/46761. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(z z))))
  3. ==[ beta  ]==> ((^y.(^z.(z z)))(^y.(^z.(z z))))
  4. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 x1))))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2393/46986. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> (^x.(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  2394/47058. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(a (^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  2395/47229. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(z z)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2396/47250. ------  

  1. ==[ start ]==> (((a a)((^a.a) a)) b)
  2. ==[ alpha ]==> (((a a)((^x.x) a)) b)
  3. ==[ beta  ]==> (((a a) a) b)

     REDUCED to normal form.

  ------  2397/47265. ------  

  1. ==[ start ]==> ((^a.a)(b (^b.a)))
  2. ==[ alpha ]==> ((^x.x)(b (^y.a)))
  3. ==[ beta  ]==> (b (^y.a))
  4. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  2398/47274. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2399/47292. ------  

  1. ==[ start ]==> ((^a.(a a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x x))(a (^y.(y y))))
  3. ==[ beta  ]==> ((a (^y.(y y)))(a (^y.(y y))))
  4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(y y))))

     REDUCED to normal form.

  ------  2400/47295. ------  

  1. ==[ start ]==> ((a (a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2401/47319. ------  

  1. ==[ start ]==> ((^a.b)((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.b)((^y.a)(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2402/47355. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b c))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b c))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2403/47367. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a)))
  3. ==[ beta  ]==> (b (^y.(^z.a)))
  4. ==[ alpha ]==> (b (^x.(^y.a)))

     REDUCED to normal form.

  ------  2404/47376. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(a a))(^x.a))

     REDUCED to normal form.

  ------  2405/47400. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> (((^z.a)(^x1.x1))(^y.y))
  4. ==[ alpha ]==> (((^x.a)(^y.y))(^z.z))
  5. ==[ beta  ]==> (a (^z.z))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2406/47466. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.x)(a (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2407/47517. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)(a (^z.z))))
  3. ==[ beta  ]==> (^y.((a a)(a (^z.z))))
  4. ==[ alpha ]==> (^x.((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  2408/47520. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  2409/47538. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.y)))

     REDUCED to normal form.

  ------  2410/47589. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(a (^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2411/47592. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  2412/47601. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.c))
  3. ==[ beta  ]==> ((^y.a)(^z.c))
  4. ==[ alpha ]==> ((^x.a)(^y.c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2413/47637. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.b))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.b))

     REDUCED to normal form.

  ------  2414/47691. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.b))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  2415/47760. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a (a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2416/47763. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y y)))

     REDUCED to normal form.

  ------  2417/47781. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.z)))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2418/47802. ------  

  1. ==[ start ]==> ((a a)(b (^b.a)))
  2. ==[ alpha ]==> ((a a)(b (^x.a)))

     REDUCED to normal form.

  ------  2419/47811. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a)))
  3. ==[ beta  ]==> ((a (^x.x))((a a) a))

     REDUCED to normal form.

  ------  2420/47829. ------  

  1. ==[ start ]==> ((a (a a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((a (a a))(a (^x.(x x))))

     REDUCED to normal form.

  ------  2421/47847. ------  

  1. ==[ start ]==> (((a a) a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a) a)(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> (((a a) a)(a (^y.y)))
  4. ==[ alpha ]==> (((a a) a)(a (^x.x)))

     REDUCED to normal form.

  ------  2422/47856. ------  

  1. ==[ start ]==> ((a b)((^b.a)(a a)))
  2. ==[ alpha ]==> ((a b)((^x.a)(a a)))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  2423/47874. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2424/47892. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b c))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b c))

     REDUCED to normal form.

  ------  2425/47901. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)((a a)(^y.a)))
  3. ==[ beta  ]==> (b ((a a)(^y.a)))
  4. ==[ alpha ]==> (b ((a a)(^x.a)))

     REDUCED to normal form.

  ------  2426/47910. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(a a))((^y.y) a))
  4. ==[ alpha ]==> (((a a)(a a))((^x.x) a))
  5. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  2427/47928. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2428/47937. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  2429/47955. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x)) b))

     REDUCED to normal form.

  ------  2430/47973. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  2431/48000. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((a (^y.y))(a ((^z.z) a)))
  4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a)))
  5. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2432/48009. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a) a))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  2433/48027. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2434/48036. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  2435/48054. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  2436/48072. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.a)))

     REDUCED to normal form.

  ------  2437/48090. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2438/48099. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  2439/48126. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a a)((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2440/48135. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a c))
  3. ==[ beta  ]==> ((^y.a)(a c))
  4. ==[ alpha ]==> ((^x.a)(a c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2441/48162. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  2442/48171. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a) b))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a) b))

     REDUCED to normal form.

  ------  2443/48198. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2444/48216. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(a a)))
  3. ==[ beta  ]==> (((^y.y) a)((a a)(a a)))
  4. ==[ alpha ]==> (((^x.x) a)((a a)(a a)))
  5. ==[ beta  ]==> (a ((a a)(a a)))

     REDUCED to normal form.

  ------  2445/48225. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a) b))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b))
  3. ==[ beta  ]==> (((a a)(^x.a)) b)

     REDUCED to normal form.

  ------  2446/48243. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  2447/48252. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.x1)))

     REDUCED to normal form.

  ------  2448/48279. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a) a))
  3. ==[ beta  ]==> ((a (^y.y))((a a) a))
  4. ==[ alpha ]==> ((a (^x.x))((a a) a))

     REDUCED to normal form.

  ------  2449/48297. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a (a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a (a a)))

     REDUCED to normal form.

  ------  2450/48315. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a (^y.y)))
  3. ==[ beta  ]==> (((a a) a)(a (^y.y)))
  4. ==[ alpha ]==> (((a a) a)(a (^x.x)))

     REDUCED to normal form.

  ------  2451/48831. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2452/48885. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2453/48915. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  2454/48930. ------  

  1. ==[ start ]==> ((^a.b)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2455/48966. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2456/49011. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a) a))
  3. ==[ beta  ]==> ((((^z.z) a) a)(^y.y))
  4. ==[ alpha ]==> ((((^x.x) a) a)(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2457/49077. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.a)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.a)))

     REDUCED to normal form.

  ------  2458/49086. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2459/49128. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> (^x.(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2460/49149. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.c))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.c))

     REDUCED to normal form.

  ------  2461/49200. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(^z.(^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2462/49212. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(a (^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2463/49275. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  2464/49302. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a a)))

     REDUCED to normal form.

  ------  2465/49320. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  2466/49356. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.b))
  3. ==[ beta  ]==> ((a (^y.y))(^z.b))
  4. ==[ alpha ]==> ((a (^x.x))(^y.b))

     REDUCED to normal form.

  ------  2467/49371. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2468/49374. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2469/49392. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.a))
  3. ==[ beta  ]==> (((a a) a)(^y.a))
  4. ==[ alpha ]==> (((a a) a)(^x.a))

     REDUCED to normal form.

  ------  2470/49431. ------  

  1. ==[ start ]==> ((a (^a.a))(b (^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))(b (^y.a)))

     REDUCED to normal form.

  ------  2471/49440. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)((a a)((^y.y) a)))
  3. ==[ beta  ]==> (a ((a a)((^y.y) a)))
  4. ==[ alpha ]==> (a ((a a)((^x.x) a)))
  5. ==[ beta  ]==> (a ((a a) a))

     REDUCED to normal form.

  ------  2472/49458. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(z z))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  2473/49476. ------  

  1. ==[ start ]==> ((a b)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a b)(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> ((a b)(a (^y.y)))
  4. ==[ alpha ]==> ((a b)(a (^x.x)))

     REDUCED to normal form.

  ------  2474/49485. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.a)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.a)(a a)))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2475/49512. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2476/49521. ------  

  1. ==[ start ]==> (((^a.a) b)(b c))
  2. ==[ alpha ]==> (((^x.x) b)(b c))
  3. ==[ beta  ]==> (b (b c))

     REDUCED to normal form.

  ------  2477/49530. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))((a a)(^x.a)))

     REDUCED to normal form.

  ------  2478/49557. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a) a))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a a))

     REDUCED to normal form.

  ------  2479/49566. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.a)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2480/49575. ------  

  1. ==[ start ]==> (((a a) b)(c (a a)))

     REDUCED to normal form.

  ------  2481/49593. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2))))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(^x2.x2))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2482/49602. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b (a (^y.y))))

     REDUCED to normal form.

  ------  2483/49620. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.a))
  6. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  2484/49629. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  2485/49656. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a a)))

     REDUCED to normal form.

  ------  2486/49674. ------  

  1. ==[ start ]==> ((a (^b.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2487/49710. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(c a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(c a))
  3. ==[ beta  ]==> ((^y.y)(c a))
  4. ==[ alpha ]==> ((^x.x)(c a))
  5. ==[ beta  ]==> (c a)

     REDUCED to normal form.

  ------  2488/49719. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  2489/49746. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  2490/49755. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2491/49782. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2)))
  3. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2492/49791. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b (a a)))

     REDUCED to normal form.

  ------  2493/49818. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a (a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  2494/49836. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (^z.z)))
  3. ==[ beta  ]==> (((^y.y) a)(b (^z.z)))
  4. ==[ alpha ]==> (((^x.x) a)(b (^y.y)))
  5. ==[ beta  ]==> (a (b (^y.y)))
  6. ==[ alpha ]==> (a (b (^x.x)))

     REDUCED to normal form.

  ------  2495/49845. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a)(a a)))

     REDUCED to normal form.

  ------  2496/49863. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  2497/49872. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b a))

     REDUCED to normal form.

  ------  2498/49899. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a b))
  3. ==[ beta  ]==> ((a (^y.y))(a b))
  4. ==[ alpha ]==> ((a (^x.x))(a b))

     REDUCED to normal form.

  ------  2499/49917. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.z))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  2500/49935. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a) a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y) a))
  3. ==[ beta  ]==> (((a a) a)((^y.y) a))
  4. ==[ alpha ]==> (((a a) a)((^x.x) a))
  5. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  2501/49961. ------  

  1. ==[ start ]==> (^a.((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (^x.((x (^y.y))(x (^z.z))))

     REDUCED to normal form.

  ------  2502/49962. ------  

  1. ==[ start ]==> (a ((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (a ((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2503/50508. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a))) a)
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y))) a)

     REDUCED to normal form.

  ------  2504/50514. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2505/50541. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))((a a)((^y.y) a)))
  3. ==[ beta  ]==> (((a a)((^y.y) a))((a a)((^y.y) a)))
  4. ==[ alpha ]==> (((a a)((^x.x) a))((a a)((^y.y) a)))
  5. ==[ beta  ]==> (((a a) a)((a a)((^y.y) a)))
  6. ==[ alpha ]==> (((a a) a)((a a)((^x.x) a)))
  7. ==[ beta  ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  2506/50562. ------  

  1. ==[ start ]==> (((a a) a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2507/50604. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2508/50643. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  2509/50724. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.a)))

     REDUCED to normal form.

  ------  2510/50766. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> (^x.((^y.(^z.z)) b))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2511/50805. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  2512/50838. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b b))
  3. ==[ eta   ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  2513/50850. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2514/50913. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2515/50958. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2516/50967. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))

     REDUCED to normal form.

  ------  2517/50994. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a a)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(a a)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(a a)))

     REDUCED to normal form.

  ------  2518/51009. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a) a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a) a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2519/51030. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(y y)))
  3. ==[ beta  ]==> (((a a) a)(^y.(y y)))
  4. ==[ alpha ]==> (((a a) a)(^x.(x x)))

     REDUCED to normal form.

  ------  2520/51057. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2521/51069. ------  

  1. ==[ start ]==> ((a a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a a)((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2522/51087. ------  

  1. ==[ start ]==> (((^a.a) a)(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)(b (^y.a)))
  3. ==[ beta  ]==> (a (b (^y.a)))
  4. ==[ alpha ]==> (a (b (^x.a)))

     REDUCED to normal form.

  ------  2523/51096. ------  

  1. ==[ start ]==> ((a (a a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))((a a)((^x.x) a)))
  3. ==[ beta  ]==> ((a (a a))((a a) a))

     REDUCED to normal form.

  ------  2524/51114. ------  

  1. ==[ start ]==> (((a a) a)(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a) a)(a (^x.(x x))))

     REDUCED to normal form.

  ------  2525/51132. ------  

  1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> ((a a)(((^y.y) a)(^z.z)))
  4. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2526/51141. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  2527/51159. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  2528/51168. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (b ((^y.(^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z))))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  2529/51177. ------  

  1. ==[ start ]==> (((a a)(a a))(b c))

     REDUCED to normal form.

  ------  2530/51195. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2531/51213. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a) a))
  3. ==[ beta  ]==> ((^y.(^z.z))(((^x1.x1) a) a))
  4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2532/51222. ------  

  1. ==[ start ]==> (((a a) b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a) b)((^x.a)(^y.y)))
  3. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  2533/51240. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  2534/51249. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  2535/51276. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.a))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  2536/51294. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.a) a))
  3. ==[ beta  ]==> ((^y.y)((^z.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2537/51321. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  2538/51339. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  2539/51357. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  2540/51393. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b b))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b b))
  3. ==[ beta  ]==> ((a a)(b b))

     REDUCED to normal form.

  ------  2541/51402. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2542/51429. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^y1.y1)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2543/51438. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  2544/51465. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2545/51483. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (((^y.y) a)((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) a))
  5. ==[ beta  ]==> (a ((^y.(^z.z)) a))
  6. ==[ alpha ]==> (a ((^x.(^y.y)) a))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2546/51492. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(b (^y.y)))

     REDUCED to normal form.

  ------  2547/51510. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2548/51519. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  2549/51546. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a)))
  5. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2550/51564. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a) a))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a) a))

     REDUCED to normal form.

  ------  2551/51582. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a (a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a (a a)))
  3. ==[ beta  ]==> (((a a) a)(a (a a)))

     REDUCED to normal form.

  ------  2552/51609. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a a))

     REDUCED to normal form.

  ------  2553/51675. ------  

  1. ==[ start ]==> ((^a.b)(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(z z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2554/51756. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^z.((^x1.x1) a))(^y.y))
  4. ==[ alpha ]==> ((^x.((^y.y) a))(^z.z))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2555/52116. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2556/52164. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a))) b)
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y))) b)

     REDUCED to normal form.

  ------  2557/52188. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2558/52206. ------  

  1. ==[ start ]==> ((^a.(a a))(b (^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))(b (^y.a)))
  3. ==[ beta  ]==> ((b (^y.a))(b (^y.a)))
  4. ==[ alpha ]==> ((b (^x.a))(b (^y.a)))

     REDUCED to normal form.

  ------  2559/52233. ------  

  1. ==[ start ]==> ((^a.b)(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)(a (^y.(y y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2560/52236. ------  

  1. ==[ start ]==> ((a b)(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2561/52314. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> (((^z.z)((^x1.x1) a))(^y.y))
  4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.z))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2562/52317. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  2563/52407. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.(^y.y))(a a))(^x1.x1))
  4. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2564/52431. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(a a)))
  3. ==[ beta  ]==> (^y.((a (^z.z))(a a)))
  4. ==[ alpha ]==> (^x.((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2565/52470. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.c))
  3. ==[ beta  ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  2566/52479. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.y)))

     REDUCED to normal form.

  ------  2567/52503. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(a a)))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2568/52596. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (a (^y.(y (^z.z))))
  6. ==[ alpha ]==> (a (^x.(x (^y.y))))

     REDUCED to normal form.

  ------  2569/52632. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  2570/52674. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2571/52677. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.b))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.b))

     REDUCED to normal form.

  ------  2572/52695. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.z)))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2573/52722. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  2574/52752. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  2575/52770. ------  

  1. ==[ start ]==> ((a (a a))(b (^b.a)))
  2. ==[ alpha ]==> ((a (a a))(b (^x.a)))

     REDUCED to normal form.

  ------  2576/52779. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)((a a)((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2577/52797. ------  

  1. ==[ start ]==> ((a b)(a (^a.(a a))))
  2. ==[ alpha ]==> ((a b)(a (^x.(x x))))

     REDUCED to normal form.

  ------  2578/52815. ------  

  1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.x))(a (^z.z)))
  4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2579/52842. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b ((a (^y.y))(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2580/52851. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  2581/52869. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(^z.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  2582/52878. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))((^z.z) a))
  4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a))
  5. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  2583/52896. ------  

  1. ==[ start ]==> (((a a) b)(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a) b)(((^x.x) a) a))
  3. ==[ beta  ]==> (((a a) b)(a a))

     REDUCED to normal form.

  ------  2584/52923. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y)) b))

     REDUCED to normal form.

  ------  2585/52941. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))(b (a (^z.z))))
  4. ==[ alpha ]==> ((a (^x.x))(b (a (^y.y))))

     REDUCED to normal form.

  ------  2586/52968. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2587/52977. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  2588/52995. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2589/53013. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2590/53031. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a) c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z) c))
  3. ==[ beta  ]==> ((^y.y)((^z.z) c))
  4. ==[ alpha ]==> ((^x.x)((^y.y) c))
  5. ==[ beta  ]==> ((^y.y) c)
  6. ==[ alpha ]==> ((^x.x) c)
  7. ==[ beta  ]==> c

     REDUCED to normal form.

  ------  2591/53040. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.a)))

     REDUCED to normal form.

  ------  2592/53067. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2593/53076. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b b))
  3. ==[ beta  ]==> ((^y.a)(b b))
  4. ==[ alpha ]==> ((^x.a)(b b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2594/53112. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y)) a))

     REDUCED to normal form.

  ------  2595/53139. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a) b))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a) b))
  3. ==[ beta  ]==> ((a a)((a a) b))

     REDUCED to normal form.

  ------  2596/53157. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (a (^z.z))))
  3. ==[ beta  ]==> (((^y.y) a)(a (a (^z.z))))
  4. ==[ alpha ]==> (((^x.x) a)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (a (^y.y))))
  6. ==[ alpha ]==> (a (a (a (^x.x))))

     REDUCED to normal form.

  ------  2597/53166. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  2598/53184. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2599/53193. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) b))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z))) b)

     REDUCED to normal form.

  ------  2600/53220. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  2601/53238. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a b))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a b))

     REDUCED to normal form.

  ------  2602/53256. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a a) a)((^y.y)(^z.z)))
  4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  2603/53283. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  2604/53300. ------  

  1. ==[ start ]==> (^a.((^b.a) b))
  2. ==[ alpha ]==> (^x.((^y.x) b))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  2605/53301. ------  

  1. ==[ start ]==> (a ((^b.a) b))
  2. ==[ alpha ]==> (a ((^x.a) b))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2606/53799. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2607/53871. ------  

  1. ==[ start ]==> ((^a.a)((^b.a) b))
  2. ==[ alpha ]==> ((^x.x)((^y.a) b))
  3. ==[ beta  ]==> ((^y.a) b)
  4. ==[ alpha ]==> ((^x.a) b)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2608/53937. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z z))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(z z))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2609/53961. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2610/54006. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.a)))
  3. ==[ beta  ]==> (((a a)(^z.a))(^y.y))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  2611/54018. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2612/54099. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  2613/54108. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  2614/54123. ------  

  1. ==[ start ]==> ((^a.(^b.a))(c (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(c (^z.z)))
  3. ==[ beta  ]==> (^y.(c (^z.z)))
  4. ==[ alpha ]==> (^x.(c (^y.y)))

     REDUCED to normal form.

  ------  2615/54162. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  2616/54171. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.c))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.c))

     REDUCED to normal form.

  ------  2617/54195. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2618/54234. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(a (^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^y1.(a (^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  2619/54243. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.c))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.c))

     REDUCED to normal form.

  ------  2620/54288. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (a (^y.(^z.(^x1.x1))))
  6. ==[ alpha ]==> (a (^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2621/54297. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  2622/54366. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2623/54369. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(a a)))

     REDUCED to normal form.

  ------  2624/54414. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.a))

     REDUCED to normal form.

  ------  2625/54444. ------  

  1. ==[ start ]==> ((a a)((^b.a) b))
  2. ==[ alpha ]==> ((a a)((^x.a) b))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2626/54462. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (a ((a (^y.y))(a (^z.z))))
  4. ==[ alpha ]==> (a ((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2627/54480. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.a)))
  5. ==[ beta  ]==> (b (^y.a))
  6. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  2628/54489. ------  

  1. ==[ start ]==> (((a a) a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)((a a)((^x.x) a)))
  3. ==[ beta  ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  2629/54507. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(y y))))
  3. ==[ beta  ]==> ((a a)(a (^y.(y y))))
  4. ==[ alpha ]==> ((a a)(a (^x.(x x))))

     REDUCED to normal form.

  ------  2630/54534. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  2631/54543. ------  

  1. ==[ start ]==> (((^a.a) b)(c b))
  2. ==[ alpha ]==> (((^x.x) b)(c b))
  3. ==[ beta  ]==> (b (c b))

     REDUCED to normal form.

  ------  2632/54552. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2633/54570. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b c))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  2634/54579. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.a)))

     REDUCED to normal form.

  ------  2635/54588. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2636/54615. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.a)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2637/54642. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2638/54651. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a (^z.z))))

     REDUCED to normal form.

  ------  2639/54669. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  2640/54678. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(a a))

     REDUCED to normal form.

  ------  2641/54696. ------  

  1. ==[ start ]==> ((a (^b.a))(c (^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(c (^y.y)))

     REDUCED to normal form.

  ------  2642/54714. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2643/54732. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2644/54768. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  2645/54777. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2646/54804. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)(a (^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2647/54813. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a c))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a c))

     REDUCED to normal form.

  ------  2648/54840. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b (a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b (a a)))
  3. ==[ beta  ]==> ((a a)(b (a a)))

     REDUCED to normal form.

  ------  2649/54858. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> (a ((^y.y)(^z.(^x1.x1))))
  6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z))))
  7. ==[ beta  ]==> (a (^y.(^z.z)))
  8. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  2650/54867. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(a (a (^y.y))))

     REDUCED to normal form.

  ------  2651/54885. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  2652/54894. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a a)))

     REDUCED to normal form.

  ------  2653/54921. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(b a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b a))
  3. ==[ beta  ]==> ((a (^y.y))(b a))
  4. ==[ alpha ]==> ((a (^x.x))(b a))

     REDUCED to normal form.

  ------  2654/54939. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (^x.(x x)))(a a))

     REDUCED to normal form.

  ------  2655/54957. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a) a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a) a))
  3. ==[ beta  ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  2656/54984. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) a))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y))) a)

     REDUCED to normal form.

  ------  2657/55010. ------  

  1. ==[ start ]==> (^a.(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (^x.(((^y.y) x)(x x)))
  3. ==[ beta  ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  2658/55011. ------  

  1. ==[ start ]==> (a (((^a.a) a)(a a)))
  2. ==[ alpha ]==> (a (((^x.x) a)(a a)))
  3. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  2659/55068. ------  

  1. ==[ start ]==> ((^a.b)(^c.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)(^y.((^z.z) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2660/55584. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a)) a)
  2. ==[ alpha ]==> ((((^x.x) a)(a a)) a)
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  2661/55590. ------  

  1. ==[ start ]==> ((^a.a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a)))
  3. ==[ beta  ]==> (((^y.y) a)(a a))
  4. ==[ alpha ]==> (((^x.x) a)(a a))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2662/55599. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a) b))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2663/55617. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (((a (^y.y))(a (^z.z)))((a (^y.y))(a (^z.z))))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(a (^x1.x1))))

     REDUCED to normal form.

  ------  2664/55644. ------  

  1. ==[ start ]==> ((^a.b)((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)((a a)((^y.y) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2665/55647. ------  

  1. ==[ start ]==> ((a b)(^c.((^a.a) a)))
  2. ==[ alpha ]==> ((a b)(^x.((^y.y) a)))
  3. ==[ beta  ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  2666/55665. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  2667/55680. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2668/55725. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b c))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b c))
  3. ==[ beta  ]==> ((b c)(^y.y))
  4. ==[ alpha ]==> ((b c)(^x.x))

     REDUCED to normal form.

  ------  2669/55746. ------  

  1. ==[ start ]==> (((a a) b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)(^x.((^y.y) a)))
  3. ==[ beta  ]==> (((a a) b)(^x.a))

     REDUCED to normal form.

  ------  2670/55827. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.a)))

     REDUCED to normal form.

  ------  2671/55842. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^b.a) a))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.a) a))
  3. ==[ beta  ]==> (^y.((^z.a) a))
  4. ==[ alpha ]==> (^x.((^y.a) a))
  5. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  2672/55962. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  2673/56016. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2674/56070. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2675/56085. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(^z.z)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2676/56106. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.b))
  3. ==[ beta  ]==> (((a a) a)(^y.b))
  4. ==[ alpha ]==> (((a a) a)(^x.b))

     REDUCED to normal form.

  ------  2677/56133. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z z)))

     REDUCED to normal form.

  ------  2678/56160. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.y))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  2679/56172. ------  

  1. ==[ start ]==> ((a a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a a)(((^x.x) a)(a a)))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  2680/56181. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a) b))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a) b))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2681/56199. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2682/56217. ------  

  1. ==[ start ]==> (((a a) a)(b (^b.a)))
  2. ==[ alpha ]==> (((a a) a)(b (^x.a)))

     REDUCED to normal form.

  ------  2683/56226. ------  

  1. ==[ start ]==> ((a b)((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a b)((a a)((^x.x) a)))
  3. ==[ beta  ]==> ((a b)((a a) a))

     REDUCED to normal form.

  ------  2684/56244. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(y y))))

     REDUCED to normal form.

  ------  2685/56262. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a (^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  2686/56271. ------  

  1. ==[ start ]==> (((^a.a) b)((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.a)(a a)))
  3. ==[ beta  ]==> (b ((^y.a)(a a)))
  4. ==[ alpha ]==> (b ((^x.a)(a a)))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  2687/56298. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2688/56307. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b c))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b c))

     REDUCED to normal form.

  ------  2689/56316. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)(^x1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2690/56325. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y) a)))
  3. ==[ beta  ]==> (((a a) b)((^y.y) a))
  4. ==[ alpha ]==> (((a a) b)((^x.x) a))
  5. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  2691/56343. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^x1.x1) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2692/56352. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  2693/56370. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z)) b))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z)) b))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) b))

     REDUCED to normal form.

  ------  2694/56379. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2695/56406. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.a))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.a))

     REDUCED to normal form.

  ------  2696/56424. ------  

  1. ==[ start ]==> ((a (^b.a))((^b.a) a))
  2. ==[ alpha ]==> ((a (^x.a))((^y.a) a))
  3. ==[ beta  ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  2697/56442. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2698/56460. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  2699/56469. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  2700/56505. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2701/56532. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2702/56541. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a (^x.x)) b)(a (^z.z)))
  4. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.y)))

     REDUCED to normal form.

  ------  2703/56568. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2704/56586. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a) b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a) b))
  3. ==[ beta  ]==> (((^y.y) a)((a a) b))
  4. ==[ alpha ]==> (((^x.x) a)((a a) b))
  5. ==[ beta  ]==> (a ((a a) b))

     REDUCED to normal form.

  ------  2705/56595. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2706/56613. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2707/56622. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.x1)))

     REDUCED to normal form.

  ------  2708/56649. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  2709/56667. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.y)))

     REDUCED to normal form.

  ------  2710/56685. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a b))
  3. ==[ beta  ]==> (((a a) a)(a b))

     REDUCED to normal form.

  ------  2711/56712. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a a)))

     REDUCED to normal form.

  ------  2712/56739. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a a))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  2713/57003. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((^x.(^y.x))(^x1.x1))
  4. ==[ alpha ]==> ((^x.(^y.x))(^z.z))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2714/57075. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.z)))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  2715/57321. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a)) b)
  2. ==[ alpha ]==> ((((^x.x) a)(a a)) b)
  3. ==[ beta  ]==> ((a (a a)) b)

     REDUCED to normal form.

  ------  2716/57345. ------  

  1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2717/57390. ------  

  1. ==[ start ]==> ((^a.b)(b (^b.a)))
  2. ==[ alpha ]==> ((^x.b)(b (^y.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2718/57471. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (((^z.(^x1.x1))(a (^y1.y1)))(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1))
  5. ==[ beta  ]==> ((^y.y)(^x1.x1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2719/57492. ------  

  1. ==[ start ]==> (((a a) b)(^c.(^b.a)))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.a)))

     REDUCED to normal form.

  ------  2720/57588. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(a ((^z.z) a)))
  3. ==[ beta  ]==> (^y.(a ((^z.z) a)))
  4. ==[ alpha ]==> (^x.(a ((^y.y) a)))
  5. ==[ beta  ]==> (^x.(a a))

     REDUCED to normal form.

  ------  2721/57591. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  2722/57660. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.a)))
  3. ==[ eta   ]==> ((^y.y)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  2723/57663. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.y)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.y)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  2724/57708. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2725/57762. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.b))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.b))

     REDUCED to normal form.

  ------  2726/57780. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(x1 (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  2727/57816. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.z))
  3. ==[ beta  ]==> ((a (^y.y))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2728/57831. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(b a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(b a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2729/57852. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(a a)))
  3. ==[ beta  ]==> (((a a) a)(^y.(a a)))
  4. ==[ alpha ]==> (((a a) a)(^x.(a a)))

     REDUCED to normal form.

  ------  2730/57879. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  2731/57906. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  2732/57936. ------  

  1. ==[ start ]==> ((a (^a.a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a a)))
  3. ==[ beta  ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  2733/57945. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a) b))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a) b))
  3. ==[ beta  ]==> (a ((^y.a) b))
  4. ==[ alpha ]==> (a ((^x.a) b))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2734/57963. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  2735/57981. ------  

  1. ==[ start ]==> ((a b)(b (^b.a)))
  2. ==[ alpha ]==> ((a b)(b (^x.a)))

     REDUCED to normal form.

  ------  2736/57990. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)((^y.y) a)))
  3. ==[ beta  ]==> ((a a)((a a)((^y.y) a)))
  4. ==[ alpha ]==> ((a a)((a a)((^x.x) a)))
  5. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  2737/58026. ------  

  1. ==[ start ]==> (((^a.a) b)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (b (((^y.y) a)(^z.z)))
  4. ==[ alpha ]==> (b (((^x.x) a)(^y.y)))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  2738/58035. ------  

  1. ==[ start ]==> (((a a)(a a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.a)(a a)))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  2739/58053. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  2740/58062. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2741/58071. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b c))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b c))
  3. ==[ beta  ]==> ((^y.(^z.z))(b c))
  4. ==[ alpha ]==> ((^x.(^y.y))(b c))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2742/58080. ------  

  1. ==[ start ]==> (((a a) b)((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a) b)((a a)(^x.a)))

     REDUCED to normal form.

  ------  2743/58107. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a) a))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a a))

     REDUCED to normal form.

  ------  2744/58134. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z)) b))

     REDUCED to normal form.

  ------  2745/58152. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  2746/58179. ------  

  1. ==[ start ]==> ((a (^b.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a (^x.a))(a a))

     REDUCED to normal form.

  ------  2747/58215. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2748/58224. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  2749/58251. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a (^b.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.a)))
  3. ==[ beta  ]==> ((a a)(a (^y.a)))
  4. ==[ alpha ]==> ((a a)(a (^x.a)))

     REDUCED to normal form.

  ------  2750/58260. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(c a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(c a))
  3. ==[ beta  ]==> ((^y.a)(c a))
  4. ==[ alpha ]==> ((^x.a)(c a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2751/58287. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  2752/58296. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  2753/58323. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.y)) a))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) a))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  2754/58341. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (a a)))
  3. ==[ beta  ]==> (((^y.y) a)(b (a a)))
  4. ==[ alpha ]==> (((^x.x) a)(b (a a)))
  5. ==[ beta  ]==> (a (b (a a)))

     REDUCED to normal form.

  ------  2755/58350. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a) b))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a) b))

     REDUCED to normal form.

  ------  2756/58368. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  2757/58377. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  2758/58404. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a) b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z) b))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z) b))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y) b))
  5. ==[ beta  ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  2759/58422. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(b a))
  2. ==[ alpha ]==> ((a (^x.(x x)))(b a))

     REDUCED to normal form.

  ------  2760/58440. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a a) a)((^y.y)(a a)))
  4. ==[ alpha ]==> (((a a) a)((^x.x)(a a)))
  5. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  2761/58467. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  2762/58494. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a (^y.y)))
  3. ==[ beta  ]==> ((a (a a))(a (^y.y)))
  4. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  2763/58511. ------  

  1. ==[ start ]==> (^a.((^a.(a a)) a))
  2. ==[ alpha ]==> (^x.((^y.(y y)) x))
  3. ==[ eta   ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2764/58512. ------  

  1. ==[ start ]==> (a ((^a.(a a)) a))
  2. ==[ alpha ]==> (a ((^x.(x x)) a))
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2765/58605. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2766/58767. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.a)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.a)))
  4. ==[ alpha ]==> (^x.(^y.(^z.a)))

     REDUCED to normal form.

  ------  2767/58839. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.c))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.c))
  3. ==[ eta   ]==> ((^y.y)(^z.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  2768/59010. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2769/59103. ------  

  1. ==[ start ]==> (((^a.(a a)) a) a)
  2. ==[ alpha ]==> (((^x.(x x)) a) a)
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2770/59109. ------  

  1. ==[ start ]==> ((^a.a)((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.x)((^y.(y y)) a))
  3. ==[ beta  ]==> ((^y.(y y)) a)
  4. ==[ alpha ]==> ((^x.(x x)) a)
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2771/59136. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a) b))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a) b))
  3. ==[ beta  ]==> (((^y.a) b)((^y.a) b))
  4. ==[ alpha ]==> (((^x.a) b)((^y.a) b))
  5. ==[ beta  ]==> (a ((^y.a) b))
  6. ==[ alpha ]==> (a ((^x.a) b))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2772/59163. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a)) c))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z)) c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2773/59199. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(x1 x1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2774/59202. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1))))

     REDUCED to normal form.

  ------  2775/59244. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^z.z))(^x1.(^y1.y1)))(^y.y))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  2776/59283. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  2777/59361. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (^y.((^z.z)(^x1.a)))
  4. ==[ alpha ]==> (^x.((^y.y)(^z.a)))
  5. ==[ beta  ]==> (^x.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  2778/59364. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.a)))

     REDUCED to normal form.

  ------  2779/59436. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.c))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.c))
  3. ==[ beta  ]==> ((a a)(^y.c))
  4. ==[ alpha ]==> ((a a)(^x.c))

     REDUCED to normal form.

  ------  2780/59445. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.z)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2781/59553. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  2782/59562. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 (^y1.y1))))

     REDUCED to normal form.

  ------  2783/59604. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2784/59607. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2785/59679. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.a))
  3. ==[ beta  ]==> ((a (a a))(^y.a))
  4. ==[ alpha ]==> ((a (a a))(^x.a))

     REDUCED to normal form.

  ------  2786/59697. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.a))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2787/59702. ------  

  1. ==[ start ]==> (^a.(^a.(a (a a))))
  2. ==[ alpha ]==> (^x.(^y.(y (y y))))

     REDUCED to normal form.

  ------  2788/59703. ------  

  1. ==[ start ]==> (a (^a.(a (a a))))
  2. ==[ alpha ]==> (a (^x.(x (x x))))

     REDUCED to normal form.

  ------  2789/59709. ------  

  1. ==[ start ]==> ((a a)((^a.(a a)) a))
  2. ==[ alpha ]==> ((a a)((^x.(x x)) a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2790/59727. ------  

  1. ==[ start ]==> (((^a.a) a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(a a)))
  3. ==[ beta  ]==> (a (((^y.y) a)(a a)))
  4. ==[ alpha ]==> (a (((^x.x) a)(a a)))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  2791/59736. ------  

  1. ==[ start ]==> ((a (a a))((^b.a) b))
  2. ==[ alpha ]==> ((a (a a))((^x.a) b))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  2792/59754. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2793/59763. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a)) c))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y)) c))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  2794/59772. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(b (^y.a)))
  3. ==[ beta  ]==> ((a a)(b (^y.a)))
  4. ==[ alpha ]==> ((a a)(b (^x.a)))

     REDUCED to normal form.

  ------  2795/59781. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(^x.x))((a a) a))

     REDUCED to normal form.

  ------  2796/59799. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z z))))

     REDUCED to normal form.

  ------  2797/59817. ------  

  1. ==[ start ]==> (((a a)(a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> (((a a)(a a))(a (^y.y)))
  4. ==[ alpha ]==> (((a a)(a a))(a (^x.x)))

     REDUCED to normal form.

  ------  2798/59844. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  2799/59853. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.z1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2800/59862. ------  

  1. ==[ start ]==> (((a a) b)(b c))

     REDUCED to normal form.

  ------  2801/59880. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2802/59907. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2803/59934. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2804/59943. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (a (^z.z))))

     REDUCED to normal form.

  ------  2805/59961. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a (^x.a))(^z.a))
  4. ==[ alpha ]==> ((a (^x.a))(^y.a))

     REDUCED to normal form.

  ------  2806/59979. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a) a))
  3. ==[ beta  ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  2807/59997. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2808/60006. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  2809/60042. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.a)))
  3. ==[ beta  ]==> ((^y.a)(a (^z.a)))
  4. ==[ alpha ]==> ((^x.a)(a (^y.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2810/60069. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2811/60078. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b b))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b b))

     REDUCED to normal form.

  ------  2812/60123. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> (a ((^y.(^z.z))(^x1.x1)))
  6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2813/60132. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b (a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(b (a a)))

     REDUCED to normal form.

  ------  2814/60150. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2815/60159. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (a (^x1.x1))))

     REDUCED to normal form.

  ------  2816/60186. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(a a)))

     REDUCED to normal form.

  ------  2817/60204. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  2818/60222. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(^y.y)))
  3. ==[ beta  ]==> (((a a) a)((a a)(^y.y)))
  4. ==[ alpha ]==> (((a a) a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  2819/60249. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a) a))

     REDUCED to normal form.

  ------  2820/60276. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y) a))
  3. ==[ beta  ]==> ((a (a a))((^y.y) a))
  4. ==[ alpha ]==> ((a (a a))((^x.x) a))
  5. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  2821/60294. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a a))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a a))
  3. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2822/60300. ------  

  1. ==[ start ]==> ((^a.(a (a a))) a)
  2. ==[ alpha ]==> ((^x.(x (x x))) a)
  3. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2823/60302. ------  

  1. ==[ start ]==> (^a.(a (a (a a))))
  2. ==[ alpha ]==> (^x.(x (x (x x))))

     REDUCED to normal form.

  ------  2824/60303. ------  

  1. ==[ start ]==> (a (a (a (a a))))

     REDUCED to normal form.

  ------  2825/60306. ------  

  1. ==[ start ]==> ((^a.a)(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(y (y y))))
  3. ==[ beta  ]==> (^y.(y (y y)))
  4. ==[ alpha ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  2826/60558. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.c))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.z))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2827/60801. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2828/60894. ------  

  1. ==[ start ]==> (((^a.(a a)) a) b)
  2. ==[ alpha ]==> (((^x.(x x)) a) b)
  3. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  2829/60900. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.a))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.y))
  3. ==[ beta  ]==> ((^y.y)((^y.y)(^y.y)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2830/60903. ------  

  1. ==[ start ]==> ((a (a (a a))) a)

     REDUCED to normal form.

  ------  2831/60909. ------  

  1. ==[ start ]==> ((^a.a)(a (a (a a))))
  2. ==[ alpha ]==> ((^x.x)(a (a (a a))))
  3. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  2832/60912. ------  

  1. ==[ start ]==> ((a a)(^a.(a (a a))))
  2. ==[ alpha ]==> ((a a)(^x.(x (x x))))

     REDUCED to normal form.

  ------  2833/60918. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2834/60936. ------  

  1. ==[ start ]==> ((^a.(a a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(a a)))
  3. ==[ beta  ]==> ((((^y.y) a)(a a))(((^y.y) a)(a a)))
  4. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) a)(a a)))
  5. ==[ beta  ]==> ((a (a a))(((^y.y) a)(a a)))
  6. ==[ alpha ]==> ((a (a a))(((^x.x) a)(a a)))
  7. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  2835/60963. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2836/61011. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (b (^y.(^z.(z z))))
  4. ==[ alpha ]==> (b (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2837/61092. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^y.a))

     REDUCED to normal form.

  ------  2838/61161. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a) c))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a) c))
  3. ==[ beta  ]==> (^y.((a a) c))
  4. ==[ alpha ]==> (^x.((a a) c))

     REDUCED to normal form.

  ------  2839/61164. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.c))
  2. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  2840/61182. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  2841/61233. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(a (^z.z))))
  3. ==[ eta   ]==> ((^y.y)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2842/61245. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.c))
  3. ==[ beta  ]==> ((^y.a)(^z.c))
  4. ==[ alpha ]==> ((^x.a)(^y.c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2843/61308. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  2844/61362. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))

     REDUCED to normal form.

  ------  2845/61404. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z) b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2846/61407. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.b))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  2847/61452. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.b))

     REDUCED to normal form.

  ------  2848/61479. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(y y)))
  3. ==[ beta  ]==> ((a (a a))(^y.(y y)))
  4. ==[ alpha ]==> ((a (a a))(^x.(x x)))

     REDUCED to normal form.

  ------  2849/61497. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  2850/61503. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a a))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a a))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  2851/61506. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.a))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  2852/61511. ------  

  1. ==[ start ]==> (^a.(^b.(^a.(a a))))
  2. ==[ alpha ]==> (^x.(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  2853/61512. ------  

  1. ==[ start ]==> (a (^b.(^a.(a a))))
  2. ==[ alpha ]==> (a (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2854/61518. ------  

  1. ==[ start ]==> ((a a)(a (a (a a))))

     REDUCED to normal form.

  ------  2855/61527. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(a a)) a))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) a))
  3. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2856/61545. ------  

  1. ==[ start ]==> ((a (a a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a (a a))(((^x.x) a)(a a)))
  3. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  2857/61554. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) b))
  3. ==[ beta  ]==> ((^y.y)((^z.a) b))
  4. ==[ alpha ]==> ((^x.x)((^y.a) b))
  5. ==[ beta  ]==> ((^y.a) b)
  6. ==[ alpha ]==> ((^x.a) b)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2858/61572. ------  

  1. ==[ start ]==> ((a b)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a b)((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2859/61590. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b (^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a)))

     REDUCED to normal form.

  ------  2860/61617. ------  

  1. ==[ start ]==> (((^a.a) b)(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) b)(a (^y.(y y))))
  3. ==[ beta  ]==> (b (a (^y.(y y))))
  4. ==[ alpha ]==> (b (a (^x.(x x))))

     REDUCED to normal form.

  ------  2861/61644. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2862/61662. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2863/61671. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  2864/61689. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  2865/61698. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)((^z.z) a))
  4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) a))
  5. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  2866/61716. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a) a))
  3. ==[ beta  ]==> ((a (^y.y))(((^z.z) a) a))
  4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a) a))
  5. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  2867/61725. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  2868/61743. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  2869/61752. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  2870/61770. ------  

  1. ==[ start ]==> ((a (^b.a))((a a) c))
  2. ==[ alpha ]==> ((a (^x.a))((a a) c))

     REDUCED to normal form.

  ------  2871/61788. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(a a))

     REDUCED to normal form.

  ------  2872/61806. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(c (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(c (^z.z)))
  3. ==[ beta  ]==> ((^y.y)(c (^z.z)))
  4. ==[ alpha ]==> ((^x.x)(c (^y.y)))
  5. ==[ beta  ]==> (c (^y.y))
  6. ==[ alpha ]==> (c (^x.x))

     REDUCED to normal form.

  ------  2873/61815. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  2874/61842. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(a (^y.y))))
  3. ==[ beta  ]==> ((a a)((a a)(a (^y.y))))
  4. ==[ alpha ]==> ((a a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  2875/61851. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a) c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z) c))
  3. ==[ beta  ]==> ((^y.a)((^z.z) c))
  4. ==[ alpha ]==> ((^x.a)((^y.y) c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2876/61878. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)((a (^y1.y1))(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2877/61887. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  2878/61914. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a a)((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2879/61932. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z)) a))
  3. ==[ beta  ]==> (((^y.y) a)((a (^z.z)) a))
  4. ==[ alpha ]==> (((^x.x) a)((a (^y.y)) a))
  5. ==[ beta  ]==> (a ((a (^y.y)) a))
  6. ==[ alpha ]==> (a ((a (^x.x)) a))

     REDUCED to normal form.

  ------  2880/61941. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  2881/61959. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  2882/61968. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1)))

     REDUCED to normal form.

  ------  2883/61995. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(b (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.z)))
  3. ==[ beta  ]==> ((a (^y.y))(b (^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  2884/62013. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a) b))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) b))
  3. ==[ beta  ]==> ((a (^x.(x x))) b)

     REDUCED to normal form.

  ------  2885/62031. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(b a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(b a))
  3. ==[ beta  ]==> (((a a) a)(b a))

     REDUCED to normal form.

  ------  2886/62058. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a b))

     REDUCED to normal form.

  ------  2887/62085. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a (a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a (a a)))
  3. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  2888/62103. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a (^y.y)))
  3. ==[ beta  ]==> ((a a)(a (^y.y)))
  4. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  2889/62109. ------  

  1. ==[ start ]==> ((^a.(a (a a))) b)
  2. ==[ alpha ]==> ((^x.(x (x x))) b)
  3. ==[ beta  ]==> (b (b b))

     REDUCED to normal form.

  ------  2890/62112. ------  

  1. ==[ start ]==> ((a (a (a a)))(a a))

     REDUCED to normal form.

  ------  2891/62120. ------  

  1. ==[ start ]==> (^a.((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (^x.((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (^x.(^z.(z z)))
  4. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  2892/62121. ------  

  1. ==[ start ]==> (a ((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (a ((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> (a (^y.(y y)))
  4. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  2893/62124. ------  

  1. ==[ start ]==> ((^a.a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (^y.(^z.(z z)))
  4. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  2894/62133. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2895/62718. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.z)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^y.(^z.z))(^y.(^z.z))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2896/62721. ------  

  1. ==[ start ]==> ((a (a (a a))) b)

     REDUCED to normal form.

  ------  2897/62730. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a))) a)
  2. ==[ alpha ]==> (((^x.x)(^y.(y y))) a)
  3. ==[ beta  ]==> ((^y.(y y)) a)
  4. ==[ alpha ]==> ((^x.(x x)) a)
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2898/62736. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2899/62739. ------  

  1. ==[ start ]==> ((a a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2900/62745. ------  

  1. ==[ start ]==> ((^a.(^a.a))(a (a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(a (a (a a))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2901/62748. ------  

  1. ==[ start ]==> ((a (^a.a))(^a.(a (a a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(y (y y))))

     REDUCED to normal form.

  ------  2902/62790. ------  

  1. ==[ start ]==> ((^a.b)(c (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)(c (^y.(^z.z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2903/62826. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2904/62847. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  2905/62871. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(a a)))
  3. ==[ beta  ]==> (((^z.a)(a a))(^y.y))
  4. ==[ alpha ]==> (((^x.a)(a a))(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2906/62988. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(b (a (^z.z))))
  3. ==[ beta  ]==> (^y.(b (a (^z.z))))
  4. ==[ alpha ]==> (^x.(b (a (^y.y))))

     REDUCED to normal form.

  ------  2907/63009. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.a)))

     REDUCED to normal form.

  ------  2908/63060. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b (^z.(^x1.x1))))
  3. ==[ eta   ]==> ((^y.y)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  2909/63072. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)(^y.(a (^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2910/63231. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2911/63252. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  2912/63279. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(a a)))

     REDUCED to normal form.

  ------  2913/63306. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  2914/63324. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.a))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.a))
  3. ==[ beta  ]==> ((a a)(^y.a))
  4. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  2915/63330. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a (^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a (^y.y)))
  3. ==[ beta  ]==> ((a (^y.y))((a (^y.y))(a (^y.y))))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  2916/63333. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y)))

     REDUCED to normal form.

  ------  2917/63342. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z))
  3. ==[ beta  ]==> ((^y.(y y))(^z.z))
  4. ==[ alpha ]==> ((^x.(x x))(^y.y))
  5. ==[ beta  ]==> ((^y.y)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2918/63354. ------  

  1. ==[ start ]==> ((a a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a a)((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  2919/63363. ------  

  1. ==[ start ]==> ((a (^a.a))(a (a (a a))))
  2. ==[ alpha ]==> ((a (^x.x))(a (a (a a))))

     REDUCED to normal form.

  ------  2920/63372. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(y y)) a))
  3. ==[ beta  ]==> (a ((^y.(y y)) a))
  4. ==[ alpha ]==> (a ((^x.(x x)) a))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2921/63390. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(a a)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a)))
  5. ==[ beta  ]==> (((^y.y) a)(a a))
  6. ==[ alpha ]==> (((^x.x) a)(a a))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2922/63399. ------  

  1. ==[ start ]==> (((a a) a)((^b.a) b))
  2. ==[ alpha ]==> (((a a) a)((^x.a) b))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  2923/63408. ------  

  1. ==[ start ]==> ((a b)(c (^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)(c (^x.(^y.y))))

     REDUCED to normal form.

  ------  2924/63417. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(a (^z.z))))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  2925/63444. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))((a a) a))

     REDUCED to normal form.

  ------  2926/63462. ------  

  1. ==[ start ]==> (((a a)(a a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a a))(a (^x.(x x))))

     REDUCED to normal form.

  ------  2927/63480. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  2928/63489. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(a a)))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  2929/63507. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  2930/63525. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b c))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  2931/63534. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.a)))

     REDUCED to normal form.

  ------  2932/63561. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a) a))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  2933/63588. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z)) b))

     REDUCED to normal form.

  ------  2934/63606. ------  

  1. ==[ start ]==> ((a (^b.a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))(b (a (^y.y))))

     REDUCED to normal form.

  ------  2935/63624. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.a))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  2936/63642. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a) a))
  3. ==[ beta  ]==> ((^y.y)((^z.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2937/63678. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(b (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  2938/63687. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.a)((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((^x.a)((a a)(a (^y.y))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2939/63723. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  2940/63750. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  2941/63777. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y)) a))

     REDUCED to normal form.

  ------  2942/63795. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  2943/63804. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a) b))

     REDUCED to normal form.

  ------  2944/63831. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2945/63849. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(a a)))

     REDUCED to normal form.

  ------  2946/63867. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a (^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  2947/63894. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(a a))

     REDUCED to normal form.

  ------  2948/63921. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  2949/63939. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a) a))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y) a))
  3. ==[ beta  ]==> ((a a)((^y.y) a))
  4. ==[ alpha ]==> ((a a)((^x.x) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  2950/63948. ------  

  1. ==[ start ]==> ((a (a (a a)))(a (^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))(a (^x.x)))

     REDUCED to normal form.

  ------  2951/63957. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a a))
  3. ==[ beta  ]==> ((^y.(y y))(a a))
  4. ==[ alpha ]==> ((^x.(x x))(a a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2952/63978. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2953/64563. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.a))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.a))
  3. ==[ beta  ]==> ((^y.a)((^y.a)(^y.a)))
  4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2954/64575. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a))) b)
  2. ==[ alpha ]==> (((^x.x)(^y.(y y))) b)
  3. ==[ beta  ]==> ((^y.(y y)) b)
  4. ==[ alpha ]==> ((^x.(x x)) b)
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  2955/64599. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2956/64602. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  2957/64611. ------  

  1. ==[ start ]==> (((^a.a) a)(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(y (y y))))
  3. ==[ beta  ]==> (a (^y.(y (y y))))
  4. ==[ alpha ]==> (a (^x.(x (x x))))

     REDUCED to normal form.

  ------  2958/64617. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(y y)) a))
  3. ==[ beta  ]==> (((^y.(y y)) a)((^y.(y y)) a))
  4. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y y)) a))
  5. ==[ beta  ]==> ((a a)((^y.(y y)) a))
  6. ==[ alpha ]==> ((a a)((^x.(x x)) a))
  7. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  2959/64644. ------  

  1. ==[ start ]==> ((^a.b)((^b.a) b))
  2. ==[ alpha ]==> ((^x.b)((^y.a) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  2960/64680. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2961/64692. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (b (^y.((^z.z) a)))
  4. ==[ alpha ]==> (b (^x.((^y.y) a)))
  5. ==[ beta  ]==> (b (^x.a))

     REDUCED to normal form.

  ------  2962/64725. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((((^z.z) a)(^x1.x1))(^y.y))
  4. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  2963/64791. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) a)))
  5. ==[ beta  ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  2964/64842. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  2965/64881. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.(^y.y)) b)(^x1.x1))
  4. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2966/64914. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1)) b))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2967/64953. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  2968/65007. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (a (^y.(a (^z.z))))
  6. ==[ alpha ]==> (a (^x.(a (^y.y))))

     REDUCED to normal form.

  ------  2969/65016. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.c))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.c))

     REDUCED to normal form.

  ------  2970/65070. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  2971/65085. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(b (^z.z)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  2972/65106. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.y))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  2973/65178. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(y y)))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  2974/65184. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a) a))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y) a))
  3. ==[ beta  ]==> (((^y.y) a)(((^y.y) a)((^y.y) a)))
  4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((^z.z) a)))
  5. ==[ beta  ]==> (a (((^y.y) a)((^z.z) a)))
  6. ==[ alpha ]==> (a (((^x.x) a)((^y.y) a)))
  7. ==[ beta  ]==> (a (a ((^y.y) a)))
  8. ==[ alpha ]==> (a (a ((^x.x) a)))
  9. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  2975/65187. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.a))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.a))

     REDUCED to normal form.

  ------  2976/65196. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^y.(^z.z)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2977/65226. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> ((a (^x.x))(^z.(z z)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  2978/65235. ------  

  1. ==[ start ]==> (((^a.a) a)(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x) a)(a (a (a a))))
  3. ==[ beta  ]==> (a (a (a (a a))))

     REDUCED to normal form.

  ------  2979/65244. ------  

  1. ==[ start ]==> ((a (a a))((^a.(a a)) a))
  2. ==[ alpha ]==> ((a (a a))((^x.(x x)) a))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  2980/65262. ------  

  1. ==[ start ]==> (((a a) a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a a) a)(((^x.x) a)(a a)))
  3. ==[ beta  ]==> (((a a) a)(a (a a)))

     REDUCED to normal form.

  ------  2981/65271. ------  

  1. ==[ start ]==> ((a b)((^b.a) b))
  2. ==[ alpha ]==> ((a b)((^x.a) b))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  2982/65289. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  2983/65307. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.a)))

     REDUCED to normal form.

  ------  2984/65316. ------  

  1. ==[ start ]==> (((^a.a) b)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y) a)))
  3. ==[ beta  ]==> (b ((a a)((^y.y) a)))
  4. ==[ alpha ]==> (b ((a a)((^x.x) a)))
  5. ==[ beta  ]==> (b ((a a) a))

     REDUCED to normal form.

  ------  2985/65352. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a (^z.z)))
  4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  2986/65361. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.a)(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2987/65370. ------  

  1. ==[ start ]==> (((a a) b)(c b))

     REDUCED to normal form.

  ------  2988/65388. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(a (^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  2989/65397. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b c))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b c))

     REDUCED to normal form.

  ------  2990/65415. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((a (^x.x))((^z.z) a))
  6. ==[ alpha ]==> ((a (^x.x))((^y.y) a))
  7. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  2991/65442. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2992/65469. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  2993/65505. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  2994/65514. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^b.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a) a))
  3. ==[ beta  ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  2995/65541. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) b))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) b))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  2996/65550. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.a)(b (^y.(^z.z))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  2997/65577. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^y1.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  2998/65586. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(c a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(c a))

     REDUCED to normal form.

  ------  2999/65613. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b b))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b b))
  3. ==[ beta  ]==> ((a a)(b b))

     REDUCED to normal form.

  ------  3000/65631. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> (a ((^y.y)(a (^z.z))))
  6. ==[ alpha ]==> (a ((^x.x)(a (^y.y))))
  7. ==[ beta  ]==> (a (a (^y.y)))
  8. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  3001/65640. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a c))
  2. ==[ alpha ]==> (((a a)(^x.a))(a c))

     REDUCED to normal form.

  ------  3002/65658. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3003/65667. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (a a)))

     REDUCED to normal form.

  ------  3004/65694. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))(a (a (^z.z))))
  4. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y))))

     REDUCED to normal form.

  ------  3005/65712. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(b (^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y)))

     REDUCED to normal form.

  ------  3006/65730. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a) b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y) b))
  3. ==[ beta  ]==> (((a a) a)((^y.y) b))
  4. ==[ alpha ]==> (((a a) a)((^x.x) b))
  5. ==[ beta  ]==> (((a a) a) b)

     REDUCED to normal form.

  ------  3007/65757. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.z)))

     REDUCED to normal form.

  ------  3008/65784. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a) a))
  3. ==[ beta  ]==> ((a (a a))((a a) a))

     REDUCED to normal form.

  ------  3009/65802. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a (a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a (a a)))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  3010/65811. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a) a))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x) a))
  3. ==[ beta  ]==> ((a (a (a a))) a)

     REDUCED to normal form.

  ------  3011/65820. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.z)))
  3. ==[ beta  ]==> ((^y.(y y))(a (^z.z)))
  4. ==[ alpha ]==> ((^x.(x x))(a (^y.y)))
  5. ==[ beta  ]==> ((a (^y.y))(a (^y.y)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  3012/65837. ------  

  1. ==[ start ]==> (^a.(b ((^a.a) a)))
  2. ==[ alpha ]==> (^x.(b ((^y.y) x)))
  3. ==[ beta  ]==> (^x.(b x))
  4. ==[ eta   ]==> b

     REDUCED to normal form.

  ------  3013/65838. ------  

  1. ==[ start ]==> (a (b ((^a.a) a)))
  2. ==[ alpha ]==> (a (b ((^x.x) a)))
  3. ==[ beta  ]==> (a (b a))

     REDUCED to normal form.

  ------  3014/65868. ------  

  1. ==[ start ]==> ((^a.(a a))(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(y (y y))))
  3. ==[ beta  ]==> ((^y.(y (y y)))(^y.(y (y y))))
  4. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y (y y))))
  5. ==[ beta  ]==> ((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))
  6. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))
  7. ==[ beta  ]==> (((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))
  8. ==[ alpha ]==> (((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))
  9. ==[ beta  ]==> (((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))
 10. ==[ alpha ]==> (((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))
 11. ==[ beta  ]==> ((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))
 12. ==[ alpha ]==> ((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))
 13. ==[ beta  ]==> ((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))
 14. ==[ alpha ]==> ((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))
 15. ==[ beta  ]==> (((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))
 16. ==[ alpha ]==> (((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))
 17. ==[ beta  ]==> (((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))
 18. ==[ alpha ]==> (((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))
 19. ==[ beta  ]==> ((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))
 20. ==[ alpha ]==> ((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))
 21. ==[ beta  ]==> ((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))
 22. ==[ alpha ]==> ((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))
 23. ==[ beta  ]==> (((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))
 24. ==[ alpha ]==> (((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))
 25. ==[ beta  ]==> (((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))
 26. ==[ alpha ]==> (((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))
 27. ==[ beta  ]==> ((((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))
 28. ==[ alpha ]==> ((((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))
 29. ==[ beta  ]==> ((((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))
 30. ==[ alpha ]==> ((((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))
 31. ==[ beta  ]==> (((((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))
 32. ==[ alpha ]==> (((((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))(((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9))))))
 33. ==[ beta  ]==> (((((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))(((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9))))))
 34. ==[ alpha ]==> (((((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))(((^x9.(x9 (x9 x9)))(^y9.(y9 (y9 y9))))((^z9.(z9 (z9 z9)))(^x10.(x10 (x10 x10))))))
 35. ==[ beta  ]==> ((((((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))(((^x9.(x9 (x9 x9)))(^y9.(y9 (y9 y9))))((^z9.(z9 (z9 z9)))(^x10.(x10 (x10 x10))))))

     UNREDUCED: maximal number of reductions reached.

  ------  3015/66435. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.(a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y y)))
  3. ==[ beta  ]==> ((^y.(y y))((^y.(y y))(^y.(y y))))
  4. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.(z z))))
  5. ==[ beta  ]==> (((^y.(y y))(^z.(z z)))((^y.(y y))(^z.(z z))))
  6. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(x1 x1))))
  7. ==[ beta  ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(^x1.(x1 x1))))
  8. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(x1 x1))))

     IRREDUCIBLE: cycle.

  ------  3016/66471. ------  

  1. ==[ start ]==> ((^a.a)(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)(b ((^y.y) a)))
  3. ==[ beta  ]==> (b ((^y.y) a))
  4. ==[ alpha ]==> (b ((^x.x) a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3017/66492. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (a (^y.(^z.(z z))))
  4. ==[ alpha ]==> (a (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3018/66498. ------  

  1. ==[ start ]==> ((^a.(a a))(a (a (a a))))
  2. ==[ alpha ]==> ((^x.(x x))(a (a (a a))))
  3. ==[ beta  ]==> ((a (a (a a)))(a (a (a a))))

     REDUCED to normal form.

  ------  3019/66501. ------  

  1. ==[ start ]==> ((a (a a))(^a.(a (a a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(x (x x))))

     REDUCED to normal form.

  ------  3020/66525. ------  

  1. ==[ start ]==> ((^a.b)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.b)(((^y.y) a)(a a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3021/66600. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  3022/66681. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  3023/66723. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z)) b))
  3. ==[ beta  ]==> (^y.((a (^z.z)) b))
  4. ==[ alpha ]==> (^x.((a (^y.y)) b))

     REDUCED to normal form.

  ------  3024/66762. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3025/66771. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  3026/66795. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))(a a)))
  3. ==[ eta   ]==> ((^y.y)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  3027/66834. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.c))
  3. ==[ beta  ]==> ((^y.y)(^y1.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  3028/66843. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.y)))

     REDUCED to normal form.

  ------  3029/66897. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  3030/66951. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3031/66966. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3032/67041. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.b))
  3. ==[ beta  ]==> ((a (a a))(^y.b))
  4. ==[ alpha ]==> ((a (a a))(^x.b))

     REDUCED to normal form.

  ------  3033/67059. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3034/67065. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a (a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a (a a)))
  3. ==[ beta  ]==> ((a (a a))((a (a a))(a (a a))))

     REDUCED to normal form.

  ------  3035/67068. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.(a a)))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(x x)))

     REDUCED to normal form.

  ------  3036/67077. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.a))
  3. ==[ beta  ]==> ((^y.(y y))(^z.a))
  4. ==[ alpha ]==> ((^x.(x x))(^y.a))
  5. ==[ beta  ]==> ((^y.a)(^y.a))
  6. ==[ alpha ]==> ((^x.a)(^y.a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3037/67107. ------  

  1. ==[ start ]==> ((a a)(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a a)(b ((^x.x) a)))
  3. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  3038/67125. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (a ((^y.y)(^z.(z z))))
  4. ==[ alpha ]==> (a ((^x.x)(^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  3039/67134. ------  

  1. ==[ start ]==> ((a (a a))(a (a (a a))))

     REDUCED to normal form.

  ------  3040/67143. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(z z)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(y y)) a))
  5. ==[ beta  ]==> ((^y.(y y)) a)
  6. ==[ alpha ]==> ((^x.(x x)) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3041/67161. ------  

  1. ==[ start ]==> ((a b)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a b)(((^x.x) a)(a a)))
  3. ==[ beta  ]==> ((a b)(a (a a)))

     REDUCED to normal form.

  ------  3042/67170. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^b.a) b))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.a) b))
  3. ==[ beta  ]==> ((a a)((^y.a) b))
  4. ==[ alpha ]==> ((a a)((^x.a) b))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3043/67206. ------  

  1. ==[ start ]==> (((^a.a) b)(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)(b (^y.a)))
  3. ==[ beta  ]==> (b (b (^y.a)))
  4. ==[ alpha ]==> (b (b (^x.a)))

     REDUCED to normal form.

  ------  3044/67215. ------  

  1. ==[ start ]==> (((a a)(a a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x) a)))
  3. ==[ beta  ]==> (((a a)(a a))((a a) a))

     REDUCED to normal form.

  ------  3045/67233. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(z z))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  3046/67251. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3047/67260. ------  

  1. ==[ start ]==> (((a a) b)((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a) b)((^x.a)(a a)))
  3. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  3048/67278. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3049/67287. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y))

     REDUCED to normal form.

  ------  3050/67305. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.a)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(^z.a)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.a)))

     REDUCED to normal form.

  ------  3051/67314. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))((^x1.x1) a))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) a))
  5. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  3052/67332. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3053/67341. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  3054/67359. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y)) b))

     REDUCED to normal form.

  ------  3055/67377. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (a (^y.y))))

     REDUCED to normal form.

  ------  3056/67395. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3057/67404. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(a a))

     REDUCED to normal form.

  ------  3058/67431. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(a a)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(a a)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  3059/67440. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z)) b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3060/67476. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.a)))

     REDUCED to normal form.

  ------  3061/67503. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3062/67521. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> (a ((a a)(^y.(^z.z))))
  6. ==[ alpha ]==> (a ((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  3063/67530. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a a)(^x.a))(a (^z.z)))
  4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.y)))

     REDUCED to normal form.

  ------  3064/67548. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a))
  5. ==[ beta  ]==> ((a (^y.y)) a)
  6. ==[ alpha ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  3065/67557. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  3066/67584. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^x.x))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3067/67602. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.z))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3068/67620. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a)(a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(a a)))
  3. ==[ beta  ]==> (((a a) a)((a a)(a a)))

     REDUCED to normal form.

  ------  3069/67647. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b a))

     REDUCED to normal form.

  ------  3070/67674. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a b))
  3. ==[ beta  ]==> ((a (a a))(a b))

     REDUCED to normal form.

  ------  3071/67692. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3072/67701. ------  

  1. ==[ start ]==> ((a (a (a a)))(a (a a)))

     REDUCED to normal form.

  ------  3073/67710. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z) a))
  3. ==[ beta  ]==> ((^y.(y y))((^z.z) a))
  4. ==[ alpha ]==> ((^x.(x x))((^y.y) a))
  5. ==[ beta  ]==> (((^y.y) a)((^y.y) a))
  6. ==[ alpha ]==> (((^x.x) a)((^y.y) a))
  7. ==[ beta  ]==> (a ((^y.y) a))
  8. ==[ alpha ]==> (a ((^x.x) a))
  9. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3074/67736. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x)))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3075/67737. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3076/67767. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(z z))))
  3. ==[ beta  ]==> ((^y.(^z.(z z)))(^y.(^z.(z z))))
  4. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 x1))))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3077/67875. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^z.(^x1.(x1 x1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3078/68235. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3079/68334. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.z)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^y.(^z.z))(^y.(^z.z))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3080/68373. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a)) a)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a)) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3081/68379. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.a))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3082/68388. ------  

  1. ==[ start ]==> ((^a.(^a.a))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3083/68406. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (((^y.y)(^z.(z z)))((^y.y)(^z.(z z))))
  4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1))))
  5. ==[ beta  ]==> ((^y.(y y))((^z.z)(^x1.(x1 x1))))
  6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(z z))))

     IRREDUCIBLE: cycle.

  ------  3084/68409. ------  

  1. ==[ start ]==> ((a (a a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3085/68418. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z z))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (z z))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (y y))))
  5. ==[ beta  ]==> (^y.(y (y y)))
  6. ==[ alpha ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  3086/68469. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3087/68514. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(z z))))
  3. ==[ beta  ]==> ((a (^z.(z z)))(^y.y))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3088/68517. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3089/68631. ------  

  1. ==[ start ]==> ((^a.(^b.a))(c (a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(c (a a)))
  3. ==[ beta  ]==> (^y.(c (a a)))
  4. ==[ alpha ]==> (^x.(c (a a)))

     REDUCED to normal form.

  ------  3090/68670. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z))
  3. ==[ beta  ]==> ((^y.y)(^z.z))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3091/68679. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.a)))

     REDUCED to normal form.

  ------  3092/68751. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.c))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.c))

     REDUCED to normal form.

  ------  3093/68805. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3094/68874. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (a (^z.z))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3095/68877. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y (^z.z))))

     REDUCED to normal form.

  ------  3096/68922. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3097/68949. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(a a)))
  3. ==[ beta  ]==> ((a (a a))(^y.(a a)))
  4. ==[ alpha ]==> ((a (a a))(^x.(a a)))

     REDUCED to normal form.

  ------  3098/68973. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((^y.y)(^z.z))(((^y.y)(^z.z))((^y.y)(^z.z))))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1))))
  5. ==[ beta  ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1))))
  6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1)(^y1.y1))))
  7. ==[ beta  ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.y1)))
  8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1)))
  9. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
 10. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
 11. ==[ beta  ]==> ((^y.y)(^z.z))
 12. ==[ alpha ]==> ((^x.x)(^y.y))
 13. ==[ beta  ]==> (^y.y)
 14. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3099/68976. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y)))

     REDUCED to normal form.

  ------  3100/68985. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z z)))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(z z)))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(y y)))
  5. ==[ beta  ]==> ((^y.(y y))(^y.(y y)))
  6. ==[ alpha ]==> ((^x.(x x))(^y.(y y)))

     IRREDUCIBLE: cycle.

  ------  3101/69012. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3102/69024. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3103/69033. ------  

  1. ==[ start ]==> ((a (^a.a))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) a)))
  3. ==[ beta  ]==> ((a (^x.x))(b a))

     REDUCED to normal form.

  ------  3104/69051. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> ((a (a a))(^y.(y y)))
  4. ==[ alpha ]==> ((a (a a))(^x.(x x)))

     REDUCED to normal form.

  ------  3105/69060. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (a a))))
  3. ==[ beta  ]==> ((^y.y)(a (a (a a))))
  4. ==[ alpha ]==> ((^x.x)(a (a (a a))))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  3106/69069. ------  

  1. ==[ start ]==> (((a a) a)((^a.(a a)) a))
  2. ==[ alpha ]==> (((a a) a)((^x.(x x)) a))
  3. ==[ beta  ]==> (((a a) a)(a a))

     REDUCED to normal form.

  ------  3107/69087. ------  

  1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a a)))
  3. ==[ beta  ]==> ((a a)(((^y.y) a)(a a)))
  4. ==[ alpha ]==> ((a a)(((^x.x) a)(a a)))
  5. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  3108/69096. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^b.a) b))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.a) b))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  3109/69114. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (^x1.x1))))

     REDUCED to normal form.

  ------  3110/69123. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a)) c))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) c))
  3. ==[ beta  ]==> (b ((^y.(^z.z)) c))
  4. ==[ alpha ]==> (b ((^x.(^y.y)) c))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  3111/69132. ------  

  1. ==[ start ]==> (((a a)(a a))(b (^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))(b (^x.a)))

     REDUCED to normal form.

  ------  3112/69159. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(y y))))

     REDUCED to normal form.

  ------  3113/69177. ------  

  1. ==[ start ]==> (((a a) b)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.y)))
  3. ==[ beta  ]==> (((a a) b)(a (^y.y)))
  4. ==[ alpha ]==> (((a a) b)(a (^x.x)))

     REDUCED to normal form.

  ------  3114/69204. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3115/69222. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b c))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b c))
  3. ==[ beta  ]==> ((a (^y.y))(b c))
  4. ==[ alpha ]==> ((a (^x.x))(b c))

     REDUCED to normal form.

  ------  3116/69231. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.a)))

     REDUCED to normal form.

  ------  3117/69258. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(a a))

     REDUCED to normal form.

  ------  3118/69276. ------  

  1. ==[ start ]==> ((a (^b.a))(c (a a)))
  2. ==[ alpha ]==> ((a (^x.a))(c (a a)))

     REDUCED to normal form.

  ------  3119/69294. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  3120/69312. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a) c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a) c))
  3. ==[ beta  ]==> ((^y.y)((a a) c))
  4. ==[ alpha ]==> ((^x.x)((a a) c))
  5. ==[ beta  ]==> ((a a) c)

     REDUCED to normal form.

  ------  3121/69321. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.a))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.a))

     REDUCED to normal form.

  ------  3122/69357. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((^y.a)((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((^x.a)((a (^y.y))(a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3123/69384. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  3124/69393. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a) c))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) c))
  3. ==[ beta  ]==> (((a (^x.x)) b) c)

     REDUCED to normal form.

  ------  3125/69420. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  3126/69438. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b b))
  3. ==[ beta  ]==> (((^y.y) a)(b b))
  4. ==[ alpha ]==> (((^x.x) a)(b b))
  5. ==[ beta  ]==> (a (b b))

     REDUCED to normal form.

  ------  3127/69447. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  3128/69474. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1)) a))

     REDUCED to normal form.

  ------  3129/69501. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a) b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a) b))
  3. ==[ beta  ]==> ((a (^y.y))((a a) b))
  4. ==[ alpha ]==> ((a (^x.x))((a a) b))

     REDUCED to normal form.

  ------  3130/69519. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a (a (^y.y))))

     REDUCED to normal form.

  ------  3131/69537. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(b (^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.y)))
  3. ==[ beta  ]==> (((a a) a)(b (^y.y)))
  4. ==[ alpha ]==> (((a a) a)(b (^x.x)))

     REDUCED to normal form.

  ------  3132/69564. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3133/69591. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(a a)))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(a a)))
  5. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  3134/69609. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a a) a))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a a) a))
  3. ==[ beta  ]==> ((a a)((a a) a))

     REDUCED to normal form.

  ------  3135/69618. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.y)))
  3. ==[ beta  ]==> ((a (a (a a)))(^y.y))
  4. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  3136/69627. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (a a)))
  3. ==[ beta  ]==> ((^y.(y y))(a (a a)))
  4. ==[ alpha ]==> ((^x.(x x))(a (a a)))
  5. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  3137/69654. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3138/70161. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3139/70299. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a)) b)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a)) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3140/70323. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3141/70353. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  3142/70362. ------  

  1. ==[ start ]==> (((a a) a)(^a.(a (a a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(x (x x))))

     REDUCED to normal form.

  ------  3143/70368. ------  

  1. ==[ start ]==> ((^a.b)((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.b)((^y.(y y)) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3144/70461. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3145/70542. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3146/70566. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> (^y.((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> (^x.((^y.a)(^z.z)))
  5. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3147/70638. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^b.a) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a) a))
  3. ==[ eta   ]==> ((^y.y)((^z.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3148/70686. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  3149/70758. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z))))
  5. ==[ beta  ]==> (^y.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  3150/70809. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3151/70812. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3152/70857. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3153/70902. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.b))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.b))
  3. ==[ beta  ]==> ((a a)(^y.b))
  4. ==[ alpha ]==> ((a a)(^x.b))

     REDUCED to normal form.

  ------  3154/70908. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a a) a))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a a) a))
  3. ==[ beta  ]==> (((a a) a)(((a a) a)((a a) a)))

     REDUCED to normal form.

  ------  3155/70920. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.x1)))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^y.(^z.z)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3156/70947. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3157/70977. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3158/70986. ------  

  1. ==[ start ]==> (((^a.a) a)(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)(b ((^y.y) a)))
  3. ==[ beta  ]==> (a (b ((^y.y) a)))
  4. ==[ alpha ]==> (a (b ((^x.x) a)))
  5. ==[ beta  ]==> (a (b a))

     REDUCED to normal form.

  ------  3159/71004. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z))))
  5. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  6. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  7. ==[ beta  ]==> (^y.(y y))
  8. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3160/71013. ------  

  1. ==[ start ]==> (((a a) a)(a (a (a a))))

     REDUCED to normal form.

  ------  3161/71022. ------  

  1. ==[ start ]==> ((a b)((^a.(a a)) a))
  2. ==[ alpha ]==> ((a b)((^x.(x x)) a))
  3. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  3162/71040. ------  

  1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(a (a a)))

     REDUCED to normal form.

  ------  3163/71067. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a (^z.z))))
  3. ==[ beta  ]==> (b ((a (^y.y))(a (^z.z))))
  4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  3164/71094. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)((a a)((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3165/71112. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z z))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3166/71139. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3167/71166. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3168/71175. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b c))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b c))

     REDUCED to normal form.

  ------  3169/71193. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3170/71220. ------  

  1. ==[ start ]==> ((a (^b.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  3171/71238. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y)) b))

     REDUCED to normal form.

  ------  3172/71256. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (a (^z.z))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  3173/71292. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^b.a) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a) a))
  3. ==[ beta  ]==> ((a a)((^y.a) a))
  4. ==[ alpha ]==> ((a a)((^x.a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3174/71301. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(c (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(c (^z.z)))
  3. ==[ beta  ]==> ((^y.a)(c (^z.z)))
  4. ==[ alpha ]==> ((^x.a)(c (^y.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3175/71328. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(b (^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  3176/71337. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  3177/71382. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (((^y.y) a)((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> (a ((^y.(^z.z))(a a)))
  6. ==[ alpha ]==> (a ((^x.(^y.y))(a a)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3178/71391. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b b))
  2. ==[ alpha ]==> (((a a)(^x.a))(b b))

     REDUCED to normal form.

  ------  3179/71409. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3180/71445. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(b (a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (a a)))
  3. ==[ beta  ]==> ((a (^y.y))(b (a a)))
  4. ==[ alpha ]==> ((a (^x.x))(b (a a)))

     REDUCED to normal form.

  ------  3181/71463. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3182/71481. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((a a) a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) a))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3183/71508. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a) b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) b))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y))) b)

     REDUCED to normal form.

  ------  3184/71535. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(^y.y)))
  3. ==[ beta  ]==> ((a (a a))((a a)(^y.y)))
  4. ==[ alpha ]==> ((a (a a))((a a)(^x.x)))

     REDUCED to normal form.

  ------  3185/71553. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a b))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a b))
  3. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  3186/71562. ------  

  1. ==[ start ]==> ((a (a (a a)))((a a) a))

     REDUCED to normal form.

  ------  3187/71571. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.(y y))((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z)))
  5. ==[ beta  ]==> (((^y.y)(^z.z))((^y.y)(^z.z)))
  6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1)))
  7. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  9. ==[ beta  ]==> ((^y.y)(^z.z))
 10. ==[ alpha ]==> ((^x.x)(^y.y))
 11. ==[ beta  ]==> (^y.y)
 12. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3188/71598. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3189/71673. ------  

  1. ==[ start ]==> ((^a.b)(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(y (y y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3190/71943. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((^y.y)(^z.((^x1.x1) z)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) y)))
  5. ==[ eta   ]==> ((^x.x)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3191/72213. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.b))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.b))
  3. ==[ beta  ]==> ((^y.b)((^y.b)(^y.b)))
  4. ==[ alpha ]==> ((^x.b)((^y.b)(^z.b)))
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3192/72252. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a)) c)
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a)) c)
  3. ==[ beta  ]==> ((^y.y) c)
  4. ==[ alpha ]==> ((^x.x) c)
  5. ==[ beta  ]==> c

     REDUCED to normal form.

  ------  3193/72303. ------  

  1. ==[ start ]==> ((^a.(a a))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))(b ((^y.y) a)))
  3. ==[ beta  ]==> ((b ((^y.y) a))(b ((^y.y) a)))
  4. ==[ alpha ]==> ((b ((^x.x) a))(b ((^y.y) a)))
  5. ==[ beta  ]==> ((b a)(b ((^y.y) a)))
  6. ==[ alpha ]==> ((b a)(b ((^x.x) a)))
  7. ==[ beta  ]==> ((b a)(b a))

     REDUCED to normal form.

  ------  3194/72324. ------  

  1. ==[ start ]==> (((a a) a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3195/72330. ------  

  1. ==[ start ]==> ((^a.b)(a (a (a a))))
  2. ==[ alpha ]==> ((^x.b)(a (a (a a))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3196/72333. ------  

  1. ==[ start ]==> ((a b)(^a.(a (a a))))
  2. ==[ alpha ]==> ((a b)(^x.(x (x x))))

     REDUCED to normal form.

  ------  3197/72366. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.a) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3198/72411. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)((^z.z) a)))
  3. ==[ beta  ]==> (((a a)((^z.z) a))(^y.y))
  4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.y))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3199/72432. ------  

  1. ==[ start ]==> (((a a) b)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3200/72513. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^z.a))

     REDUCED to normal form.

  ------  3201/72528. ------  

  1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) a) a))
  3. ==[ beta  ]==> (^y.(((^z.z) a) a))
  4. ==[ alpha ]==> (^x.(((^y.y) a) a))
  5. ==[ beta  ]==> (^x.(a a))

     REDUCED to normal form.

  ------  3202/72600. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(a ((^z.z) a)))
  3. ==[ eta   ]==> ((^y.y)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3203/72603. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((a ((^x.x) a))(^z.z))
  4. ==[ alpha ]==> ((a ((^x.x) a))(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3204/72675. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.(^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.y)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.y)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  3205/72729. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(a (^y1.y1))))

     REDUCED to normal form.

  ------  3206/72771. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a) b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a) b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3207/72792. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(y (^z.z))))
  3. ==[ beta  ]==> (((a a) a)(^y.(y (^z.z))))
  4. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  3208/72864. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(a a)))
  3. ==[ beta  ]==> ((a a)(^y.(a a)))
  4. ==[ alpha ]==> ((a a)(^x.(a a)))

     REDUCED to normal form.

  ------  3209/72870. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a b))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a b))
  3. ==[ beta  ]==> ((a b)((a b)(a b)))

     REDUCED to normal form.

  ------  3210/72873. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.b))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.b))

     REDUCED to normal form.

  ------  3211/72909. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.a))
  3. ==[ beta  ]==> ((^y.y)(^x1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3212/72957. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> (a ((^y.(^z.z))(^x1.a)))
  4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.a)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3213/72966. ------  

  1. ==[ start ]==> ((a (a a))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))(b ((^x.x) a)))
  3. ==[ beta  ]==> ((a (a a))(b a))

     REDUCED to normal form.

  ------  3214/72984. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> (((a a) a)(^y.(y y)))
  4. ==[ alpha ]==> (((a a) a)(^x.(x x)))

     REDUCED to normal form.

  ------  3215/72993. ------  

  1. ==[ start ]==> ((a b)(a (a (a a))))

     REDUCED to normal form.

  ------  3216/73002. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y)) a))
  3. ==[ beta  ]==> ((a a)((^y.(y y)) a))
  4. ==[ alpha ]==> ((a a)((^x.(x x)) a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3217/73029. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^b.a) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) b))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  3218/73038. ------  

  1. ==[ start ]==> (((^a.a) b)(c (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(c (^y.(^z.z))))
  3. ==[ beta  ]==> (b (c (^y.(^z.z))))
  4. ==[ alpha ]==> (b (c (^x.(^y.y))))

     REDUCED to normal form.

  ------  3219/73047. ------  

  1. ==[ start ]==> (((a a)(a a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  3220/73065. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.a)))
  5. ==[ beta  ]==> (b (^y.a))
  6. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  3221/73074. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a a)((^y.y) a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))((a a) a))

     REDUCED to normal form.

  ------  3222/73092. ------  

  1. ==[ start ]==> (((a a) b)(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a) b)(a (^x.(x x))))

     REDUCED to normal form.

  ------  3223/73110. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(((^x1.x1) a)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3224/73119. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^b.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  3225/73137. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3226/73146. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3227/73164. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(^z.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3228/73173. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))((^x1.x1) a))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a))
  5. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  3229/73191. ------  

  1. ==[ start ]==> ((a (^b.a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a) a))
  3. ==[ beta  ]==> ((a (^x.a))(a a))

     REDUCED to normal form.

  ------  3230/73227. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3231/73236. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b (a (^y.y))))

     REDUCED to normal form.

  ------  3232/73263. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(a ((^a.a) a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a a)(a ((^y.y) a)))
  4. ==[ alpha ]==> ((a a)(a ((^x.x) a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3233/73272. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a) a))
  3. ==[ beta  ]==> ((^y.a)((^z.a) a))
  4. ==[ alpha ]==> ((^x.a)((^y.a) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3234/73299. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1)) b))
  3. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3235/73308. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  3236/73335. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a (^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a (^y.a)))
  3. ==[ beta  ]==> ((a a)(a (^y.a)))
  4. ==[ alpha ]==> ((a a)(a (^x.a)))

     REDUCED to normal form.

  ------  3237/73353. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y) a)((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> (a ((a (^y.y))(^z.z)))
  6. ==[ alpha ]==> (a ((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  3238/73362. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  3239/73380. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3240/73389. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.y1)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1)))

     REDUCED to normal form.

  ------  3241/73416. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3242/73434. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a) b))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a) b))

     REDUCED to normal form.

  ------  3243/73452. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a (a (^y.y))))
  3. ==[ beta  ]==> (((a a) a)(a (a (^y.y))))
  4. ==[ alpha ]==> (((a a) a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  3244/73479. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(a a)))

     REDUCED to normal form.

  ------  3245/73506. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(b a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(b a))
  3. ==[ beta  ]==> ((a (a a))(b a))

     REDUCED to normal form.

  ------  3246/73524. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3247/73533. ------  

  1. ==[ start ]==> ((a (a (a a)))(a b))

     REDUCED to normal form.

  ------  3248/73542. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a) a))
  3. ==[ beta  ]==> ((^y.(y y))((a a) a))
  4. ==[ alpha ]==> ((^x.(x x))((a a) a))
  5. ==[ beta  ]==> (((a a) a)((a a) a))

     REDUCED to normal form.

  ------  3249/73569. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3250/73595. ------  

  1. ==[ start ]==> (^a.((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.((^y.x)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  3251/73596. ------  

  1. ==[ start ]==> (a ((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3252/73653. ------  

  1. ==[ start ]==> ((^a.b)(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(z z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3253/73923. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.a)))
  3. ==[ eta   ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3254/74193. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.(a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(a a)))
  3. ==[ beta  ]==> ((^y.(a a))((^y.(a a))(^y.(a a))))
  4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.(a a))))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3255/74265. ------  

  1. ==[ start ]==> ((^a.a)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3256/74292. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> (((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a)))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a)))
  5. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a)))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a)))
  7. ==[ beta  ]==> ((^y.(^z.z))(^x1.a))
  8. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3257/74319. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3258/74322. ------  

  1. ==[ start ]==> ((a b)(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3259/74331. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(y (y y))))
  3. ==[ beta  ]==> ((a a)(^y.(y (y y))))
  4. ==[ alpha ]==> ((a a)(^x.(x (x x))))

     REDUCED to normal form.

  ------  3260/74355. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(a a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3261/74400. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.a)))
  3. ==[ beta  ]==> ((b (^z.a))(^y.y))
  4. ==[ alpha ]==> ((b (^x.a))(^y.y))

     REDUCED to normal form.

  ------  3262/74589. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(^x1.a)))
  3. ==[ eta   ]==> ((^y.y)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3263/74592. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.(^b.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.a)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.a)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.a)))

     REDUCED to normal form.

  ------  3264/74601. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.x)(^y.a))(^x1.x1))
  4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3265/74664. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.c))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.c))
  3. ==[ beta  ]==> ((a a)(^y.c))
  4. ==[ alpha ]==> ((a a)(^x.c))

     REDUCED to normal form.

  ------  3266/74760. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(b (a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(b (a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3267/74781. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3268/74835. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3269/74859. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(a a)))
  3. ==[ beta  ]==> (((^y.y)(a a))(((^y.y)(a a))((^y.y)(a a))))
  4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))((^z.z)(a a))))
  5. ==[ beta  ]==> ((a a)(((^y.y)(a a))((^z.z)(a a))))
  6. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(a a))))
  7. ==[ beta  ]==> ((a a)((a a)((^y.y)(a a))))
  8. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a))))
  9. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  3270/74862. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.(a a)))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(a a)))

     REDUCED to normal form.

  ------  3271/74871. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.b))
  3. ==[ beta  ]==> ((^y.(y y))(^z.b))
  4. ==[ alpha ]==> ((^x.(x x))(^y.b))
  5. ==[ beta  ]==> ((^y.b)(^y.b))
  6. ==[ alpha ]==> ((^x.b)(^y.b))
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3272/74898. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3273/74937. ------  

  1. ==[ start ]==> ((a a)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3274/74964. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3275/74973. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(b ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(b ((^y.y) a)))
  5. ==[ beta  ]==> (b ((^y.y) a))
  6. ==[ alpha ]==> (b ((^x.x) a))
  7. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3276/74991. ------  

  1. ==[ start ]==> ((a b)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a b)((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> ((a b)(^y.(y y)))
  4. ==[ alpha ]==> ((a b)(^x.(x x)))

     REDUCED to normal form.

  ------  3277/75000. ------  

  1. ==[ start ]==> (((^a.a)(a a))(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(a (a (a a))))
  3. ==[ beta  ]==> ((a a)(a (a (a a))))

     REDUCED to normal form.

  ------  3278/75009. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(a a)) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y)) a))
  3. ==[ beta  ]==> (((a a)(^x.x))(a a))

     REDUCED to normal form.

  ------  3279/75027. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a (a a)))

     REDUCED to normal form.

  ------  3280/75036. ------  

  1. ==[ start ]==> (((^a.a) b)((^b.a) b))
  2. ==[ alpha ]==> (((^x.x) b)((^y.a) b))
  3. ==[ beta  ]==> (b ((^y.a) b))
  4. ==[ alpha ]==> (b ((^x.a) b))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3281/75072. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.a)))

     REDUCED to normal form.

  ------  3282/75081. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((a a)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3283/75117. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a (^z.z)))
  4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y)))

     REDUCED to normal form.

  ------  3284/75144. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3285/75162. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b c))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  3286/75171. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.a)))

     REDUCED to normal form.

  ------  3287/75207. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  3288/75225. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  3289/75234. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  3290/75261. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3291/75270. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(a ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.a)(a ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.a)(a ((^y.y) a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3292/75297. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^y1.y1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  3293/75306. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  3294/75360. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  3295/75378. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b b))
  3. ==[ beta  ]==> ((^y.y)(b b))
  4. ==[ alpha ]==> ((^x.x)(b b))
  5. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  3296/75387. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3297/75414. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z)) a))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z)) a))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) a))

     REDUCED to normal form.

  ------  3298/75432. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(b (a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(b (a a)))

     REDUCED to normal form.

  ------  3299/75450. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a) a)((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> (((a a) a)(^y.(^z.z)))
  6. ==[ alpha ]==> (((a a) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3300/75477. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.z)))

     REDUCED to normal form.

  ------  3301/75504. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a a))(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  3302/75522. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(^y.y)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.y)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  3303/75531. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a a)))
  3. ==[ beta  ]==> ((a (a (a a)))(a a))

     REDUCED to normal form.

  ------  3304/75540. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a b))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a b))
  3. ==[ beta  ]==> ((^y.(y y))(a b))
  4. ==[ alpha ]==> ((^x.(x x))(a b))
  5. ==[ beta  ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  3305/75567. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3306/75602. ------  

  1. ==[ start ]==> (^a.(((^a.a) a) b))
  2. ==[ alpha ]==> (^x.(((^y.y) x) b))
  3. ==[ beta  ]==> (^x.(x b))

     REDUCED to normal form.

  ------  3307/75603. ------  

  1. ==[ start ]==> (a (((^a.a) a) b))
  2. ==[ alpha ]==> (a (((^x.x) a) b))
  3. ==[ beta  ]==> (a (a b))

     REDUCED to normal form.

  ------  3308/75660. ------  

  1. ==[ start ]==> ((^a.b)(^c.d))
  2. ==[ alpha ]==> ((^x.b)(^y.d))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3309/75858. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> (^x.(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3310/76275. ------  

  1. ==[ start ]==> ((((^a.a) a) b) a)
  2. ==[ alpha ]==> ((((^x.x) a) b) a)
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  3311/76281. ------  

  1. ==[ start ]==> ((^a.a)(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.x)(((^y.y) a) b))
  3. ==[ beta  ]==> (((^y.y) a) b)
  4. ==[ alpha ]==> (((^x.x) a) b)
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  3312/76290. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3313/76338. ------  

  1. ==[ start ]==> ((a b)(^c.d))
  2. ==[ alpha ]==> ((a b)(^x.d))

     REDUCED to normal form.

  ------  3314/76347. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z z))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(z z))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3315/76356. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^a.(a (a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (y y))))

     REDUCED to normal form.

  ------  3316/76437. ------  

  1. ==[ start ]==> (((a a) b)(^c.((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)(^x.((^y.y) a)))
  3. ==[ beta  ]==> (((a a) b)(^x.a))

     REDUCED to normal form.

  ------  3317/76455. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  3318/76533. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> (^x.((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> (^x.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3319/76536. ------  

  1. ==[ start ]==> ((a (^b.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.a))(^y.a))

     REDUCED to normal form.

  ------  3320/76617. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3321/76698. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.z)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.z)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.y)))
  5. ==[ beta  ]==> (a (^y.(^z.y)))
  6. ==[ alpha ]==> (a (^x.(^y.x)))

     REDUCED to normal form.

  ------  3322/76776. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3323/76851. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.y))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3324/76875. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(^y.y)))
  3. ==[ beta  ]==> (((a a)(^y.y))(((a a)(^y.y))((a a)(^y.y))))
  4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((a a)(^z.z))))

     REDUCED to normal form.

  ------  3325/76887. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(a a)))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(a a)))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(a a)))
  5. ==[ beta  ]==> ((^y.(a a))(^y.(a a)))
  6. ==[ alpha ]==> ((^x.(a a))(^y.(a a)))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3326/76914. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3327/76950. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.a))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.y))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  3328/76962. ------  

  1. ==[ start ]==> ((a a)(((^a.a) a) b))
  2. ==[ alpha ]==> ((a a)(((^x.x) a) b))
  3. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  3329/76971. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  3330/76998. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.a))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3331/77007. ------  

  1. ==[ start ]==> (((a a) a)(b ((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)(b ((^x.x) a)))
  3. ==[ beta  ]==> (((a a) a)(b a))

     REDUCED to normal form.

  ------  3332/77025. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.(z z))))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.(y y))))
  5. ==[ beta  ]==> ((a a)(^y.(y y)))
  6. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  3333/77034. ------  

  1. ==[ start ]==> (((a a)(^a.a))(a (a (a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(a (a (a a))))

     REDUCED to normal form.

  ------  3334/77061. ------  

  1. ==[ start ]==> (((^a.a) b)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(a a)))
  3. ==[ beta  ]==> (b (((^y.y) a)(a a)))
  4. ==[ alpha ]==> (b (((^x.x) a)(a a)))
  5. ==[ beta  ]==> (b (a (a a)))

     REDUCED to normal form.

  ------  3335/77070. ------  

  1. ==[ start ]==> (((a a)(a a))((^b.a) b))
  2. ==[ alpha ]==> (((a a)(a a))((^x.a) b))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  3336/77088. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  3337/77106. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(b (^x1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3338/77115. ------  

  1. ==[ start ]==> (((a a) b)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)((a a)((^x.x) a)))
  3. ==[ beta  ]==> (((a a) b)((a a) a))

     REDUCED to normal form.

  ------  3339/77133. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  3340/77160. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.a)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a a)))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  3341/77187. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3342/77196. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b c))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b c))

     REDUCED to normal form.

  ------  3343/77214. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.a))((^z.z) a))
  4. ==[ alpha ]==> ((a (^x.a))((^y.y) a))
  5. ==[ beta  ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  3344/77232. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a) a))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(a a))

     REDUCED to normal form.

  ------  3345/77250. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(c (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(c (a a)))
  3. ==[ beta  ]==> ((^y.y)(c (a a)))
  4. ==[ alpha ]==> ((^x.x)(c (a a)))
  5. ==[ beta  ]==> (c (a a))

     REDUCED to normal form.

  ------  3346/77259. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y)) b))

     REDUCED to normal form.

  ------  3347/77295. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> ((^y.a)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> ((^x.a)((^y.y)(^z.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3348/77331. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  3349/77358. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(a (^y.y))))
  3. ==[ beta  ]==> ((a a)((a a)(a (^y.y))))
  4. ==[ alpha ]==> ((a a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  3350/77376. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (^z.a)))
  3. ==[ beta  ]==> (((^y.y) a)(a (^z.a)))
  4. ==[ alpha ]==> (((^x.x) a)(a (^y.a)))
  5. ==[ beta  ]==> (a (a (^y.a)))
  6. ==[ alpha ]==> (a (a (^x.a)))

     REDUCED to normal form.

  ------  3351/77385. ------  

  1. ==[ start ]==> (((a a)(^b.a))(c a))
  2. ==[ alpha ]==> (((a a)(^x.a))(c a))

     REDUCED to normal form.

  ------  3352/77403. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(a a))
  6. ==[ alpha ]==> ((^x.(^y.y))(a a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3353/77412. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b b))

     REDUCED to normal form.

  ------  3354/77457. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.z))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3355/77475. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a) b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a) b))
  3. ==[ beta  ]==> (((a a) a)((a a) b))

     REDUCED to normal form.

  ------  3356/77502. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3357/77529. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a) b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y) b))
  3. ==[ beta  ]==> ((a (a a))((^y.y) b))
  4. ==[ alpha ]==> ((a (a a))((^x.x) b))
  5. ==[ beta  ]==> ((a (a a)) b)

     REDUCED to normal form.

  ------  3358/77547. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(b a))
  2. ==[ alpha ]==> (((^x.(x x)) a)(b a))
  3. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  3359/77556. ------  

  1. ==[ start ]==> ((a (a (a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))((a a)(^x.x)))

     REDUCED to normal form.

  ------  3360/77565. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(a a)))
  3. ==[ beta  ]==> ((^y.(y y))((^z.z)(a a)))
  4. ==[ alpha ]==> ((^x.(x x))((^y.y)(a a)))
  5. ==[ beta  ]==> (((^y.y)(a a))((^y.y)(a a)))
  6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a)))
  7. ==[ beta  ]==> ((a a)((^y.y)(a a)))
  8. ==[ alpha ]==> ((a a)((^x.x)(a a)))
  9. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3361/77592. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3362/77628. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(a a))
  2. ==[ alpha ]==> ((((^x.x) a) b)(a a))
  3. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  3363/77892. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.a)))
  3. ==[ beta  ]==> (^y.(^z.(^x1.a)))
  4. ==[ alpha ]==> (^x.(^y.(^z.a)))

     REDUCED to normal form.

  ------  3364/78309. ------  

  1. ==[ start ]==> ((((^a.a) a) b) b)
  2. ==[ alpha ]==> ((((^x.x) a) b) b)
  3. ==[ beta  ]==> ((a b) b)

     REDUCED to normal form.

  ------  3365/78333. ------  

  1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) b))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3366/78378. ------  

  1. ==[ start ]==> ((^a.b)(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)(b ((^y.y) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3367/78399. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3368/78414. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1)) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3369/78459. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((a (^z.z))(a (^x1.x1)))(^y.y))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3370/78507. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3371/78576. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)(^z.a)))
  3. ==[ beta  ]==> (^y.((a a)(^z.a)))
  4. ==[ alpha ]==> (^x.((a a)(^y.a)))

     REDUCED to normal form.

  ------  3372/78579. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.a)))

     REDUCED to normal form.

  ------  3373/78648. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b (a (^z.z))))
  3. ==[ eta   ]==> ((^y.y)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  3374/78660. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z))
  3. ==[ beta  ]==> ((^y.a)(^z.z))
  4. ==[ alpha ]==> ((^x.a)(^y.y))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3375/78741. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.c))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.c))
  3. ==[ beta  ]==> (((^y.y) a)(^z.c))
  4. ==[ alpha ]==> (((^x.x) a)(^y.c))
  5. ==[ beta  ]==> (a (^y.c))
  6. ==[ alpha ]==> (a (^x.c))

     REDUCED to normal form.

  ------  3376/78750. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.y)))

     REDUCED to normal form.

  ------  3377/78804. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  3378/78819. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.z)) a))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3379/78867. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (^x1.x1))))

     REDUCED to normal form.

  ------  3380/78912. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3381/78918. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(b a))
  2. ==[ alpha ]==> ((^x.(x (x x)))(b a))
  3. ==[ beta  ]==> ((b a)((b a)(b a)))

     REDUCED to normal form.

  ------  3382/78957. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.a))
  3. ==[ beta  ]==> ((^y.y)(^x1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3383/78993. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a b)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3384/79023. ------  

  1. ==[ start ]==> ((a (^a.a))(((^a.a) a) b))
  2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a) b))
  3. ==[ beta  ]==> ((a (^x.x))(a b))

     REDUCED to normal form.

  ------  3385/79032. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a ((^y.a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z))))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3386/79059. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3387/79068. ------  

  1. ==[ start ]==> ((a b)(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a b)(b ((^x.x) a)))
  3. ==[ beta  ]==> ((a b)(b a))

     REDUCED to normal form.

  ------  3388/79086. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.(z z)))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y)))

     REDUCED to normal form.

  ------  3389/79104. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z)) a))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  3390/79122. ------  

  1. ==[ start ]==> (((a a)(a a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(a a)))
  3. ==[ beta  ]==> (((a a)(a a))(a (a a)))

     REDUCED to normal form.

  ------  3391/79149. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  3392/79167. ------  

  1. ==[ start ]==> (((a a) b)(b (^b.a)))
  2. ==[ alpha ]==> (((a a) b)(b (^x.a)))

     REDUCED to normal form.

  ------  3393/79194. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(y y))))

     REDUCED to normal form.

  ------  3394/79212. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  3395/79221. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  3396/79239. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3397/79248. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z))

     REDUCED to normal form.

  ------  3398/79266. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))((a a)(^y.a)))

     REDUCED to normal form.

  ------  3399/79302. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3400/79338. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b (a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(b (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(b (a (^x.x))))

     REDUCED to normal form.

  ------  3401/79347. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a) c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a) c))
  3. ==[ beta  ]==> ((^y.a)((a a) c))
  4. ==[ alpha ]==> ((^x.a)((a a) c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3402/79374. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a) a))
  3. ==[ beta  ]==> ((^y.y)((^y1.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3403/79383. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(c (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.y)))

     REDUCED to normal form.

  ------  3404/79410. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(b (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  3405/79437. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(a (^y.a)))

     REDUCED to normal form.

  ------  3406/79455. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3407/79464. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  3408/79491. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))((^z.z)(a (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z))))
  5. ==[ beta  ]==> ((a (^x.x))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  3409/79509. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y)) a))

     REDUCED to normal form.

  ------  3410/79527. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(b (a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(b (a a)))
  3. ==[ beta  ]==> (((a a) a)(b (a a)))

     REDUCED to normal form.

  ------  3411/79554. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a (^z.z))))

     REDUCED to normal form.

  ------  3412/79581. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(a a)))
  3. ==[ beta  ]==> ((a (a a))((a a)(a a)))

     REDUCED to normal form.

  ------  3413/79599. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  3414/79608. ------  

  1. ==[ start ]==> ((a (a (a a)))(b a))

     REDUCED to normal form.

  ------  3415/79617. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(^z.z)))
  3. ==[ beta  ]==> ((^y.(y y))((a a)(^z.z)))
  4. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y)))
  5. ==[ beta  ]==> (((a a)(^y.y))((a a)(^y.y)))
  6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y)))

     REDUCED to normal form.

  ------  3416/79644. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3417/79680. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(a (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(a (^y.y)))
  3. ==[ beta  ]==> ((a b)(a (^y.y)))
  4. ==[ alpha ]==> ((a b)(a (^x.x)))

     REDUCED to normal form.

  ------  3418/79697. ------  

  1. ==[ start ]==> (^a.((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (^x.((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> (^x.((^z.z)(^z.z)))
  4. ==[ alpha ]==> (^x.((^y.y)(^z.z)))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3419/79698. ------  

  1. ==[ start ]==> (a ((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (a ((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> (a ((^y.y)(^y.y)))
  4. ==[ alpha ]==> (a ((^x.x)(^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3420/79791. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 (x1 x1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3421/80295. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.(^z2.z2)))))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3422/80370. ------  

  1. ==[ start ]==> ((((^a.a) a) b) c)
  2. ==[ alpha ]==> ((((^x.x) a) b) c)
  3. ==[ beta  ]==> ((a b) c)

     REDUCED to normal form.

  ------  3423/80388. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a)) a)
  2. ==[ alpha ]==> (((^x.(x x))(^y.y)) a)
  3. ==[ beta  ]==> (((^y.y)(^y.y)) a)
  4. ==[ alpha ]==> (((^x.x)(^y.y)) a)
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3424/80394. ------  

  1. ==[ start ]==> ((^a.a)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> ((^y.(y y))(^z.z))
  4. ==[ alpha ]==> ((^x.(x x))(^y.y))
  5. ==[ beta  ]==> ((^y.y)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3425/80421. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.a)(^z.(^x1.x1)))((^y.a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1))))
  5. ==[ beta  ]==> (a ((^x1.a)(^y1.(^z1.z1))))
  6. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z))))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3426/80448. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3427/80484. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a (a a))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3428/80487. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (z z))))

     REDUCED to normal form.

  ------  3429/80646. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b c))
  2. ==[ alpha ]==> ((^x.(^y.x))(b c))
  3. ==[ beta  ]==> (^y.(b c))
  4. ==[ alpha ]==> (^x.(b c))

     REDUCED to normal form.

  ------  3430/80667. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^y.a))

     REDUCED to normal form.

  ------  3431/80718. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3432/80757. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1) y1)))
  3. ==[ eta   ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^z1.z1))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1))
  5. ==[ beta  ]==> ((^y.y)(^y1.y1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3433/80820. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.c))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.c))

     REDUCED to normal form.

  ------  3434/80937. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3435/80982. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.b))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.y))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3436/80988. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))((a (^y.(^z.z)))(a (^y.(^z.z)))))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1)))))

     REDUCED to normal form.

  ------  3437/80991. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3438/81027. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.b))
  3. ==[ beta  ]==> ((^y.y)(^x1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  3439/81063. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^b.a))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.a))
  3. ==[ beta  ]==> ((a b)(^y.a))
  4. ==[ alpha ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  3440/81081. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.z))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.z))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3441/81093. ------  

  1. ==[ start ]==> ((a a)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((a a)((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^y.y)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3442/81111. ------  

  1. ==[ start ]==> (((^a.a) a)(((^a.a) a) b))
  2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a) b))
  3. ==[ beta  ]==> (a (((^y.y) a) b))
  4. ==[ alpha ]==> (a (((^x.x) a) b))
  5. ==[ beta  ]==> (a (a b))

     REDUCED to normal form.

  ------  3443/81120. ------  

  1. ==[ start ]==> ((a (a a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  3444/81147. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  3445/81156. ------  

  1. ==[ start ]==> (((^a.a)(a a))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))(b ((^y.y) a)))
  3. ==[ beta  ]==> ((a a)(b ((^y.y) a)))
  4. ==[ alpha ]==> ((a a)(b ((^x.x) a)))
  5. ==[ beta  ]==> ((a a)(b a))

     REDUCED to normal form.

  ------  3446/81183. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (a a))))

     REDUCED to normal form.

  ------  3447/81192. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(y y)) a))
  3. ==[ beta  ]==> (b ((^y.(y y)) a))
  4. ==[ alpha ]==> (b ((^x.(x x)) a))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  3448/81219. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a) b))
  3. ==[ beta  ]==> ((^y.y)((^z.a) b))
  4. ==[ alpha ]==> ((^x.x)((^y.a) b))
  5. ==[ beta  ]==> ((^y.a) b)
  6. ==[ alpha ]==> ((^x.a) b)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3449/81237. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3450/81246. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a)) c))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) c))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  3451/81264. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)((a a)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3452/81300. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a (^x1.x1)))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  3453/81327. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3454/81345. ------  

  1. ==[ start ]==> ((a (^b.a))(b c))
  2. ==[ alpha ]==> ((a (^x.a))(b c))

     REDUCED to normal form.

  ------  3455/81363. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))((^z.z) a))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) a))
  5. ==[ beta  ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  3456/81381. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3457/81390. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  3458/81417. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3459/81426. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b (a (^z.z))))
  3. ==[ beta  ]==> ((^y.a)(b (a (^z.z))))
  4. ==[ alpha ]==> ((^x.a)(b (a (^y.y))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3460/81453. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a ((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3461/81462. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^b.a) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a) a))
  3. ==[ beta  ]==> (((a (^x.x)) b) a)

     REDUCED to normal form.

  ------  3462/81489. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) b))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) b))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3463/81507. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(a (^z.z))))
  3. ==[ beta  ]==> (((^y.y) a)((a a)(a (^z.z))))
  4. ==[ alpha ]==> (((^x.x) a)((a a)(a (^y.y))))
  5. ==[ beta  ]==> (a ((a a)(a (^y.y))))
  6. ==[ alpha ]==> (a ((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  3464/81516. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a) c))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y) c))
  3. ==[ beta  ]==> (((a a)(^x.a)) c)

     REDUCED to normal form.

  ------  3465/81543. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.y1)))

     REDUCED to normal form.

  ------  3466/81570. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  3467/81606. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((a a) a)((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3468/81633. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  3469/81660. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(b (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(b (^y.y)))
  3. ==[ beta  ]==> ((a (a a))(b (^y.y)))
  4. ==[ alpha ]==> ((a (a a))(b (^x.x)))

     REDUCED to normal form.

  ------  3470/81678. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a) b))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y) b))
  3. ==[ beta  ]==> ((a a)((^y.y) b))
  4. ==[ alpha ]==> ((a a)((^x.x) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  3471/81687. ------  

  1. ==[ start ]==> ((a (a (a a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  3472/81696. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(b a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b a))
  3. ==[ beta  ]==> ((^y.(y y))(b a))
  4. ==[ alpha ]==> ((^x.(x x))(b a))
  5. ==[ beta  ]==> ((b a)(b a))

     REDUCED to normal form.

  ------  3473/81723. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  3474/81759. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((^a.a) a))
  2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y) a))
  3. ==[ beta  ]==> ((a b)((^y.y) a))
  4. ==[ alpha ]==> ((a b)((^x.x) a))
  5. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  3475/81777. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(a a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a a))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(a a))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(a a))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3476/81785. ------  

  1. ==[ start ]==> (^a.((a (a a)) a))
  2. ==[ alpha ]==> (^x.((x (x x)) x))

     REDUCED to normal form.

  ------  3477/81786. ------  

  1. ==[ start ]==> (a ((a (a a)) a))

     REDUCED to normal form.

  ------  3478/81879. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3479/82284. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3480/82383. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.b))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.y))
  3. ==[ beta  ]==> ((^y.y)((^y.y)(^y.y)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3481/82476. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a)) b)
  2. ==[ alpha ]==> (((^x.(x x))(^y.y)) b)
  3. ==[ beta  ]==> (((^y.y)(^y.y)) b)
  4. ==[ alpha ]==> (((^x.x)(^y.y)) b)
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3482/82485. ------  

  1. ==[ start ]==> (((a (a a)) a) a)

     REDUCED to normal form.

  ------  3483/82491. ------  

  1. ==[ start ]==> ((^a.a)((a (a a)) a))
  2. ==[ alpha ]==> ((^x.x)((a (a a)) a))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  3484/82500. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3485/82518. ------  

  1. ==[ start ]==> ((^a.(a a))(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a) b))
  3. ==[ beta  ]==> ((((^y.y) a) b)(((^y.y) a) b))
  4. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) a) b))
  5. ==[ beta  ]==> ((a b)(((^y.y) a) b))
  6. ==[ alpha ]==> ((a b)(((^x.x) a) b))
  7. ==[ beta  ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  3486/82545. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a)) c))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y)) c))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3487/82581. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3488/82584. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1))))

     REDUCED to normal form.

  ------  3489/82593. ------  

  1. ==[ start ]==> (((^a.a) b)(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(y (y y))))
  3. ==[ beta  ]==> (b (^y.(y (y y))))
  4. ==[ alpha ]==> (b (^x.(x (x x))))

     REDUCED to normal form.

  ------  3490/82626. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a) b))
  3. ==[ beta  ]==> (((^z.a) b)(^y.y))
  4. ==[ alpha ]==> (((^x.a) b)(^y.y))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3491/82692. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3492/82743. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> (^x.((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3493/82815. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z)) b))
  3. ==[ eta   ]==> ((^y.y)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  3494/82854. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.a)))
  3. ==[ beta  ]==> ((^y.y)(^y1.(^z1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3495/82863. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  3496/82917. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  3497/82935. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.y)))
  5. ==[ beta  ]==> (^y.(^z.y))
  6. ==[ alpha ]==> (^x.(^y.x))

     REDUCED to normal form.

  ------  3498/82986. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3499/82989. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(a (^z.z))))

     REDUCED to normal form.

  ------  3500/83085. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a) b))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y) b))
  3. ==[ beta  ]==> (((^y.y) b)(((^y.y) b)((^y.y) b)))
  4. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)((^z.z) b)))
  5. ==[ beta  ]==> (b (((^y.y) b)((^z.z) b)))
  6. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b)))
  7. ==[ beta  ]==> (b (b ((^y.y) b)))
  8. ==[ alpha ]==> (b (b ((^x.x) b)))
  9. ==[ beta  ]==> (b (b b))

     REDUCED to normal form.

  ------  3501/83088. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.b))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  3502/83097. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))
  6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3503/83124. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  3504/83160. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(y y)))
  3. ==[ beta  ]==> ((a b)(^y.(y y)))
  4. ==[ alpha ]==> ((a b)(^x.(x x)))

     REDUCED to normal form.

  ------  3505/83178. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3506/83187. ------  

  1. ==[ start ]==> (((a (a a)) a)(^a.a))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.x))

     REDUCED to normal form.

  ------  3507/83199. ------  

  1. ==[ start ]==> ((a a)((a (a a)) a))

     REDUCED to normal form.

  ------  3508/83208. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> ((a (^x.x))((^z.z)(^z.z)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3509/83226. ------  

  1. ==[ start ]==> ((a (a a))(((^a.a) a) b))
  2. ==[ alpha ]==> ((a (a a))(((^x.x) a) b))
  3. ==[ beta  ]==> ((a (a a))(a b))

     REDUCED to normal form.

  ------  3510/83235. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3511/83253. ------  

  1. ==[ start ]==> ((a b)((a (^a.a)) c))
  2. ==[ alpha ]==> ((a b)((a (^x.x)) c))

     REDUCED to normal form.

  ------  3512/83262. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.a)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.a)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3513/83271. ------  

  1. ==[ start ]==> (((a a)(^a.a))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(b a))

     REDUCED to normal form.

  ------  3514/83289. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z)))

     REDUCED to normal form.

  ------  3515/83298. ------  

  1. ==[ start ]==> (((^a.a) b)(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x) b)(a (a (a a))))
  3. ==[ beta  ]==> (b (a (a (a a))))

     REDUCED to normal form.

  ------  3516/83307. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(a a)) a))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(x x)) a))
  3. ==[ beta  ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  3517/83325. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(a a)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a)))
  5. ==[ beta  ]==> (((^y.y) a)(a a))
  6. ==[ alpha ]==> (((^x.x) a)(a a))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3518/83334. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^b.a) b))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a) b))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  3519/83352. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x))(a (^y.y))))

     REDUCED to normal form.

  ------  3520/83370. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.a)))
  5. ==[ beta  ]==> (b (^y.a))
  6. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  3521/83379. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a a)((^y.y) a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)((a a) a))

     REDUCED to normal form.

  ------  3522/83397. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(z z))))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.(z z))))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y))))

     REDUCED to normal form.

  ------  3523/83424. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3524/83451. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  3525/83469. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.a)))

     REDUCED to normal form.

  ------  3526/83496. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a) a))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(a a))

     REDUCED to normal form.

  ------  3527/83523. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a)) b))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y)) b))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) b))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) b))

     REDUCED to normal form.

  ------  3528/83532. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3529/83559. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.a)))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)(^z1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3530/83568. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(a a))

     REDUCED to normal form.

  ------  3531/83595. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.y))(a a)))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(a a)))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  3532/83613. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.x) a)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (a (b (^y.(^z.z))))
  6. ==[ alpha ]==> (a (b (^x.(^y.y))))

     REDUCED to normal form.

  ------  3533/83622. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  3534/83640. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.a)))
  5. ==[ beta  ]==> (a (^y.a))
  6. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  3535/83676. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(b b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b b))
  3. ==[ beta  ]==> ((a (^y.y))(b b))
  4. ==[ alpha ]==> ((a (^x.x))(b b))

     REDUCED to normal form.

  ------  3536/83694. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^x.(x x)))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y)))

     REDUCED to normal form.

  ------  3537/83712. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y)) a))
  3. ==[ beta  ]==> (((a a) a)((a (^y.y)) a))
  4. ==[ alpha ]==> (((a a) a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  3538/83739. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a) b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a) b))

     REDUCED to normal form.

  ------  3539/83766. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a (a a))((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a (a a))((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3540/83784. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(a a)))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  3541/83793. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a) b))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x) b))
  3. ==[ beta  ]==> ((a (a (a a))) b)

     REDUCED to normal form.

  ------  3542/83802. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.(y y))(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z))))
  5. ==[ beta  ]==> ((a (^y.(^z.z)))(a (^y.(^z.z))))
  6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3543/83829. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  5. ==[ beta  ]==> ((^y.y)(a a))
  6. ==[ alpha ]==> ((^x.x)(a a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3544/83865. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(a (a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(a (a a)))
  3. ==[ beta  ]==> ((a b)(a (a a)))

     REDUCED to normal form.

  ------  3545/83883. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.z)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(a (^z.z)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z)))
  5. ==[ beta  ]==> ((^y.y)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3546/83892. ------  

  1. ==[ start ]==> (((a (a a)) a)(a a))

     REDUCED to normal form.

  ------  3547/84600. ------  

  1. ==[ start ]==> (((a (a a)) a) b)

     REDUCED to normal form.

  ------  3548/84624. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (a a)) a))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (a a)) a))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3549/84669. ------  

  1. ==[ start ]==> ((^a.b)(c (a (^a.a))))
  2. ==[ alpha ]==> ((^x.b)(c (a (^y.y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3550/84717. ------  

  1. ==[ start ]==> (((^a.a) b)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z))))
  3. ==[ beta  ]==> (b (^y.(^z.(z z))))
  4. ==[ alpha ]==> (b (^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3551/84726. ------  

  1. ==[ start ]==> (((a a)(a a))(^a.(a (a a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(x (x x))))

     REDUCED to normal form.

  ------  3552/84750. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((((^z.z) a)(a a))(^y.y))
  4. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.y))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3553/84825. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 x1))))

     REDUCED to normal form.

  ------  3554/84867. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (^x.((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3555/84906. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3556/84987. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.a)))

     REDUCED to normal form.

  ------  3557/85059. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.c))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.c))
  3. ==[ beta  ]==> ((^y.y)(^x1.c))
  4. ==[ alpha ]==> ((^x.x)(^y.c))
  5. ==[ beta  ]==> (^y.c)
  6. ==[ alpha ]==> (^x.c)

     REDUCED to normal form.

  ------  3558/85068. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.x1)))

     REDUCED to normal form.

  ------  3559/85110. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3560/85185. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a (a a))(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a (a a))(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  3561/85209. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a a)(a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(a a)))
  3. ==[ beta  ]==> (((a a)(a a))(((a a)(a a))((a a)(a a))))

     REDUCED to normal form.

  ------  3562/85221. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.b))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z))
  3. ==[ beta  ]==> ((^y.(y y))(^z.z))
  4. ==[ alpha ]==> ((^x.(x x))(^y.y))
  5. ==[ beta  ]==> ((^y.y)(^y.y))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3563/85248. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3564/85284. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^b.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a b)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3565/85302. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.a))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.a))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3566/85311. ------  

  1. ==[ start ]==> (((a (a a)) a)(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3567/85325. ------  

  1. ==[ start ]==> (^a.(^b.(a (a a))))
  2. ==[ alpha ]==> (^x.(^y.(x (x x))))

     REDUCED to normal form.

  ------  3568/85326. ------  

  1. ==[ start ]==> (a (^b.(a (a a))))
  2. ==[ alpha ]==> (a (^x.(a (a a))))

     REDUCED to normal form.

  ------  3569/85341. ------  

  1. ==[ start ]==> ((a (^a.a))((a (a a)) a))
  2. ==[ alpha ]==> ((a (^x.x))((a (a a)) a))

     REDUCED to normal form.

  ------  3570/85350. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> (a ((^y.(y y))(^z.z)))
  4. ==[ alpha ]==> (a ((^x.(x x))(^y.y)))
  5. ==[ beta  ]==> (a ((^y.y)(^y.y)))
  6. ==[ alpha ]==> (a ((^x.x)(^y.y)))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3571/85368. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) b))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) b))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) b))
  5. ==[ beta  ]==> (((^y.y) a) b)
  6. ==[ alpha ]==> (((^x.x) a) b)
  7. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  3572/85377. ------  

  1. ==[ start ]==> (((a a) a)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) a) a)

     REDUCED to normal form.

  ------  3573/85386. ------  

  1. ==[ start ]==> ((a b)(c (a (^a.a))))
  2. ==[ alpha ]==> ((a b)(c (a (^x.x))))

     REDUCED to normal form.

  ------  3574/85404. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  3575/85431. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (b ((^y.y)(^z.(z z))))
  4. ==[ alpha ]==> (b ((^x.x)(^y.(y y))))
  5. ==[ beta  ]==> (b (^y.(y y)))
  6. ==[ alpha ]==> (b (^x.(x x)))

     REDUCED to normal form.

  ------  3576/85440. ------  

  1. ==[ start ]==> (((a a)(a a))(a (a (a a))))

     REDUCED to normal form.

  ------  3577/85467. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(a a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a (a a)))

     REDUCED to normal form.

  ------  3578/85476. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a) b))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.a) b))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3579/85485. ------  

  1. ==[ start ]==> (((a a) b)(c (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a) b)(c (^x.(^y.y))))

     REDUCED to normal form.

  ------  3580/85512. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(b (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.a)))

     REDUCED to normal form.

  ------  3581/85539. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(z z))))

     REDUCED to normal form.

  ------  3582/85557. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3583/85566. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  3584/85584. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3585/85602. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b c))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b c))

     REDUCED to normal form.

  ------  3586/85620. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3587/85665. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z)) b))
  3. ==[ beta  ]==> ((^y.a)((a (^z.z)) b))
  4. ==[ alpha ]==> ((^x.a)((a (^y.y)) b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3588/85701. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.a))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.a))

     REDUCED to normal form.

  ------  3589/85746. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (((^y.y) a)((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) b))
  5. ==[ beta  ]==> (a ((^y.(^z.z)) b))
  6. ==[ alpha ]==> (a ((^x.(^y.y)) b))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3590/85755. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  3591/85782. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.a)))

     REDUCED to normal form.

  ------  3592/85809. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1))(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a)))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3593/85827. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.(^z.z))))

     REDUCED to normal form.

  ------  3594/85872. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (a a)))

     REDUCED to normal form.

  ------  3595/85899. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(a (a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(a (a (^y.y))))
  3. ==[ beta  ]==> ((a (a a))(a (a (^y.y))))
  4. ==[ alpha ]==> ((a (a a))(a (a (^x.x))))

     REDUCED to normal form.

  ------  3596/85917. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(b (^y.y)))
  3. ==[ beta  ]==> ((a a)(b (^y.y)))
  4. ==[ alpha ]==> ((a a)(b (^x.x)))

     REDUCED to normal form.

  ------  3597/85926. ------  

  1. ==[ start ]==> ((a (a (a a)))((a a)(a a)))

     REDUCED to normal form.

  ------  3598/85935. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z) b))
  3. ==[ beta  ]==> ((^y.(y y))((^z.z) b))
  4. ==[ alpha ]==> ((^x.(x x))((^y.y) b))
  5. ==[ beta  ]==> (((^y.y) b)((^y.y) b))
  6. ==[ alpha ]==> (((^x.x) b)((^y.y) b))
  7. ==[ beta  ]==> (b ((^y.y) b))
  8. ==[ alpha ]==> (b ((^x.x) b))
  9. ==[ beta  ]==> (b b)

     REDUCED to normal form.

  ------  3599/85962. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3600/85998. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((^a.a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a b)((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a b)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a b)(^y.y))
  6. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  3601/86016. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z) a))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((^z.z) a))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3602/86025. ------  

  1. ==[ start ]==> (((a (a a)) a)(a (^a.a)))
  2. ==[ alpha ]==> (((a (a a)) a)(a (^x.x)))

     REDUCED to normal form.

  ------  3603/86042. ------  

  1. ==[ start ]==> (^a.((^a.a)(a (a a))))
  2. ==[ alpha ]==> (^x.((^y.y)(x (x x))))
  3. ==[ beta  ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  3604/86043. ------  

  1. ==[ start ]==> (a ((^a.a)(a (a a))))
  2. ==[ alpha ]==> (a ((^x.x)(a (a a))))
  3. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  3605/86046. ------  

  1. ==[ start ]==> ((^a.a)(^b.(a (a a))))
  2. ==[ alpha ]==> ((^x.x)(^y.(a (a a))))
  3. ==[ beta  ]==> (^y.(a (a a)))
  4. ==[ alpha ]==> (^x.(a (a a)))

     REDUCED to normal form.

  ------  3606/86760. ------  

  1. ==[ start ]==> (((^a.a)(a (a a))) a)
  2. ==[ alpha ]==> (((^x.x)(a (a a))) a)
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  3607/86766. ------  

  1. ==[ start ]==> ((^a.a)((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a))))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3608/86769. ------  

  1. ==[ start ]==> ((a a)(^b.(a (a a))))
  2. ==[ alpha ]==> ((a a)(^x.(a (a a))))

     REDUCED to normal form.

  ------  3609/86793. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> (((^y.(y y))(^z.z))((^y.(y y))(^z.z)))
  4. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.x1)))
  5. ==[ beta  ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.x1)))
  6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1)))
  7. ==[ beta  ]==> ((^y.y)((^z.(z z))(^x1.x1)))
  8. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z)))
  9. ==[ beta  ]==> ((^y.(y y))(^z.z))
 10. ==[ alpha ]==> ((^x.(x x))(^y.y))
 11. ==[ beta  ]==> ((^y.y)(^y.y))
 12. ==[ alpha ]==> ((^x.x)(^y.y))
 13. ==[ beta  ]==> (^y.y)
 14. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3610/86820. ------  

  1. ==[ start ]==> ((^a.b)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3611/86856. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3612/86868. ------  

  1. ==[ start ]==> (((^a.a) b)(^c.d))
  2. ==[ alpha ]==> (((^x.x) b)(^y.d))
  3. ==[ beta  ]==> (b (^y.d))
  4. ==[ alpha ]==> (b (^x.d))

     REDUCED to normal form.

  ------  3613/86877. ------  

  1. ==[ start ]==> (((a a)(a a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3614/87018. ------  

  1. ==[ start ]==> ((^a.(^b.a))(c b))
  2. ==[ alpha ]==> ((^x.(^y.x))(c b))
  3. ==[ beta  ]==> (^y.(c b))
  4. ==[ alpha ]==> (^x.(c b))

     REDUCED to normal form.

  ------  3615/87057. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3616/87066. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^y.a))

     REDUCED to normal form.

  ------  3617/87090. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3618/87138. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.c))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  3619/87219. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.c))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.c))

     REDUCED to normal form.

  ------  3620/87261. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(b b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(b b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3621/87282. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(a (^z.z))))
  3. ==[ beta  ]==> (((a a) a)(^y.(a (^z.z))))
  4. ==[ alpha ]==> (((a a) a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  3622/87336. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3623/87360. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(b (^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(b (^y.y)))
  3. ==[ beta  ]==> ((b (^y.y))((b (^y.y))(b (^y.y))))
  4. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(b (^z.z))))

     REDUCED to normal form.

  ------  3624/87435. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^c.a))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.a))
  3. ==[ beta  ]==> ((a b)(^y.a))
  4. ==[ alpha ]==> ((a b)(^x.a))

     REDUCED to normal form.

  ------  3625/87453. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(z z)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.(z z)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z z)))
  5. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  6. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  7. ==[ beta  ]==> (^y.(y y))
  8. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3626/87462. ------  

  1. ==[ start ]==> (((a (a a)) a)(^b.a))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.a))

     REDUCED to normal form.

  ------  3627/87480. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^a.a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.y))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3628/87492. ------  

  1. ==[ start ]==> ((a a)((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((a a)((^x.x)(a (a a))))
  3. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  3629/87510. ------  

  1. ==[ start ]==> (((^a.a) a)((a (a a)) a))
  2. ==[ alpha ]==> (((^x.x) a)((a (a a)) a))
  3. ==[ beta  ]==> (a ((a (a a)) a))

     REDUCED to normal form.

  ------  3630/87519. ------  

  1. ==[ start ]==> ((a (a a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((a (a a))((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(^y.y)))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3631/87537. ------  

  1. ==[ start ]==> (((a a) a)(((^a.a) a) b))
  2. ==[ alpha ]==> (((a a) a)(((^x.x) a) b))
  3. ==[ beta  ]==> (((a a) a)(a b))

     REDUCED to normal form.

  ------  3632/87546. ------  

  1. ==[ start ]==> ((a b)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a b) a)

     REDUCED to normal form.

  ------  3633/87582. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(b a))

     REDUCED to normal form.

  ------  3634/87600. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> (((a a)(a a))(^y.(y y)))
  4. ==[ alpha ]==> (((a a)(a a))(^x.(x x)))

     REDUCED to normal form.

  ------  3635/87618. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z)) a))
  3. ==[ beta  ]==> ((^y.y)((^z.(z z)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(y y)) a))
  5. ==[ beta  ]==> ((^y.(y y)) a)
  6. ==[ alpha ]==> ((^x.(x x)) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3636/87636. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(((^x1.x1) a)(a a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3637/87645. ------  

  1. ==[ start ]==> (((a a) b)((^b.a) b))
  2. ==[ alpha ]==> (((a a) b)((^x.a) b))
  3. ==[ beta  ]==> (((a a) b) a)

     REDUCED to normal form.

  ------  3638/87663. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  3639/87690. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)((^z.z) a)))
  3. ==[ beta  ]==> ((a (^y.y))((a a)((^z.z) a)))
  4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a)))
  5. ==[ beta  ]==> ((a (^x.x))((a a) a))

     REDUCED to normal form.

  ------  3640/87726. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))(a (^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z)))

     REDUCED to normal form.

  ------  3641/87744. ------  

  1. ==[ start ]==> ((a (^b.a))(c b))
  2. ==[ alpha ]==> ((a (^x.a))(c b))

     REDUCED to normal form.

  ------  3642/87762. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  3643/87780. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(^z.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3644/87789. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))((^z.z) a))
  4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) a))
  5. ==[ beta  ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  3645/87816. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.a)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.a)(^y.y)))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3646/87825. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(c (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(c (a a)))
  3. ==[ beta  ]==> ((^y.a)(c (a a)))
  4. ==[ alpha ]==> ((^x.a)(c (a a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3647/87852. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  3648/87861. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a) c))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a) c))

     REDUCED to normal form.

  ------  3649/87888. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^b.a) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.a) a))
  3. ==[ beta  ]==> ((a a)((^y.a) a))
  4. ==[ alpha ]==> ((a a)((^x.a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3650/87906. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))(a a)))
  3. ==[ beta  ]==> (((^y.y) a)((a (^z.z))(a a)))
  4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a a)))
  5. ==[ beta  ]==> (a ((a (^y.y))(a a)))
  6. ==[ alpha ]==> (a ((a (^x.x))(a a)))

     REDUCED to normal form.

  ------  3651/87915. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z)) b))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  3652/87933. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a a)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  3653/87969. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  3654/87987. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(b b))
  2. ==[ alpha ]==> ((a (^x.(x x)))(b b))

     REDUCED to normal form.

  ------  3655/88005. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((a a) a)((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> (((a a) a)(a (^y.y)))
  6. ==[ alpha ]==> (((a a) a)(a (^x.x)))

     REDUCED to normal form.

  ------  3656/88032. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3657/88059. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  6. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  3658/88077. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3659/88086. ------  

  1. ==[ start ]==> ((a (a (a a)))(b (^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))(b (^x.x)))

     REDUCED to normal form.

  ------  3660/88095. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.(y y))((a a)(a a)))
  4. ==[ alpha ]==> ((^x.(x x))((a a)(a a)))
  5. ==[ beta  ]==> (((a a)(a a))((a a)(a a)))

     REDUCED to normal form.

  ------  3661/88122. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(b a))
  3. ==[ beta  ]==> ((^y.y)(b a))
  4. ==[ alpha ]==> ((^x.x)(b a))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3662/88158. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((a a) a))
  2. ==[ alpha ]==> ((((^x.x) a) b)((a a) a))
  3. ==[ beta  ]==> ((a b)((a a) a))

     REDUCED to normal form.

  ------  3663/88176. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(a (a a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (a a)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(a (a a)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a a)))
  5. ==[ beta  ]==> ((^y.y)(a (a a)))
  6. ==[ alpha ]==> ((^x.x)(a (a a)))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3664/88185. ------  

  1. ==[ start ]==> (((a (a a)) a)((^a.a) a))
  2. ==[ alpha ]==> (((a (a a)) a)((^x.x) a))
  3. ==[ beta  ]==> (((a (a a)) a) a)

     REDUCED to normal form.

  ------  3665/88203. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(a a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(a a))
  3. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  3666/88211. ------  

  1. ==[ start ]==> (^a.((a a)(^a.(a a))))
  2. ==[ alpha ]==> (^x.((x x)(^y.(y y))))

     REDUCED to normal form.

  ------  3667/88212. ------  

  1. ==[ start ]==> (a ((a a)(^a.(a a))))
  2. ==[ alpha ]==> (a ((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  3668/88224. ------  

  1. ==[ start ]==> ((^a.(^a.a))(^b.(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a a))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3669/88929. ------  

  1. ==[ start ]==> (((^a.a)(a (a a))) b)
  2. ==[ alpha ]==> (((^x.x)(a (a a))) b)
  3. ==[ beta  ]==> ((a (a a)) b)

     REDUCED to normal form.

  ------  3670/88938. ------  

  1. ==[ start ]==> (((a a)(^a.(a a))) a)
  2. ==[ alpha ]==> (((a a)(^x.(x x))) a)

     REDUCED to normal form.

  ------  3671/88944. ------  

  1. ==[ start ]==> ((^a.a)((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.x)((a a)(^y.(y y))))
  3. ==[ beta  ]==> ((a a)(^y.(y y)))
  4. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  3672/88953. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a a))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3673/88956. ------  

  1. ==[ start ]==> ((a (^a.a))(^b.(a (a a))))
  2. ==[ alpha ]==> ((a (^x.x))(^y.(a (a a))))

     REDUCED to normal form.

  ------  3674/88971. ------  

  1. ==[ start ]==> ((^a.(a a))((a (a a)) a))
  2. ==[ alpha ]==> ((^x.(x x))((a (a a)) a))
  3. ==[ beta  ]==> (((a (a a)) a)((a (a a)) a))

     REDUCED to normal form.

  ------  3675/88998. ------  

  1. ==[ start ]==> ((^a.b)(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.b)(((^y.y) a) b))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3676/89034. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3677/89073. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(z (z z))))
  3. ==[ beta  ]==> ((^y.y)(^z.(z (z z))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (y y))))
  5. ==[ beta  ]==> (^y.(y (y y)))
  6. ==[ alpha ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  3678/89079. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z)) a))
  3. ==[ beta  ]==> (((^z.(z z)) a)(^y.y))
  4. ==[ alpha ]==> (((^x.(x x)) a)(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3679/89172. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  3680/89196. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(a a)))
  3. ==[ beta  ]==> (^y.((^z.a)(a a)))
  4. ==[ alpha ]==> (^x.((^y.a)(a a)))
  5. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3681/89268. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) a) a))
  3. ==[ eta   ]==> ((^y.y)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3682/89343. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.((^z.z) y)))
  3. ==[ eta   ]==> ((((^x.x) a) a)(^z.z))
  4. ==[ alpha ]==> ((((^x.x) a) a)(^y.y))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3683/89439. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3684/89532. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  3685/89538. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z)) a))
  3. ==[ beta  ]==> (((^y.(^z.z)) a)(((^y.(^z.z)) a)((^y.(^z.z)) a)))
  4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.(^x1.x1)) a)((^y1.(^z1.z1)) a)))
  5. ==[ beta  ]==> ((^y.y)(((^z.(^x1.x1)) a)((^y1.(^z1.z1)) a)))
  6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)((^x1.(^y1.y1)) a)))
  7. ==[ beta  ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1)) a))
  8. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) a))
  9. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
 11. ==[ beta  ]==> ((^y.(^z.z)) a)
 12. ==[ alpha ]==> ((^x.(^y.y)) a)
 13. ==[ beta  ]==> (^y.y)
 14. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3686/89577. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  3687/89613. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.b))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.b))
  3. ==[ beta  ]==> ((a b)(^y.b))
  4. ==[ alpha ]==> ((a b)(^x.b))

     REDUCED to normal form.

  ------  3688/89631. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1)))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3689/89640. ------  

  1. ==[ start ]==> (((a (a a)) a)(^a.(a a)))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.(x x)))

     REDUCED to normal form.

  ------  3690/89658. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  3691/89667. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^a.a))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3692/89679. ------  

  1. ==[ start ]==> ((a a)((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((a a)((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  3693/89688. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a))))
  3. ==[ beta  ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  3694/89706. ------  

  1. ==[ start ]==> ((a (a a))((a (a a)) a))

     REDUCED to normal form.

  ------  3695/89715. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)((^z.(z z))(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z)))
  5. ==[ beta  ]==> ((^y.(y y))(^z.z))
  6. ==[ alpha ]==> ((^x.(x x))(^y.y))
  7. ==[ beta  ]==> ((^y.y)(^y.y))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3696/89733. ------  

  1. ==[ start ]==> ((a b)(((^a.a) a) b))
  2. ==[ alpha ]==> ((a b)(((^x.x) a) b))
  3. ==[ beta  ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  3697/89742. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3698/89769. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.a)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  3699/89778. ------  

  1. ==[ start ]==> (((^a.a) b)(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) b)(b ((^y.y) a)))
  3. ==[ beta  ]==> (b (b ((^y.y) a)))
  4. ==[ alpha ]==> (b (b ((^x.x) a)))
  5. ==[ beta  ]==> (b (b a))

     REDUCED to normal form.

  ------  3700/89805. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(a (a (a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (a (a a))))
  3. ==[ beta  ]==> ((^y.y)(a (a (a a))))
  4. ==[ alpha ]==> ((^x.x)(a (a (a a))))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  3701/89814. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y)) a))
  3. ==[ beta  ]==> ((a (a (^x.x)))(a a))

     REDUCED to normal form.

  ------  3702/89832. ------  

  1. ==[ start ]==> (((a a) b)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a a) b)(((^x.x) a)(a a)))
  3. ==[ beta  ]==> (((a a) b)(a (a a)))

     REDUCED to normal form.

  ------  3703/89859. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  3704/89877. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.a)))
  3. ==[ beta  ]==> ((a (^y.y))(b (^z.a)))
  4. ==[ alpha ]==> ((a (^x.x))(b (^y.a)))

     REDUCED to normal form.

  ------  3705/89886. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z) a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))((a a) a))

     REDUCED to normal form.

  ------  3706/89904. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(z z))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  3707/89931. ------  

  1. ==[ start ]==> ((a (^b.a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a (^x.a))((^y.a)(a a)))
  3. ==[ beta  ]==> ((a (^x.a)) a)

     REDUCED to normal form.

  ------  3708/89949. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3709/89967. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(b c))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  3710/89976. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.a)))

     REDUCED to normal form.

  ------  3711/90003. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) a) a))
  2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a) a))
  3. ==[ beta  ]==> ((a a)(((^y.y) a) a))
  4. ==[ alpha ]==> ((a a)(((^x.x) a) a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3712/90012. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.a)((^z.a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.z)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3713/90039. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2))))
  3. ==[ beta  ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.y1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3714/90048. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(b (a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)(b (a (^y.y))))

     REDUCED to normal form.

  ------  3715/90075. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(a ((^a.a) a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(a ((^y.y) a)))
  3. ==[ beta  ]==> ((a a)(a ((^y.y) a)))
  4. ==[ alpha ]==> ((a a)(a ((^x.x) a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3716/90102. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  3717/90120. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z))))
  5. ==[ beta  ]==> (b (^y.(^z.z)))
  6. ==[ alpha ]==> (b (^x.(^y.y)))

     REDUCED to normal form.

  ------  3718/90129. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a (^x1.x1))))

     REDUCED to normal form.

  ------  3719/90174. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.z))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3720/90192. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) a)((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> (((a a) a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  3721/90219. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z)) a))

     REDUCED to normal form.

  ------  3722/90246. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a a) b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a) b))
  3. ==[ beta  ]==> ((a (a a))((a a) b))

     REDUCED to normal form.

  ------  3723/90264. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(a (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(a (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(a (a (^x.x))))

     REDUCED to normal form.

  ------  3724/90273. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y)) a))
  3. ==[ beta  ]==> ((a (a (a a)))(^y.y))
  4. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  3725/90282. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (^z.z)))
  3. ==[ beta  ]==> ((^y.(y y))(b (^z.z)))
  4. ==[ alpha ]==> ((^x.(x x))(b (^y.y)))
  5. ==[ beta  ]==> ((b (^y.y))(b (^y.y)))
  6. ==[ alpha ]==> ((b (^x.x))(b (^y.y)))

     REDUCED to normal form.

  ------  3726/90309. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  3727/90345. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(a b))
  2. ==[ alpha ]==> ((((^x.x) a) b)(a b))
  3. ==[ beta  ]==> ((a b)(a b))

     REDUCED to normal form.

  ------  3728/90363. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((^z.z)(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1)))
  5. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  7. ==[ beta  ]==> ((^y.y)(^z.z))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3729/90372. ------  

  1. ==[ start ]==> (((a (a a)) a)(a (a a)))

     REDUCED to normal form.

  ------  3730/90390. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(a (^y.y)))
  3. ==[ beta  ]==> ((a (a a))(a (^y.y)))
  4. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  3731/90399. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(a a))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(a a))

     REDUCED to normal form.

  ------  3732/90546. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (z z))))
  3. ==[ beta  ]==> ((^z.(z (z z)))(^y.y))
  4. ==[ alpha ]==> ((^x.(x (x x)))(^y.y))
  5. ==[ beta  ]==> ((^y.y)((^y.y)(^y.y)))
  6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  7. ==[ beta  ]==> ((^y.y)(^z.z))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3733/91005. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((^y.(y (^z.z)))((^y.(y (^z.z)))(^y.(y (^z.z)))))
  4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z (^x1.x1)))(^y1.(y1 (^z1.z1)))))
  5. ==[ beta  ]==> (((^z.(z (^x1.x1)))(^y1.(y1 (^z1.z1))))(^y.y))
  6. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(z (^x1.x1))))(^y1.y1))
  7. ==[ beta  ]==> (((^z.(z (^x1.x1)))(^y.y))(^y1.y1))
  8. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.x1))
  9. ==[ beta  ]==> (((^z.z)(^y.y))(^x1.x1))
 10. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
 11. ==[ beta  ]==> ((^y.y)(^z.z))
 12. ==[ alpha ]==> ((^x.x)(^y.y))
 13. ==[ beta  ]==> (^y.y)
 14. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3734/91134. ------  

  1. ==[ start ]==> (((a a)(^a.(a a))) b)
  2. ==[ alpha ]==> (((a a)(^x.(x x))) b)

     REDUCED to normal form.

  ------  3735/91158. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3736/91170. ------  

  1. ==[ start ]==> (((^a.a) a)(^b.(a (a a))))
  2. ==[ alpha ]==> (((^x.x) a)(^y.(a (a a))))
  3. ==[ beta  ]==> (a (^y.(a (a a))))
  4. ==[ alpha ]==> (a (^x.(a (a a))))

     REDUCED to normal form.

  ------  3737/91278. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  3738/91284. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (a (a a))))
  3. ==[ beta  ]==> ((a (a (a a)))(^y.y))
  4. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  3739/91287. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (y y))))

     REDUCED to normal form.

  ------  3740/91386. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 x1))))

     REDUCED to normal form.

  ------  3741/91401. ------  

  1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> (^y.(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> (^x.(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (^x.(a (^z.z)))
  6. ==[ alpha ]==> (^x.(a (^y.y)))

     REDUCED to normal form.

  ------  3742/91548. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(^b.(^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.a)))
  3. ==[ beta  ]==> ((a a)(^y.(^z.a)))
  4. ==[ alpha ]==> ((a a)(^x.(^y.a)))

     REDUCED to normal form.

  ------  3743/91629. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.z)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.z)))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y)))

     REDUCED to normal form.

  ------  3744/91644. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3745/91737. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3746/91743. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(a (a (^y.y))))
  3. ==[ beta  ]==> ((a (a (^y.y)))((a (a (^y.y)))(a (a (^y.y)))))
  4. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(a (a (^z.z)))))

     REDUCED to normal form.

  ------  3747/91746. ------  

  1. ==[ start ]==> ((a (a (a a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  3748/91782. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3749/91818. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^b.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(a a)))
  3. ==[ beta  ]==> ((a b)(^y.(a a)))
  4. ==[ alpha ]==> ((a b)(^x.(a a)))

     REDUCED to normal form.

  ------  3750/91845. ------  

  1. ==[ start ]==> (((a (a a)) a)(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3751/91863. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^b.a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.a))
  3. ==[ beta  ]==> ((a (a a))(^y.a))
  4. ==[ alpha ]==> ((a (a a))(^x.a))

     REDUCED to normal form.

  ------  3752/91872. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3753/91902. ------  

  1. ==[ start ]==> ((a (^a.a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y y))))

     REDUCED to normal form.

  ------  3754/91911. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.a)(a (a a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (a a))))
  3. ==[ beta  ]==> (a ((^y.y)(a (a a))))
  4. ==[ alpha ]==> (a ((^x.x)(a (a a))))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  3755/91929. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (a a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a)) a))
  3. ==[ beta  ]==> ((^y.y)((a (a a)) a))
  4. ==[ alpha ]==> ((^x.x)((a (a a)) a))
  5. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  3756/91938. ------  

  1. ==[ start ]==> (((a a) a)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> (((a a) a)((^y.y)(^y.y)))
  4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y)))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3757/91956. ------  

  1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a) b))
  2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a) b))
  3. ==[ beta  ]==> ((a a)(((^y.y) a) b))
  4. ==[ alpha ]==> ((a a)(((^x.x) a) b))
  5. ==[ beta  ]==> ((a a)(a b))

     REDUCED to normal form.

  ------  3758/91965. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((a a)(^x.x)) a)

     REDUCED to normal form.

  ------  3759/91992. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> (b ((^y.(^z.z))(^x1.a)))
  4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  3760/92001. ------  

  1. ==[ start ]==> (((a a)(a a))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a a))(b ((^x.x) a)))
  3. ==[ beta  ]==> (((a a)(a a))(b a))

     REDUCED to normal form.

  ------  3761/92019. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z))))
  5. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  6. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  7. ==[ beta  ]==> (^y.(y y))
  8. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3762/92028. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(a (a (a a))))

     REDUCED to normal form.

  ------  3763/92037. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1)) a))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(x1 x1)) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3764/92064. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.a) b))
  4. ==[ alpha ]==> ((^x.x)((^y.a) b))
  5. ==[ beta  ]==> ((^y.a) b)
  6. ==[ alpha ]==> ((^x.a) b)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3765/92100. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.a)))

     REDUCED to normal form.

  ------  3766/92127. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(z z))))

     REDUCED to normal form.

  ------  3767/92145. ------  

  1. ==[ start ]==> ((a (^b.a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> ((a (^x.a))(a (^z.z)))
  4. ==[ alpha ]==> ((a (^x.a))(a (^y.y)))

     REDUCED to normal form.

  ------  3768/92181. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3769/92190. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(b c))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(b c))

     REDUCED to normal form.

  ------  3770/92226. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a) a))
  3. ==[ beta  ]==> ((^y.a)(((^z.z) a) a))
  4. ==[ alpha ]==> ((^x.a)(((^y.y) a) a))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3771/92253. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1)) b))
  3. ==[ beta  ]==> ((^y.y)((a (^y1.y1)) b))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b))
  5. ==[ beta  ]==> ((a (^y.y)) b)
  6. ==[ alpha ]==> ((a (^x.x)) b)

     REDUCED to normal form.

  ------  3772/92262. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^z.z))
  4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y))

     REDUCED to normal form.

  ------  3773/92289. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(^z.a)))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.a)))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3774/92307. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.a) a))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a) a))
  3. ==[ beta  ]==> (((^y.y) a)((^z.a) a))
  4. ==[ alpha ]==> (((^x.x) a)((^y.a) a))
  5. ==[ beta  ]==> (a ((^y.a) a))
  6. ==[ alpha ]==> (a ((^x.a) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3775/92316. ------  

  1. ==[ start ]==> (((a a)(^b.a))(c (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(c (^y.y)))

     REDUCED to normal form.

  ------  3776/92334. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1)) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1)) b))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((^y.(^z.z)) b)
  6. ==[ alpha ]==> ((^x.(^y.y)) b)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3777/92343. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.(^y1.y1))))

     REDUCED to normal form.

  ------  3778/92370. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (^b.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.a)))
  3. ==[ beta  ]==> ((a (^y.y))(a (^z.a)))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.a)))

     REDUCED to normal form.

  ------  3779/92388. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(^z.z)))

     REDUCED to normal form.

  ------  3780/92406. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(b b))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(b b))
  3. ==[ beta  ]==> (((a a) a)(b b))

     REDUCED to normal form.

  ------  3781/92460. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(b (a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(b (a a)))
  3. ==[ beta  ]==> ((a (a a))(b (a a)))

     REDUCED to normal form.

  ------  3782/92478. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.y)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.(^z.z)))
  6. ==[ alpha ]==> ((a a)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3783/92487. ------  

  1. ==[ start ]==> ((a (a (a a)))(a (a (^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(a (a (^x.x))))

     REDUCED to normal form.

  ------  3784/92496. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1)) a))
  3. ==[ beta  ]==> ((^y.(y y))((^z.(^x1.x1)) a))
  4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z)) a))
  5. ==[ beta  ]==> (((^y.(^z.z)) a)((^y.(^z.z)) a))
  6. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) a))
  7. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1)) a))
  8. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  9. ==[ beta  ]==> ((^y.(^z.z)) a)
 10. ==[ alpha ]==> ((^x.(^y.y)) a)
 11. ==[ beta  ]==> (^y.y)
 12. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3785/92523. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1) b))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) b))
  4. ==[ alpha ]==> ((^x.x)((^y.y) b))
  5. ==[ beta  ]==> ((^y.y) b)
  6. ==[ alpha ]==> ((^x.x) b)
  7. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3786/92559. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((^a.a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(a a)))
  3. ==[ beta  ]==> ((a b)((^y.y)(a a)))
  4. ==[ alpha ]==> ((a b)((^x.x)(a a)))
  5. ==[ beta  ]==> ((a b)(a a))

     REDUCED to normal form.

  ------  3787/92577. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((a a) a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a) a))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((a a) a))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((a a) a))
  5. ==[ beta  ]==> ((^y.y)((a a) a))
  6. ==[ alpha ]==> ((^x.x)((a a) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3788/92586. ------  

  1. ==[ start ]==> (((a (a a)) a)((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.y)))
  3. ==[ beta  ]==> (((a (a a)) a)(^y.y))
  4. ==[ alpha ]==> (((a (a a)) a)(^x.x))

     REDUCED to normal form.

  ------  3789/92604. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))((^a.a) a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y) a))
  3. ==[ beta  ]==> ((a (a a))((^y.y) a))
  4. ==[ alpha ]==> ((a (a a))((^x.x) a))
  5. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  3790/92613. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(a (^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.y)))

     REDUCED to normal form.

  ------  3791/92630. ------  

  1. ==[ start ]==> (^a.((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1) x)))
  3. ==[ beta  ]==> (^x.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3792/92631. ------  

  1. ==[ start ]==> (a ((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) a)))
  3. ==[ beta  ]==> (a (^y.y))
  4. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3793/92661. ------  

  1. ==[ start ]==> ((^a.(a a))(^b.(a (a a))))
  2. ==[ alpha ]==> ((^x.(x x))(^y.(a (a a))))
  3. ==[ beta  ]==> ((^y.(a (a a)))(^y.(a (a a))))
  4. ==[ alpha ]==> ((^x.(a (a a)))(^y.(a (a a))))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3794/92769. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^z.(^x1.(x1 x1)))(^y.y))
  4. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.z))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3795/92958. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.((^x1.x1) a)))
  3. ==[ eta   ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  3796/93228. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))))
  4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.(^z2.z2)))))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3797/93375. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a)) a)
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a)) a)
  3. ==[ beta  ]==> ((^y.y) a)
  4. ==[ alpha ]==> ((^x.x) a)
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3798/93381. ------  

  1. ==[ start ]==> ((^a.a)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3799/93408. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.y)(a (a a))))
  3. ==[ beta  ]==> (((^y.y)(a (a a)))((^y.y)(a (a a))))
  4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(a (a a))))
  5. ==[ beta  ]==> ((a (a a))((^y.y)(a (a a))))
  6. ==[ alpha ]==> ((a (a a))((^x.x)(a (a a))))
  7. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  3800/93411. ------  

  1. ==[ start ]==> ((a (a a))(^b.(a (a a))))
  2. ==[ alpha ]==> ((a (a a))(^x.(a (a a))))

     REDUCED to normal form.

  ------  3801/93435. ------  

  1. ==[ start ]==> ((^a.b)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3802/93516. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(x1 x1))))
  3. ==[ beta  ]==> (((^z.z)(^x1.(x1 x1)))(^y.y))
  4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z))
  5. ==[ beta  ]==> ((^y.(y y))(^z.z))
  6. ==[ alpha ]==> ((^x.(x x))(^y.y))
  7. ==[ beta  ]==> ((^y.y)(^y.y))
  8. ==[ alpha ]==> ((^x.x)(^y.y))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3803/93519. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3804/93528. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (x1 x1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(x1 (x1 x1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z z))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3805/93705. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)((^x1.x1) a)))
  3. ==[ eta   ]==> ((^y.y)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3806/93708. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a a)(^y.((^z.z) a)))
  4. ==[ alpha ]==> ((a a)(^x.((^y.y) a)))
  5. ==[ beta  ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3807/93798. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> (((^x.x)((^y.y) a))(^x1.x1))
  4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.z))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3808/93861. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.c))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.c))
  3. ==[ beta  ]==> ((a (^y.y))(^z.c))
  4. ==[ alpha ]==> ((a (^x.x))(^y.c))

     REDUCED to normal form.

  ------  3809/93924. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(a (^x1.x1))))

     REDUCED to normal form.

  ------  3810/93975. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y)(^z.(^x1.x1)))(((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1)))))
  4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.(^z1.z1)))((^x2.x2)(^y2.(^z2.z2)))))
  5. ==[ beta  ]==> ((^y.(^z.z))(((^x1.x1)(^y1.(^z1.z1)))((^x2.x2)(^y2.(^z2.z2)))))
  6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.(^y1.y1)))((^z1.z1)(^x2.(^y2.y2)))))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3811/93978. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3812/93987. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(z (^x1.x1))))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(y (^z.z))))
  5. ==[ beta  ]==> ((^y.(y (^z.z)))(^y.(y (^z.z))))
  6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1))))
  7. ==[ beta  ]==> ((^z.(z (^x1.x1)))(^y.y))
  8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z))
  9. ==[ beta  ]==> ((^z.z)(^y.y))
 10. ==[ alpha ]==> ((^x.x)(^y.y))
 11. ==[ beta  ]==> (^y.y)
 12. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3813/94014. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  3814/94050. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^c.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.z)))
  3. ==[ beta  ]==> ((a b)(^y.(^z.z)))
  4. ==[ alpha ]==> ((a b)(^x.(^y.y)))

     REDUCED to normal form.

  ------  3815/94068. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.b))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.b))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.b))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.b))
  5. ==[ beta  ]==> ((^y.y)(^z.b))
  6. ==[ alpha ]==> ((^x.x)(^y.b))
  7. ==[ beta  ]==> (^y.b)
  8. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  3816/94095. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(y y)))
  3. ==[ beta  ]==> ((a (a a))(^y.(y y)))
  4. ==[ alpha ]==> ((a (a a))(^x.(x x)))

     REDUCED to normal form.

  ------  3817/94104. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^b.a))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.a))

     REDUCED to normal form.

  ------  3818/94122. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.a))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.x1))
  3. ==[ beta  ]==> ((^y.y)(^x1.x1))
  4. ==[ alpha ]==> ((^x.x)(^y.y))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3819/94134. ------  

  1. ==[ start ]==> ((a a)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) a)))
  3. ==[ beta  ]==> ((a a)(^y.y))
  4. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3820/94152. ------  

  1. ==[ start ]==> (((^a.a) a)((a a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(y y))))
  3. ==[ beta  ]==> (a ((a a)(^y.(y y))))
  4. ==[ alpha ]==> (a ((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  3821/94161. ------  

  1. ==[ start ]==> ((a (a a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((a (a a))((^x.x)(a (a a))))
  3. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  3822/94179. ------  

  1. ==[ start ]==> (((a a) a)((a (a a)) a))

     REDUCED to normal form.

  ------  3823/94188. ------  

  1. ==[ start ]==> ((a b)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((a b)((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> ((a b)((^y.y)(^y.y)))
  4. ==[ alpha ]==> ((a b)((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a b)(^y.y))
  6. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  3824/94206. ------  

  1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a) b))
  2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a) b))
  3. ==[ beta  ]==> (((a a)(^x.x))(a b))

     REDUCED to normal form.

  ------  3825/94233. ------  

  1. ==[ start ]==> (((^a.a) b)((a (^a.a)) c))
  2. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) c))
  3. ==[ beta  ]==> (b ((a (^y.y)) c))
  4. ==[ alpha ]==> (b ((a (^x.x)) c))

     REDUCED to normal form.

  ------  3826/94242. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  3827/94269. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.(z z)))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y y)))

     REDUCED to normal form.

  ------  3828/94278. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (a a))))
  3. ==[ beta  ]==> ((^y.(^z.z))(a (a (a a))))
  4. ==[ alpha ]==> ((^x.(^y.y))(a (a (a a))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3829/94287. ------  

  1. ==[ start ]==> (((a a) b)((^a.(a a)) a))
  2. ==[ alpha ]==> (((a a) b)((^x.(x x)) a))
  3. ==[ beta  ]==> (((a a) b)(a a))

     REDUCED to normal form.

  ------  3830/94305. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(a a)))
  3. ==[ beta  ]==> ((^y.y)(((^x1.x1) a)(a a)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a)))
  5. ==[ beta  ]==> (((^y.y) a)(a a))
  6. ==[ alpha ]==> (((^x.x) a)(a a))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3831/94314. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^b.a) b))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.a) b))
  3. ==[ beta  ]==> (((a (^x.x)) a) a)

     REDUCED to normal form.

  ------  3832/94332. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  3833/94359. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)((a a)((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3834/94404. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(a a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x))) a)

     REDUCED to normal form.

  ------  3835/94422. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3836/94431. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(^z.z))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y))

     REDUCED to normal form.

  ------  3837/94458. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> ((a a)((^y.y)((^z.z) a)))
  4. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a)))
  5. ==[ beta  ]==> ((a a)((^y.y) a))
  6. ==[ alpha ]==> ((a a)((^x.x) a))
  7. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  3838/94503. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y)) b))

     REDUCED to normal form.

  ------  3839/94548. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a ((^z.z) a)))
  3. ==[ beta  ]==> (((^y.y) a)(a ((^z.z) a)))
  4. ==[ alpha ]==> (((^x.x) a)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a (a ((^y.y) a)))
  6. ==[ alpha ]==> (a (a ((^x.x) a)))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3840/94557. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^b.a) a))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.a) a))
  3. ==[ beta  ]==> (((a a)(^x.a)) a)

     REDUCED to normal form.

  ------  3841/94575. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.x1))(a a)))
  3. ==[ beta  ]==> ((^y.y)((a (^x1.x1))(a a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a)))
  5. ==[ beta  ]==> ((a (^y.y))(a a))
  6. ==[ alpha ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  3842/94584. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) b))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  3843/94647. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> (((a a) a)((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> (((a a) a)(^y.y))
  6. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  3844/94674. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.x1))))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1)))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  3845/94701. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (a a))((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3846/94719. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a a) b))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a a) b))
  3. ==[ beta  ]==> ((a a)((a a) b))

     REDUCED to normal form.

  ------  3847/94728. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a (a a)))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y)))

     REDUCED to normal form.

  ------  3848/94737. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (a (^z.z))))
  3. ==[ beta  ]==> ((^y.(y y))(a (a (^z.z))))
  4. ==[ alpha ]==> ((^x.(x x))(a (a (^y.y))))
  5. ==[ beta  ]==> ((a (a (^y.y)))(a (a (^y.y))))
  6. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y))))

     REDUCED to normal form.

  ------  3849/94764. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  3850/94800. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((a a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)((a a)(^y.y)))
  3. ==[ beta  ]==> ((a b)((a a)(^y.y)))
  4. ==[ alpha ]==> ((a b)((a a)(^x.x)))

     REDUCED to normal form.

  ------  3851/94818. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(a b))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a b))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(a b))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(a b))
  5. ==[ beta  ]==> ((^y.y)(a b))
  6. ==[ alpha ]==> ((^x.x)(a b))
  7. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  3852/94827. ------  

  1. ==[ start ]==> (((a (a a)) a)((a a) a))

     REDUCED to normal form.

  ------  3853/94845. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(a (a a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(a (a a)))
  3. ==[ beta  ]==> ((a (a a))(a (a a)))

     REDUCED to normal form.

  ------  3854/94854. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))((^a.a) a))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) a))
  3. ==[ beta  ]==> (((a a)(^x.(x x))) a)

     REDUCED to normal form.

  ------  3855/94872. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a a))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a a))
  3. ==[ beta  ]==> ((^y.y)(a a))
  4. ==[ alpha ]==> ((^x.x)(a a))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3856/94880. ------  

  1. ==[ start ]==> (^a.((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> (^x.((x (^y.y))(^z.x)))

     REDUCED to normal form.

  ------  3857/94881. ------  

  1. ==[ start ]==> (a ((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> (a ((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  3858/95136. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> (^y.(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> (^x.(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3859/95379. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.z)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3860/95625. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a)) b)
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a)) b)
  3. ==[ beta  ]==> ((^y.y) b)
  4. ==[ alpha ]==> ((^x.x) b)
  5. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3861/95634. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a)) a)
  2. ==[ alpha ]==> (((a (^x.x))(^y.a)) a)

     REDUCED to normal form.

  ------  3862/95640. ------  

  1. ==[ start ]==> ((^a.a)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a)))
  3. ==[ beta  ]==> ((a (^y.y))(^z.a))
  4. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  3863/95649. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3864/95667. ------  

  1. ==[ start ]==> ((^a.(a a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.(x x))((a a)(^y.(y y))))
  3. ==[ beta  ]==> (((a a)(^y.(y y)))((a a)(^y.(y y))))
  4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(y y))))

     REDUCED to normal form.

  ------  3865/95679. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))(^b.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a a))))
  3. ==[ beta  ]==> ((^y.y)(^z.(a (a a))))
  4. ==[ alpha ]==> ((^x.x)(^y.(a (a a))))
  5. ==[ beta  ]==> (^y.(a (a a)))
  6. ==[ alpha ]==> (^x.(a (a a)))

     REDUCED to normal form.

  ------  3866/95694. ------  

  1. ==[ start ]==> ((^a.b)((a (a a)) a))
  2. ==[ alpha ]==> ((^x.b)((a (a a)) a))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3867/95730. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3868/95787. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3869/95796. ------  

  1. ==[ start ]==> (((a a) b)(^a.(a (a a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(x (x x))))

     REDUCED to normal form.

  ------  3870/95892. ------  

  1. ==[ start ]==> ((^a.(^b.a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.(z z))))
  3. ==[ beta  ]==> (^y.(a (^z.(z z))))
  4. ==[ alpha ]==> (^x.(a (^y.(y y))))

     REDUCED to normal form.

  ------  3871/95895. ------  

  1. ==[ start ]==> ((a (^b.a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3872/95964. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(^z.a)))
  3. ==[ eta   ]==> ((^y.y)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  3873/95976. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.a)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.a)(^y.((^z.z) a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3874/96057. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.a)))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.a)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.a)))
  5. ==[ beta  ]==> (a (^y.(^z.a)))
  6. ==[ alpha ]==> (a (^x.(^y.a)))

     REDUCED to normal form.

  ------  3875/96066. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z) y)))
  3. ==[ eta   ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  3876/96135. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(a (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (^z.a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3877/96138. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^a.(^b.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.y)))

     REDUCED to normal form.

  ------  3878/96234. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a a) b))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a a) b))
  3. ==[ beta  ]==> (((a a) b)(((a a) b)((a a) b)))

     REDUCED to normal form.

  ------  3879/96246. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))
  6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3880/96327. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(a a)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.(a a)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a)))
  5. ==[ beta  ]==> ((^y.y)(^z.(a a)))
  6. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  7. ==[ beta  ]==> (^y.(a a))
  8. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  3881/96336. ------  

  1. ==[ start ]==> (((a (a a)) a)(^a.b))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.b))

     REDUCED to normal form.

  ------  3882/96354. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.z)))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.z)))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  3883/96363. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(y y)))

     REDUCED to normal form.

  ------  3884/96381. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3885/96390. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z))

     REDUCED to normal form.

  ------  3886/96402. ------  

  1. ==[ start ]==> ((a a)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a a)((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  3887/96411. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> ((a (^x.x))(^z.z))
  4. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  3888/96429. ------  

  1. ==[ start ]==> ((a (a a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((a (a a))((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  3889/96438. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a a))))
  3. ==[ beta  ]==> ((^y.y)((^z.z)(a (a a))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a))))
  5. ==[ beta  ]==> ((^y.y)(a (a a)))
  6. ==[ alpha ]==> ((^x.x)(a (a a)))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  3890/96456. ------  

  1. ==[ start ]==> ((a b)((a (a a)) a))

     REDUCED to normal form.

  ------  3891/96465. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.(y y))(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.(x x))(^y.y)))
  5. ==[ beta  ]==> ((a a)((^y.y)(^y.y)))
  6. ==[ alpha ]==> ((a a)((^x.x)(^y.y)))
  7. ==[ beta  ]==> ((a a)(^y.y))
  8. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3892/96492. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  3893/96501. ------  

  1. ==[ start ]==> (((^a.a) b)(c (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)(c (a (^y.y))))
  3. ==[ beta  ]==> (b (c (a (^y.y))))
  4. ==[ alpha ]==> (b (c (a (^x.x))))

     REDUCED to normal form.

  ------  3894/96528. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(b ((^z.z) a)))
  3. ==[ beta  ]==> ((^y.y)(b ((^z.z) a)))
  4. ==[ alpha ]==> ((^x.x)(b ((^y.y) a)))
  5. ==[ beta  ]==> (b ((^y.y) a))
  6. ==[ alpha ]==> (b ((^x.x) a))
  7. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3895/96546. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 x1))))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3896/96555. ------  

  1. ==[ start ]==> (((a a) b)(a (a (a a))))

     REDUCED to normal form.

  ------  3897/96582. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)(a a)))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a (a a)))

     REDUCED to normal form.

  ------  3898/96609. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(a (^x1.x1))))

     REDUCED to normal form.

  ------  3899/96627. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(b (^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (^z.a)))
  3. ==[ beta  ]==> ((^y.y)(b (^z.a)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.a)))
  5. ==[ beta  ]==> (b (^y.a))
  6. ==[ alpha ]==> (b (^x.a))

     REDUCED to normal form.

  ------  3900/96636. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y))((a a) a))

     REDUCED to normal form.

  ------  3901/96654. ------  

  1. ==[ start ]==> ((a (^b.a))(a (^a.(a a))))
  2. ==[ alpha ]==> ((a (^x.a))(a (^y.(y y))))

     REDUCED to normal form.

  ------  3902/96672. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))(a (^z.z)))
  4. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y)))

     REDUCED to normal form.

  ------  3903/96690. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(c b))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(c b))
  3. ==[ beta  ]==> ((^y.y)(c b))
  4. ==[ alpha ]==> ((^x.x)(c b))
  5. ==[ beta  ]==> (c b)

     REDUCED to normal form.

  ------  3904/96699. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3905/96726. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a a)(^b.a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(^y.a)))
  3. ==[ beta  ]==> ((a a)((a a)(^y.a)))
  4. ==[ alpha ]==> ((a a)((a a)(^x.a)))

     REDUCED to normal form.

  ------  3906/96735. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.a)((^z.z)((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.a)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3907/96762. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.z1)))
  3. ==[ beta  ]==> ((^y.y)((^y1.a)(^z1.z1)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z)))
  5. ==[ beta  ]==> ((^y.a)(^z.z))
  6. ==[ alpha ]==> ((^x.a)(^y.y))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3908/96771. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(c (a a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(c (a a)))

     REDUCED to normal form.

  ------  3909/96798. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(b (a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)(b (a (^y.y))))
  3. ==[ beta  ]==> ((a a)(b (a (^y.y))))
  4. ==[ alpha ]==> ((a a)(b (a (^x.x))))

     REDUCED to normal form.

  ------  3910/96816. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.a)))
  3. ==[ beta  ]==> (((^y.y) a)((^z.z)(^x1.a)))
  4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.a)))
  5. ==[ beta  ]==> (a ((^y.y)(^z.a)))
  6. ==[ alpha ]==> (a ((^x.x)(^y.a)))
  7. ==[ beta  ]==> (a (^y.a))
  8. ==[ alpha ]==> (a (^x.a))

     REDUCED to normal form.

  ------  3911/96825. ------  

  1. ==[ start ]==> (((a a)(^b.a))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(a ((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(^x.a))(a a))

     REDUCED to normal form.

  ------  3912/96852. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(a a)))

     REDUCED to normal form.

  ------  3913/96879. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^y.y))((a a)(a (^z.z))))
  4. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  3914/96897. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(a (^b.a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.a)))

     REDUCED to normal form.

  ------  3915/96915. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))(^z.z)))
  3. ==[ beta  ]==> (((a a) a)((a (^y.y))(^z.z)))
  4. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y)))

     REDUCED to normal form.

  ------  3916/96942. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(^x1.x1))))

     REDUCED to normal form.

  ------  3917/96969. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a (^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (^y.y)) a))
  3. ==[ beta  ]==> ((a (a a))((a (^y.y)) a))
  4. ==[ alpha ]==> ((a (a a))((a (^x.x)) a))

     REDUCED to normal form.

  ------  3918/96987. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(b (a a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)(b (a a)))
  3. ==[ beta  ]==> ((a a)(b (a a)))

     REDUCED to normal form.

  ------  3919/96996. ------  

  1. ==[ start ]==> ((a (a (a a)))((a a) b))

     REDUCED to normal form.

  ------  3920/97005. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.(y y))((^z.z)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> (((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1))))
  6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))
  7. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1))))
  8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1))))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3921/97032. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(b (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(b (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(b (^y.y)))
  5. ==[ beta  ]==> (b (^y.y))
  6. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  3922/97068. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(b a))
  2. ==[ alpha ]==> ((((^x.x) a) b)(b a))
  3. ==[ beta  ]==> ((a b)(b a))

     REDUCED to normal form.

  ------  3923/97086. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(a a)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((^z.z)(a a)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z)(a a)))
  6. ==[ alpha ]==> ((^x.x)((^y.y)(a a)))
  7. ==[ beta  ]==> ((^y.y)(a a))
  8. ==[ alpha ]==> ((^x.x)(a a))
  9. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3924/97095. ------  

  1. ==[ start ]==> (((a (a a)) a)(a b))

     REDUCED to normal form.

  ------  3925/97113. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(^z.z)))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y)))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  3926/97122. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(a (a a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (a a)))

     REDUCED to normal form.

  ------  3927/97140. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a (^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a (^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(a (^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(a (^y.y)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3928/97149. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(a a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a a))

     REDUCED to normal form.

  ------  3929/97656. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(^b.c))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.c))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  3930/97911. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a)) b)
  2. ==[ alpha ]==> (((a (^x.x))(^y.a)) b)

     REDUCED to normal form.

  ------  3931/97935. ------  

  1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3932/97974. ------  

  1. ==[ start ]==> (((a a) a)(^b.(a (a a))))
  2. ==[ alpha ]==> (((a a) a)(^x.(a (a a))))

     REDUCED to normal form.

  ------  3933/98016. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a) b))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  3934/98061. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(b ((^z.z) a)))
  3. ==[ beta  ]==> ((b ((^z.z) a))(^y.y))
  4. ==[ alpha ]==> ((b ((^x.x) a))(^y.y))
  5. ==[ beta  ]==> ((b a)(^y.y))
  6. ==[ alpha ]==> ((b a)(^x.x))

     REDUCED to normal form.

  ------  3935/98082. ------  

  1. ==[ start ]==> (((a a) b)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((a a) b)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  3936/98250. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(b c))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(b c))
  3. ==[ eta   ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  3937/98262. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(^c.(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.a)))
  3. ==[ beta  ]==> ((^y.a)(^z.(^x1.a)))
  4. ==[ alpha ]==> ((^x.a)(^y.(^z.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3938/98352. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.a)))

     REDUCED to normal form.

  ------  3939/98424. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(^b.c))
  2. ==[ alpha ]==> ((a (^x.(x x)))(^y.c))

     REDUCED to normal form.

  ------  3940/98520. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(b (a a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))(b (a a)))
  3. ==[ beta  ]==> ((b (a a))((b (a a))(b (a a))))

     REDUCED to normal form.

  ------  3941/98595. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a b)(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  3942/98622. ------  

  1. ==[ start ]==> (((a (a a)) a)(^b.(a a)))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.(a a)))

     REDUCED to normal form.

  ------  3943/98649. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z)))

     REDUCED to normal form.

  ------  3944/98667. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.a))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.a))
  3. ==[ beta  ]==> ((^y.y)(^x1.a))
  4. ==[ alpha ]==> ((^x.x)(^y.a))
  5. ==[ beta  ]==> (^y.a)
  6. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  3945/98676. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  3946/98706. ------  

  1. ==[ start ]==> ((a (^a.a))((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.a)))

     REDUCED to normal form.

  ------  3947/98715. ------  

  1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> (a ((^y.(^z.z))((^x1.x1) a)))
  4. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) a)))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  3948/98733. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)((a a)(^z.(z z))))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y y))))
  5. ==[ beta  ]==> ((a a)(^y.(y y)))
  6. ==[ alpha ]==> ((a a)(^x.(x x)))

     REDUCED to normal form.

  ------  3949/98742. ------  

  1. ==[ start ]==> (((a a) a)((^a.a)(a (a a))))
  2. ==[ alpha ]==> (((a a) a)((^x.x)(a (a a))))
  3. ==[ beta  ]==> (((a a) a)(a (a a)))

     REDUCED to normal form.

  ------  3950/98760. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a (a a)) a))
  2. ==[ alpha ]==> (((^x.x)(a a))((a (a a)) a))
  3. ==[ beta  ]==> ((a a)((a (a a)) a))

     REDUCED to normal form.

  ------  3951/98769. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.x))((^z.z)(^z.z)))
  4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z)))
  5. ==[ beta  ]==> (((a a)(^x.x))(^z.z))
  6. ==[ alpha ]==> (((a a)(^x.x))(^y.y))

     REDUCED to normal form.

  ------  3952/98787. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a) b))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a) b))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))(a b))

     REDUCED to normal form.

  ------  3953/98796. ------  

  1. ==[ start ]==> (((^a.a) b)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (b ((^y.a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z))))
  5. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  3954/98823. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a)))
  5. ==[ beta  ]==> ((^y.(^z.z))(^x1.a))
  6. ==[ alpha ]==> ((^x.(^y.y))(^z.a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3955/98832. ------  

  1. ==[ start ]==> ((a (a (^a.a)))(b ((^a.a) a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.y) a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(b a))

     REDUCED to normal form.

  ------  3956/98850. ------  

  1. ==[ start ]==> (((a a) b)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(y y))))
  3. ==[ beta  ]==> (((a a) b)(^y.(y y)))
  4. ==[ alpha ]==> (((a a) b)(^x.(x x)))

     REDUCED to normal form.

  ------  3957/98868. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1)) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.(x1 x1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(y y)) a))
  5. ==[ beta  ]==> ((^y.(y y)) a)
  6. ==[ alpha ]==> ((^x.(x x)) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3958/98895. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.a) b))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a) b))
  3. ==[ beta  ]==> ((a (^y.y))((^z.a) b))
  4. ==[ alpha ]==> ((a (^x.x))((^y.a) b))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  3959/98931. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))(b (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.a)))

     REDUCED to normal form.

  ------  3960/98985. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)((^b.a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(a a)))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3961/99021. ------  

  1. ==[ start ]==> ((a ((^a.a) a))(b c))
  2. ==[ alpha ]==> ((a ((^x.x) a))(b c))
  3. ==[ beta  ]==> ((a a)(b c))

     REDUCED to normal form.

  ------  3962/99030. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(^z.a)))
  3. ==[ beta  ]==> ((^y.a)((a a)(^z.a)))
  4. ==[ alpha ]==> ((^x.a)((a a)(^y.a)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3963/99057. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a) a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a) a))
  3. ==[ beta  ]==> ((^y.y)(((^y1.y1) a) a))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a))
  5. ==[ beta  ]==> (((^y.y) a) a)
  6. ==[ alpha ]==> (((^x.x) a) a)
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3964/99066. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^b.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x)) b) a)

     REDUCED to normal form.

  ------  3965/99093. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3966/99120. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.a)))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.a))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.a))

     REDUCED to normal form.

  ------  3967/99138. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.a) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.a) a))
  4. ==[ alpha ]==> ((^x.x)((^y.a) a))
  5. ==[ beta  ]==> ((^y.a) a)
  6. ==[ alpha ]==> ((^x.a) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3968/99174. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^y.y))(b (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  3969/99237. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b b))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b b))

     REDUCED to normal form.

  ------  3970/99282. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(^x1.x1)))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z)))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3971/99291. ------  

  1. ==[ start ]==> ((a (a (a a)))(b (a a)))

     REDUCED to normal form.

  ------  3972/99300. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a) b))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a) b))
  3. ==[ beta  ]==> ((^y.(y y))((a a) b))
  4. ==[ alpha ]==> ((^x.(x x))((a a) b))
  5. ==[ beta  ]==> (((a a) b)((a a) b))

     REDUCED to normal form.

  ------  3973/99327. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.a)) a))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1)) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1)) a))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a))
  5. ==[ beta  ]==> ((^y.(^z.z)) a)
  6. ==[ alpha ]==> ((^x.(^y.y)) a)
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3974/99363. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(a (^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) b)(a (^y.(^z.z))))
  3. ==[ beta  ]==> ((a b)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a b)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  3975/99381. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.z)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((a a)(^z.z)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)((a a)(^z.z)))
  6. ==[ alpha ]==> ((^x.x)((a a)(^y.y)))
  7. ==[ beta  ]==> ((a a)(^y.y))
  8. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  3976/99390. ------  

  1. ==[ start ]==> (((a (a a)) a)((^a.a)(a a)))
  2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(a a)))
  3. ==[ beta  ]==> (((a (a a)) a)(a a))

     REDUCED to normal form.

  ------  3977/99408. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))((a a) a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))((a a) a))
  3. ==[ beta  ]==> ((a (a a))((a a) a))

     REDUCED to normal form.

  ------  3978/99417. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.z)))
  3. ==[ beta  ]==> (((a a)(^x.(x x)))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  3979/99435. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1) a))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1) a))
  4. ==[ alpha ]==> ((^x.x)((^y.y) a))
  5. ==[ beta  ]==> ((^y.y) a)
  6. ==[ alpha ]==> ((^x.x) a)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3980/99444. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(a (^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.z)))

     REDUCED to normal form.

  ------  3981/99461. ------  

  1. ==[ start ]==> (^a.((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> (^x.((^y.x)(x (^z.z))))
  3. ==[ beta  ]==> (^x.x)

     REDUCED to normal form.

  ------  3982/99462. ------  

  1. ==[ start ]==> (a ((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> (a ((^x.a)(a (^y.y))))
  3. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  3983/99519. ------  

  1. ==[ start ]==> ((^a.b)(^b.(a (a a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(a (a a))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3984/99717. ------  

  1. ==[ start ]==> ((^a.(^b.a))(^c.((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> (^y.(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> (^x.(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  3985/100215. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a)) c)
  2. ==[ alpha ]==> (((a (^x.x))(^y.a)) c)

     REDUCED to normal form.

  ------  3986/100239. ------  

  1. ==[ start ]==> ((^a.a)((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z))))
  3. ==[ beta  ]==> ((^y.a)(a (^z.z)))
  4. ==[ alpha ]==> ((^x.a)(a (^y.y)))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  3987/100266. ------  

  1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> (((^y.(^z.z))((^x1.x1) a))((^y.(^z.z))((^x1.x1) a)))
  4. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))((^z1.z1) a)))
  5. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) a)))
  6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a)))
  7. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1) a))
  8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a))
  9. ==[ beta  ]==> (^y.y)
 10. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3988/100293. ------  

  1. ==[ start ]==> ((^a.b)((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((^x.b)((^y.y)(a (a a))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  3989/100296. ------  

  1. ==[ start ]==> ((a b)(^b.(a (a a))))
  2. ==[ alpha ]==> ((a b)(^x.(a (a a))))

     REDUCED to normal form.

  ------  3990/100374. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.a)))
  3. ==[ beta  ]==> (((^z.(^x1.x1))(^y1.a))(^y.y))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.x1))
  5. ==[ beta  ]==> ((^y.y)(^x1.x1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3991/100395. ------  

  1. ==[ start ]==> (((a a) b)(^c.d))
  2. ==[ alpha ]==> (((a a) b)(^x.d))

     REDUCED to normal form.

  ------  3992/100413. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(x1 (x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 (x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (y y))))
  5. ==[ beta  ]==> (^y.(y (y y)))
  6. ==[ alpha ]==> (^x.(x (x x)))

     REDUCED to normal form.

  ------  3993/100491. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((^x.(^y.x))((a a)((^z.z) a)))
  3. ==[ beta  ]==> (^y.((a a)((^z.z) a)))
  4. ==[ alpha ]==> (^x.((a a)((^y.y) a)))
  5. ==[ beta  ]==> (^x.((a a) a))

     REDUCED to normal form.

  ------  3994/100494. ------  

  1. ==[ start ]==> ((a (^b.a))(^c.((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.z) a)))
  3. ==[ beta  ]==> ((a (^x.a))(^y.a))

     REDUCED to normal form.

  ------  3995/100512. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  3996/100563. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ eta   ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> ((^y.(^z.z))(a (^x1.x1)))
  6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z)))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3997/100665. ------  

  1. ==[ start ]==> (((a a)(^b.a))(^c.c))
  2. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  3998/100683. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.((^y1.y1) x1)))
  3. ==[ eta   ]==> (((^x.(^y.y))(a (^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1))
  5. ==[ beta  ]==> ((^y.y)(^x1.x1))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  3999/100734. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(a (^z.z))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4000/100755. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.y)))
  3. ==[ beta  ]==> (((a a) a)(^y.(^z.y)))
  4. ==[ alpha ]==> (((a a) a)(^x.(^y.x)))

     REDUCED to normal form.

  ------  4001/100809. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((a (a a))(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((a (a a))(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  4002/100833. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z))(^x1.x1)))
  3. ==[ beta  ]==> (((^y.(^z.z))(^x1.x1))(((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1))))
  4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.(^y1.y1))(^z1.z1))((^x2.(^y2.y2))(^z2.z2))))
  5. ==[ beta  ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.z1))((^x2.(^y2.y2))(^z2.z2))))
  6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.x1))((^y1.(^z1.z1))(^x2.x2))))
  7. ==[ beta  ]==> (((^y.(^z.z))(^x1.x1))((^y1.(^z1.z1))(^x2.x2)))
  8. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1)))
  9. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1)))
 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
 11. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
 12. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
 13. ==[ beta  ]==> (^y.y)
 14. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4003/100872. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(x1 (^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 (^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z))))
  5. ==[ beta  ]==> (^y.(y (^z.z)))
  6. ==[ alpha ]==> (^x.(x (^y.y)))

     REDUCED to normal form.

  ------  4004/100908. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^b.b))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.y))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  4005/100953. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^a.b))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.b))
  3. ==[ beta  ]==> ((a (a a))(^y.b))
  4. ==[ alpha ]==> ((a (a a))(^x.b))

     REDUCED to normal form.

  ------  4006/100980. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  5. ==[ beta  ]==> (^y.(y y))
  6. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4007/100989. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^b.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.a))

     REDUCED to normal form.

  ------  4008/101019. ------  

  1. ==[ start ]==> ((a a)((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a a)((^x.a)(a (^y.y))))
  3. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  4009/101037. ------  

  1. ==[ start ]==> (((^a.a) a)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(^z.a)))
  3. ==[ beta  ]==> (a ((a (^y.y))(^z.a)))
  4. ==[ alpha ]==> (a ((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  4010/101046. ------  

  1. ==[ start ]==> ((a (a a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) a)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  4011/101064. ------  

  1. ==[ start ]==> (((a a) a)((a a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a) a)((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  4012/101073. ------  

  1. ==[ start ]==> ((a b)((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((a b)((^x.x)(a (a a))))
  3. ==[ beta  ]==> ((a b)(a (a a)))

     REDUCED to normal form.

  ------  4013/101091. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a (a a)) a))
  2. ==[ alpha ]==> (((a a)(^x.x))((a (a a)) a))

     REDUCED to normal form.

  ------  4014/101118. ------  

  1. ==[ start ]==> (((^a.a) b)(((^a.a) a) b))
  2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) b))
  3. ==[ beta  ]==> (b (((^y.y) a) b))
  4. ==[ alpha ]==> (b (((^x.x) a) b))
  5. ==[ beta  ]==> (b (a b))

     REDUCED to normal form.

  ------  4015/101127. ------  

  1. ==[ start ]==> (((a a)(a a))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  4016/101154. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.a)))
  3. ==[ beta  ]==> ((a (a (^x.x)))(^z.z))
  4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y))

     REDUCED to normal form.

  ------  4017/101163. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.(^z.z))(b ((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4018/101190. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (a (a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (a (a a))))
  3. ==[ beta  ]==> ((^y.y)(a (a (a a))))
  4. ==[ alpha ]==> ((^x.x)(a (a (a a))))
  5. ==[ beta  ]==> (a (a (a a)))

     REDUCED to normal form.

  ------  4019/101199. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.(a a)) a))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y)) a))
  3. ==[ beta  ]==> (((a (^x.x)) a)(a a))

     REDUCED to normal form.

  ------  4020/101217. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((a (^y.y))(((^z.z) a)(a a)))
  4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a a)))
  5. ==[ beta  ]==> ((a (^x.x))(a (a a)))

     REDUCED to normal form.

  ------  4021/101226. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.a) b))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a) b))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y))) a)

     REDUCED to normal form.

  ------  4022/101244. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a (^y.y))(a (^z.z)))
  6. ==[ alpha ]==> ((a (^x.x))(a (^y.y)))

     REDUCED to normal form.

  ------  4023/101271. ------  

  1. ==[ start ]==> ((a (^b.a))((a a)((^a.a) a)))
  2. ==[ alpha ]==> ((a (^x.a))((a a)((^y.y) a)))
  3. ==[ beta  ]==> ((a (^x.a))((a a) a))

     REDUCED to normal form.

  ------  4024/101289. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(y y))))

     REDUCED to normal form.

  ------  4025/101307. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z) a)(^x1.x1)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4026/101316. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))((^b.a)(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(a a)) a)

     REDUCED to normal form.

  ------  4027/101343. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.z))))
  5. ==[ beta  ]==> ((a a)(^y.y))
  6. ==[ alpha ]==> ((a a)(^x.x))

     REDUCED to normal form.

  ------  4028/101352. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(b c))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(b c))
  3. ==[ beta  ]==> ((^y.a)(b c))
  4. ==[ alpha ]==> ((^x.a)(b c))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4029/101388. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) a) a))
  2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a) a))
  3. ==[ beta  ]==> (((a (^x.x)) b)(a a))

     REDUCED to normal form.

  ------  4030/101415. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a)) b))
  2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.y)) b))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) b))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) b))

     REDUCED to normal form.

  ------  4031/101433. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (a (^z.z))))
  3. ==[ beta  ]==> (((^y.y) a)(b (a (^z.z))))
  4. ==[ alpha ]==> (((^x.x) a)(b (a (^y.y))))
  5. ==[ beta  ]==> (a (b (a (^y.y))))
  6. ==[ alpha ]==> (a (b (a (^x.x))))

     REDUCED to normal form.

  ------  4032/101442. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a a) c))
  2. ==[ alpha ]==> (((a a)(^x.a))((a a) c))

     REDUCED to normal form.

  ------  4033/101460. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a ((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(a ((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a)))
  5. ==[ beta  ]==> (a ((^y.y) a))
  6. ==[ alpha ]==> (a ((^x.x) a))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  4034/101469. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z))) a)

     REDUCED to normal form.

  ------  4035/101496. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(^x1.x1)) b))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) b))
  5. ==[ beta  ]==> ((a (^x.x))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  4036/101514. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(a (^y.y))))

     REDUCED to normal form.

  ------  4037/101532. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(a (^b.a)))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(a (^y.a)))
  3. ==[ beta  ]==> (((a a) a)(a (^y.a)))
  4. ==[ alpha ]==> (((a a) a)(a (^x.a)))

     REDUCED to normal form.

  ------  4038/101559. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(a a)))
  3. ==[ beta  ]==> (((a (^x.x))(a (^y.y)))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z))

     REDUCED to normal form.

  ------  4039/101586. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> ((a (a a))(a (^y.y)))
  6. ==[ alpha ]==> ((a (a a))(a (^x.x)))

     REDUCED to normal form.

  ------  4040/101604. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a (^y.y)) a))
  3. ==[ beta  ]==> ((a a)((a (^y.y)) a))
  4. ==[ alpha ]==> ((a a)((a (^x.x)) a))

     REDUCED to normal form.

  ------  4041/101613. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(^z.z)))
  3. ==[ beta  ]==> ((a (a (a a)))(^y.y))
  4. ==[ alpha ]==> ((a (a (a a)))(^x.x))

     REDUCED to normal form.

  ------  4042/101622. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(b (a a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (a a)))
  3. ==[ beta  ]==> ((^y.(y y))(b (a a)))
  4. ==[ alpha ]==> ((^x.(x x))(b (a a)))
  5. ==[ beta  ]==> ((b (a a))(b (a a)))

     REDUCED to normal form.

  ------  4043/101649. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(a (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(a (a (^y.y))))
  5. ==[ beta  ]==> (a (a (^y.y)))
  6. ==[ alpha ]==> (a (a (^x.x)))

     REDUCED to normal form.

  ------  4044/101685. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((^a.a) b))
  2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y) b))
  3. ==[ beta  ]==> ((a b)((^y.y) b))
  4. ==[ alpha ]==> ((a b)((^x.x) b))
  5. ==[ beta  ]==> ((a b) b)

     REDUCED to normal form.

  ------  4045/101703. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(b a))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b a))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(b a))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(b a))
  5. ==[ beta  ]==> ((^y.y)(b a))
  6. ==[ alpha ]==> ((^x.x)(b a))
  7. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  4046/101712. ------  

  1. ==[ start ]==> (((a (a a)) a)((a a)(^a.a)))
  2. ==[ alpha ]==> (((a (a a)) a)((a a)(^x.x)))

     REDUCED to normal form.

  ------  4047/101730. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(a b))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(a b))
  3. ==[ beta  ]==> ((a (a a))(a b))

     REDUCED to normal form.

  ------  4048/101739. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))((a a) a))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a) a))

     REDUCED to normal form.

  ------  4049/101757. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a (a a)))
  3. ==[ beta  ]==> ((^y.y)(a (a a)))
  4. ==[ alpha ]==> ((^x.x)(a (a a)))
  5. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  4050/101766. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z) a))
  3. ==[ beta  ]==> (((a (^x.x))(^y.a)) a)

     REDUCED to normal form.

  ------  4051/101792. ------  

  1. ==[ start ]==> (^a.(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> (^x.(((^y.y) x)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (^x.(x (^z.(^x1.x1))))
  4. ==[ alpha ]==> (^x.(x (^y.(^z.z))))

     REDUCED to normal form.

  ------  4052/101793. ------  

  1. ==[ start ]==> (a (((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> (a (((^x.x) a)(^y.(^z.z))))
  3. ==[ beta  ]==> (a (a (^y.(^z.z))))
  4. ==[ alpha ]==> (a (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  4053/101850. ------  

  1. ==[ start ]==> ((^a.b)(^c.(^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)(^y.(^z.(z z))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  4054/102573. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a))) a)
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z))) a)
  3. ==[ beta  ]==> ((a (^y.(^z.z))) a)
  4. ==[ alpha ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  4055/102579. ------  

  1. ==[ start ]==> ((^a.a)(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y) a)(^z.(^x1.x1)))
  4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z)))
  5. ==[ beta  ]==> (a (^y.(^z.z)))
  6. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  4056/102588. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4057/102606. ------  

  1. ==[ start ]==> ((^a.(a a))((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(^z.a)))
  3. ==[ beta  ]==> (((a (^y.y))(^z.a))((a (^y.y))(^z.a)))
  4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.z))(^x1.a)))

     REDUCED to normal form.

  ------  4058/102633. ------  

  1. ==[ start ]==> ((^a.b)((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((^x.b)((a a)(^y.(y y))))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  4059/102636. ------  

  1. ==[ start ]==> ((a b)(^c.(^a.(a a))))
  2. ==[ alpha ]==> ((a b)(^x.(^y.(y y))))

     REDUCED to normal form.

  ------  4060/102645. ------  

  1. ==[ start ]==> (((^a.a)(a a))(^b.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (a a))))
  3. ==[ beta  ]==> ((a a)(^y.(a (a a))))
  4. ==[ alpha ]==> ((a a)(^x.(a (a a))))

     REDUCED to normal form.

  ------  4061/102669. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1)))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4062/102753. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  4063/102762. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^a.(a (a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (y y))))

     REDUCED to normal form.

  ------  4064/102831. ------  

  1. ==[ start ]==> ((^a.(^b.a))(b (^b.a)))
  2. ==[ alpha ]==> ((^x.(^y.x))(b (^z.a)))
  3. ==[ beta  ]==> (^y.(b (^z.a)))
  4. ==[ alpha ]==> (^x.(b (^y.a)))

     REDUCED to normal form.

  ------  4065/102903. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ eta   ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z)))

     REDUCED to normal form.

  ------  4066/102942. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1) a)))
  3. ==[ beta  ]==> ((^y.y)(^y1.((^z1.z1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  4067/103023. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.a)))
  5. ==[ beta  ]==> (^y.(^z.a))
  6. ==[ alpha ]==> (^x.(^y.a))

     REDUCED to normal form.

  ------  4068/103032. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((^y1.y1) x1)))
  3. ==[ eta   ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1))

     REDUCED to normal form.

  ------  4069/103074. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))(b (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4070/103095. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(^b.c))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.c))
  3. ==[ beta  ]==> (((a a) a)(^y.c))
  4. ==[ alpha ]==> (((a a) a)(^x.c))

     REDUCED to normal form.

  ------  4071/103173. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a (^y.y)) a))
  3. ==[ beta  ]==> (((a (^y.y)) a)(((a (^y.y)) a)((a (^y.y)) a)))
  4. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y)) a)((a (^z.z)) a)))

     REDUCED to normal form.

  ------  4072/103212. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  5. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  6. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  4073/103248. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^c.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(a a)))
  3. ==[ beta  ]==> ((a b)(^y.(a a)))
  4. ==[ alpha ]==> ((a b)(^x.(a a)))

     REDUCED to normal form.

  ------  4074/103266. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.(^x1.(^y1.y1))))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.(^y1.y1))))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1))))
  7. ==[ beta  ]==> (^y.(^z.(^x1.x1)))
  8. ==[ alpha ]==> (^x.(^y.(^z.z)))

     REDUCED to normal form.

  ------  4075/103293. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(a a)))
  3. ==[ beta  ]==> ((a (a a))(^y.(a a)))
  4. ==[ alpha ]==> ((a (a a))(^x.(a a)))

     REDUCED to normal form.

  ------  4076/103302. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^a.b))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.b))

     REDUCED to normal form.

  ------  4077/103320. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  5. ==[ beta  ]==> (^y.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4078/103329. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(z z)))

     REDUCED to normal form.

  ------  4079/103356. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.x1))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(^x1.x1))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  4080/103368. ------  

  1. ==[ start ]==> ((a a)(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  4081/103377. ------  

  1. ==[ start ]==> ((a (^a.a))((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))((^y.a)(a (^z.z))))
  3. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  4082/103395. ------  

  1. ==[ start ]==> ((a (a a))((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  4083/103404. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a)))
  3. ==[ beta  ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a)))
  5. ==[ beta  ]==> ((^y.(^z.z))((^x1.x1) a))
  6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4084/103422. ------  

  1. ==[ start ]==> ((a b)((a a)(^a.(a a))))
  2. ==[ alpha ]==> ((a b)((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  4085/103431. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (a a))))
  3. ==[ beta  ]==> ((a a)((^y.y)(a (a a))))
  4. ==[ alpha ]==> ((a a)((^x.x)(a (a a))))
  5. ==[ beta  ]==> ((a a)(a (a a)))

     REDUCED to normal form.

  ------  4086/103458. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.x1)))
  3. ==[ beta  ]==> ((a (^x.(^y.y)))((^x1.x1)(^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1)))
  5. ==[ beta  ]==> ((a (^x.(^y.y)))(^x1.x1))
  6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z))

     REDUCED to normal form.

  ------  4087/103476. ------  

  1. ==[ start ]==> (((a a)(a a))(((^a.a) a) b))
  2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a) b))
  3. ==[ beta  ]==> (((a a)(a a))(a b))

     REDUCED to normal form.

  ------  4088/103512. ------  

  1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a)))
  3. ==[ beta  ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a)))
  4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a)))
  5. ==[ beta  ]==> (^y.y)
  6. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4089/103521. ------  

  1. ==[ start ]==> (((a a) b)(b ((^a.a) a)))
  2. ==[ alpha ]==> (((a a) b)(b ((^x.x) a)))
  3. ==[ beta  ]==> (((a a) b)(b a))

     REDUCED to normal form.

  ------  4090/103539. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.(y1 y1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.(y1 y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z))))
  5. ==[ beta  ]==> ((^y.y)(^z.(z z)))
  6. ==[ alpha ]==> ((^x.x)(^y.(y y)))
  7. ==[ beta  ]==> (^y.(y y))
  8. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4091/103548. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(a (a (a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(a (a (a a))))

     REDUCED to normal form.

  ------  4092/103575. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a (a a)))

     REDUCED to normal form.

  ------  4093/103602. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a (^x1.x1))))

     REDUCED to normal form.

  ------  4094/103620. ------  

  1. ==[ start ]==> ((a (^b.a))(b (^b.a)))
  2. ==[ alpha ]==> ((a (^x.a))(b (^y.a)))

     REDUCED to normal form.

  ------  4095/103665. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a)(^z.z)))
  3. ==[ beta  ]==> (((a (^x.x))(a a))(a (^z.z)))
  4. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y)))

     REDUCED to normal form.

  ------  4096/103692. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a a)((a (^y.y))(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z))))

     REDUCED to normal form.

  ------  4097/103701. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a (^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)((^z.(^x1.x1))(a (^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a (^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4098/103728. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a)))
  3. ==[ beta  ]==> ((^y.y)((^y1.y1)((^z1.z1) a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a)))
  5. ==[ beta  ]==> ((^y.y)((^z.z) a))
  6. ==[ alpha ]==> ((^x.x)((^y.y) a))
  7. ==[ beta  ]==> ((^y.y) a)
  8. ==[ alpha ]==> ((^x.x) a)
  9. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4099/103782. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1))))
  3. ==[ beta  ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(^z1.z1))))
  4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(^y1.y1))))
  5. ==[ beta  ]==> (a ((^y.(^z.z))(^x1.(^y1.y1))))
  6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1))))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4100/103791. ------  

  1. ==[ start ]==> (((a a)(^b.a))(b (a (^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))(b (a (^y.y))))

     REDUCED to normal form.

  ------  4101/103809. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a)))
  5. ==[ beta  ]==> ((^y.y)(^z.a))
  6. ==[ alpha ]==> ((^x.x)(^y.a))
  7. ==[ beta  ]==> (^y.a)
  8. ==[ alpha ]==> (^x.a)

     REDUCED to normal form.

  ------  4102/103818. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a ((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((^x1.x1) a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(a a))

     REDUCED to normal form.

  ------  4103/103845. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(a a)))
  3. ==[ beta  ]==> ((a (^y.y))((a (^z.z))(a a)))
  4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  4104/103863. ------  

  1. ==[ start ]==> ((a (^a.(a a)))(b (^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(^z.z))))

     REDUCED to normal form.

  ------  4105/103908. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.a))(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(^x1.x1)))

     REDUCED to normal form.

  ------  4106/103935. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a a))((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> ((a (a a))((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  4107/103962. ------  

  1. ==[ start ]==> ((a (a (a a)))((a (^a.a)) a))
  2. ==[ alpha ]==> ((a (a (a a)))((a (^x.x)) a))

     REDUCED to normal form.

  ------  4108/103971. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(^y1.y1)))
  3. ==[ beta  ]==> ((^y.(y y))((^z.(^x1.x1))(^y1.y1)))
  4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.x1)))
  5. ==[ beta  ]==> (((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1)))
  6. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1)))
  7. ==[ beta  ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1)))
  8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1)))
  9. ==[ beta  ]==> ((^y.(^z.z))(^x1.x1))
 10. ==[ alpha ]==> ((^x.(^y.y))(^z.z))
 11. ==[ beta  ]==> (^y.y)
 12. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4109/103998. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(^y1.(^z1.z1))))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1))))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.x)(^y.(^z.z)))
  7. ==[ beta  ]==> (^y.(^z.z))
  8. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4110/104034. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((a a)(a a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)((a a)(a a)))
  3. ==[ beta  ]==> ((a b)((a a)(a a)))

     REDUCED to normal form.

  ------  4111/104052. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.(^x1.x1))))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.y)(a (^z.(^x1.x1))))
  6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z))))
  7. ==[ beta  ]==> (a (^y.(^z.z)))
  8. ==[ alpha ]==> (a (^x.(^y.y)))

     REDUCED to normal form.

  ------  4112/104061. ------  

  1. ==[ start ]==> (((a (a a)) a)(b a))

     REDUCED to normal form.

  ------  4113/104079. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(a a)))
  3. ==[ beta  ]==> ((a (a a))((^y.y)(a a)))
  4. ==[ alpha ]==> ((a (a a))((^x.x)(a a)))
  5. ==[ beta  ]==> ((a (a a))(a a))

     REDUCED to normal form.

  ------  4114/104088. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(a b))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(a b))

     REDUCED to normal form.

  ------  4115/104106. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)(^y1.y1)))
  3. ==[ beta  ]==> ((^y.y)((^x1.x1)(^y1.y1)))
  4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z)))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4116/104115. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(a (a a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (a a)))

     REDUCED to normal form.

  ------  4117/104142. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a a))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(a a))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  4118/104931. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a))) b)
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z))) b)
  3. ==[ beta  ]==> ((a (^y.(^z.z))) b)
  4. ==[ alpha ]==> ((a (^x.(^y.y))) b)

     REDUCED to normal form.

  ------  4119/104955. ------  

  1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4120/105021. ------  

  1. ==[ start ]==> (((a a)(^a.a))(^b.(a (a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (a a))))

     REDUCED to normal form.

  ------  4121/105036. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a a)) a))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a)) a))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4122/105129. ------  

  1. ==[ start ]==> (((a (^a.a)) a)(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  4123/105198. ------  

  1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a)) c))
  2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1)) c))
  3. ==[ beta  ]==> (^y.((^z.(^x1.x1)) c))
  4. ==[ alpha ]==> (^x.((^y.(^z.z)) c))
  5. ==[ beta  ]==> (^x.(^z.z))
  6. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4124/105237. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((^y.y)(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z))))
  5. ==[ beta  ]==> (^y.(^z.(z z)))
  6. ==[ alpha ]==> (^x.(^y.(y y)))

     REDUCED to normal form.

  ------  4125/105318. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^b.((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)(^y.a))

     REDUCED to normal form.

  ------  4126/105399. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.a)))

     REDUCED to normal form.

  ------  4127/105441. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1)) b))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4128/105534. ------  

  1. ==[ start ]==> (((^a.(a a)) a)(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((a a)(^y.(a (^z.z))))
  4. ==[ alpha ]==> ((a a)(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  4129/105579. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.b))
  3. ==[ beta  ]==> ((^y.y)(^x1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  4130/105633. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.b))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.z))
  3. ==[ beta  ]==> (((^y.y)(^y.y))(^z.z))
  4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((^y.y)(^z.z))
  6. ==[ alpha ]==> ((^x.x)(^y.y))
  7. ==[ beta  ]==> (^y.y)
  8. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4131/105642. ------  

  1. ==[ start ]==> (((a (a a)) a)(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  4132/105669. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))(^b.(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(a a)))

     REDUCED to normal form.

  ------  4133/105696. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^b.(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  4134/105723. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.y1)))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1)))

     REDUCED to normal form.

  ------  4135/105753. ------  

  1. ==[ start ]==> ((a (^a.a))(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (^x.x))(a (^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z))))

     REDUCED to normal form.

  ------  4136/105762. ------  

  1. ==[ start ]==> (((^a.a) a)((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)((^y.a)(a (^z.z))))
  3. ==[ beta  ]==> (a ((^y.a)(a (^z.z))))
  4. ==[ alpha ]==> (a ((^x.a)(a (^y.y))))
  5. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  4137/105780. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.a)))
  3. ==[ beta  ]==> ((^y.y)((a (^z.z))(^x1.a)))
  4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a)))
  5. ==[ beta  ]==> ((a (^y.y))(^z.a))
  6. ==[ alpha ]==> ((a (^x.x))(^y.a))

     REDUCED to normal form.

  ------  4138/105789. ------  

  1. ==[ start ]==> (((a a) a)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z) a)))
  3. ==[ beta  ]==> (((a a) a)(^y.y))
  4. ==[ alpha ]==> (((a a) a)(^x.x))

     REDUCED to normal form.

  ------  4139/105807. ------  

  1. ==[ start ]==> (((^a.a)(a a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.(y y))))
  3. ==[ beta  ]==> ((a a)((a a)(^y.(y y))))
  4. ==[ alpha ]==> ((a a)((a a)(^x.(x x))))

     REDUCED to normal form.

  ------  4140/105816. ------  

  1. ==[ start ]==> (((a a)(^a.a))((^a.a)(a (a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (a a))))
  3. ==[ beta  ]==> (((a a)(^x.x))(a (a a)))

     REDUCED to normal form.

  ------  4141/105834. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))((a (a a)) a))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a)) a))

     REDUCED to normal form.

  ------  4142/105843. ------  

  1. ==[ start ]==> (((^a.a) b)((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.z)))
  3. ==[ beta  ]==> (b ((^y.(y y))(^z.z)))
  4. ==[ alpha ]==> (b ((^x.(x x))(^y.y)))
  5. ==[ beta  ]==> (b ((^y.y)(^y.y)))
  6. ==[ alpha ]==> (b ((^x.x)(^y.y)))
  7. ==[ beta  ]==> (b (^y.y))
  8. ==[ alpha ]==> (b (^x.x))

     REDUCED to normal form.

  ------  4143/105870. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1))))
  5. ==[ beta  ]==> ((^y.a)(^z.(^x1.x1)))
  6. ==[ alpha ]==> ((^x.a)(^y.(^z.z)))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4144/105897. ------  

  1. ==[ start ]==> (((a a) b)((^a.(^a.a))(^b.a)))
  2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.a)))
  3. ==[ beta  ]==> (((a a) b)(^y.y))
  4. ==[ alpha ]==> (((a a) b)(^x.x))

     REDUCED to normal form.

  ------  4145/105924. ------  

  1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(z z))))
  3. ==[ beta  ]==> (((a (^x.x)) a)(^z.(z z)))
  4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y y)))

     REDUCED to normal form.

  ------  4146/105942. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z)) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.(z z)) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) a))
  5. ==[ beta  ]==> ((a (^x.x))(a a))

     REDUCED to normal form.

  ------  4147/105969. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.a) b))
  3. ==[ beta  ]==> ((^y.y)((^z.a) b))
  4. ==[ alpha ]==> ((^x.x)((^y.a) b))
  5. ==[ beta  ]==> ((^y.a) b)
  6. ==[ alpha ]==> ((^x.a) b)
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4148/105996. ------  

  1. ==[ start ]==> ((a (^b.a))((^a.(^a.a)) c))
  2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z)) c))
  3. ==[ beta  ]==> ((a (^x.a))(^z.z))
  4. ==[ alpha ]==> ((a (^x.a))(^y.y))

     REDUCED to normal form.

  ------  4149/106014. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))((a a)((^a.a) a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)((^y.y) a)))
  3. ==[ beta  ]==> (((a a)(a (^x.x)))((a a) a))

     REDUCED to normal form.

  ------  4150/106032. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(a (^a.(a a))))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (^z.(z z))))
  3. ==[ beta  ]==> ((^y.y)(a (^z.(z z))))
  4. ==[ alpha ]==> ((^x.x)(a (^y.(y y))))
  5. ==[ beta  ]==> (a (^y.(y y)))
  6. ==[ alpha ]==> (a (^x.(x x)))

     REDUCED to normal form.

  ------  4151/106077. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> ((^y.a)((a (^z.z))(^x1.(^y1.y1))))
  4. ==[ alpha ]==> ((^x.a)((a (^y.y))(^z.(^x1.x1))))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4152/106104. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^b.a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.a)))
  3. ==[ beta  ]==> ((^y.y)((a a)(^y1.a)))
  4. ==[ alpha ]==> ((^x.x)((a a)(^y.a)))
  5. ==[ beta  ]==> ((a a)(^y.a))
  6. ==[ alpha ]==> ((a a)(^x.a))

     REDUCED to normal form.

  ------  4153/106113. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((^a.a)((^a.a) a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z) a)))
  3. ==[ beta  ]==> (((a (^x.x)) b)((^z.z) a))
  4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) a))
  5. ==[ beta  ]==> (((a (^x.x)) b) a)

     REDUCED to normal form.

  ------  4154/106140. ------  

  1. ==[ start ]==> ((((^a.a) a) a)((^b.a)(^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) a)((^y.a)(^z.z)))
  3. ==[ beta  ]==> ((a a)((^y.a)(^z.z)))
  4. ==[ alpha ]==> ((a a)((^x.a)(^y.y)))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  4155/106158. ------  

  1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z)) b))
  3. ==[ beta  ]==> (((^y.y) a)((a (^z.z)) b))
  4. ==[ alpha ]==> (((^x.x) a)((a (^y.y)) b))
  5. ==[ beta  ]==> (a ((a (^y.y)) b))
  6. ==[ alpha ]==> (a ((a (^x.x)) b))

     REDUCED to normal form.

  ------  4156/106167. ------  

  1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))(^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((a a)(^x.a))(^z.z))
  4. ==[ alpha ]==> (((a a)(^x.a))(^y.y))

     REDUCED to normal form.

  ------  4157/106194. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.a)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.(^z.z)))(^y1.a))
  4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.a))

     REDUCED to normal form.

  ------  4158/106239. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a)) b))
  2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z)) b))
  3. ==[ beta  ]==> ((a (^x.(x x)))(^z.z))
  4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y))

     REDUCED to normal form.

  ------  4159/106257. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))((a a)(a (^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(a (^y.y))))
  3. ==[ beta  ]==> (((a a) a)((a a)(a (^y.y))))
  4. ==[ alpha ]==> (((a a) a)((a a)(a (^x.x))))

     REDUCED to normal form.

  ------  4160/106311. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))(b b))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))(b b))
  3. ==[ beta  ]==> ((a (a a))(b b))

     REDUCED to normal form.

  ------  4161/106329. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> ((a a)((^y.y)(a (^z.z))))
  4. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y))))
  5. ==[ beta  ]==> ((a a)(a (^y.y)))
  6. ==[ alpha ]==> ((a a)(a (^x.x)))

     REDUCED to normal form.

  ------  4162/106347. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.a)) a))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z)) a))
  3. ==[ beta  ]==> ((^y.(y y))((a (^z.z)) a))
  4. ==[ alpha ]==> ((^x.(x x))((a (^y.y)) a))
  5. ==[ beta  ]==> (((a (^y.y)) a)((a (^y.y)) a))
  6. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y)) a))

     REDUCED to normal form.

  ------  4163/106374. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a) b))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a) b))
  3. ==[ beta  ]==> ((^y.y)((a a) b))
  4. ==[ alpha ]==> ((^x.x)((a a) b))
  5. ==[ beta  ]==> ((a a) b)

     REDUCED to normal form.

  ------  4164/106410. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(b (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a) b)(b (^y.y)))
  3. ==[ beta  ]==> ((a b)(b (^y.y)))
  4. ==[ alpha ]==> ((a b)(b (^x.x)))

     REDUCED to normal form.

  ------  4165/106428. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a) b))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z) b))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((^z.z) b))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b))
  5. ==[ beta  ]==> ((^y.y)((^z.z) b))
  6. ==[ alpha ]==> ((^x.x)((^y.y) b))
  7. ==[ beta  ]==> ((^y.y) b)
  8. ==[ alpha ]==> ((^x.x) b)
  9. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  4166/106437. ------  

  1. ==[ start ]==> (((a (a a)) a)(a (^a.(^a.a))))
  2. ==[ alpha ]==> (((a (a a)) a)(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  4167/106455. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)(^y.y)))
  3. ==[ beta  ]==> ((a (a a))((a a)(^y.y)))
  4. ==[ alpha ]==> ((a (a a))((a a)(^x.x)))

     REDUCED to normal form.

  ------  4168/106464. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))((^a.a)(a a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a a)))
  3. ==[ beta  ]==> (((a a)(^x.(x x)))(a a))

     REDUCED to normal form.

  ------  4169/106482. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a a) a))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a a) a))
  3. ==[ beta  ]==> ((^y.y)((a a) a))
  4. ==[ alpha ]==> ((^x.x)((a a) a))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  4170/106491. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.a)(^a.a)))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.x1)))
  3. ==[ beta  ]==> (((a (^x.x))(^y.a))(^x1.x1))
  4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z))

     REDUCED to normal form.

  ------  4171/106518. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a (^a.a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (^x1.x1)))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(a (^x1.x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z)))

     REDUCED to normal form.

  ------  4172/106535. ------  

  1. ==[ start ]==> (^a.((^a.(a a))(a a)))
  2. ==[ alpha ]==> (^x.((^y.(y y))(x x)))
  3. ==[ beta  ]==> (^x.((x x)(x x)))

     REDUCED to normal form.

  ------  4173/106536. ------  

  1. ==[ start ]==> (a ((^a.(a a))(a a)))
  2. ==[ alpha ]==> (a ((^x.(x x))(a a)))
  3. ==[ beta  ]==> (a ((a a)(a a)))

     REDUCED to normal form.

  ------  4174/107133. ------  

  1. ==[ start ]==> ((^a.(a (a a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(a (^z.z))))
  3. ==[ beta  ]==> ((^y.(a (^z.z)))((^y.(a (^z.z)))(^y.(a (^z.z)))))
  4. ==[ alpha ]==> ((^x.(a (^y.y)))((^z.(a (^x1.x1)))(^y1.(a (^z1.z1)))))
  5. ==[ beta  ]==> (a (^y.y))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4175/107334. ------  

  1. ==[ start ]==> (((^a.(a a))(a a)) a)
  2. ==[ alpha ]==> (((^x.(x x))(a a)) a)
  3. ==[ beta  ]==> (((a a)(a a)) a)

     REDUCED to normal form.

  ------  4176/107340. ------  

  1. ==[ start ]==> ((^a.a)((^a.(a a))(a a)))
  2. ==[ alpha ]==> ((^x.x)((^y.(y y))(a a)))
  3. ==[ beta  ]==> ((^y.(y y))(a a))
  4. ==[ alpha ]==> ((^x.(x x))(a a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  4177/107367. ------  

  1. ==[ start ]==> ((^a.(a a))((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))((^y.a)(a (^z.z))))
  3. ==[ beta  ]==> (((^y.a)(a (^z.z)))((^y.a)(a (^z.z))))
  4. ==[ alpha ]==> (((^x.a)(a (^y.y)))((^z.a)(a (^x1.x1))))
  5. ==[ beta  ]==> (a ((^z.a)(a (^x1.x1))))
  6. ==[ alpha ]==> (a ((^x.a)(a (^y.y))))
  7. ==[ beta  ]==> (a a)

     REDUCED to normal form.

  ------  4178/107394. ------  

  1. ==[ start ]==> ((^a.b)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  4179/107475. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.(^y1.y1))))
  3. ==[ beta  ]==> (((^z.a)(^x1.(^y1.y1)))(^y.y))
  4. ==[ alpha ]==> (((^x.a)(^y.(^z.z)))(^x1.x1))
  5. ==[ beta  ]==> (a (^x1.x1))
  6. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4180/107541. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(z (z z))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(z (z z))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(y (y y))))

     REDUCED to normal form.

  ------  4181/107592. ------  

  1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(a (^x1.x1))))
  3. ==[ beta  ]==> (^y.((a (^z.z))(a (^x1.x1))))
  4. ==[ alpha ]==> (^x.((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  4182/107640. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  4183/107664. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)(a a)))
  3. ==[ eta   ]==> ((^y.y)((^z.a)(a a)))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a a)))
  5. ==[ beta  ]==> ((^y.a)(a a))
  6. ==[ alpha ]==> ((^x.a)(a a))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4184/107712. ------  

  1. ==[ start ]==> (((a (^a.a)) b)(^c.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.a)))

     REDUCED to normal form.

  ------  4185/107835. ------  

  1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.z))(a a)))
  3. ==[ beta  ]==> (^y.(y y))
  4. ==[ alpha ]==> (^x.(x x))

     REDUCED to normal form.

  ------  4186/107883. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.z)))

     REDUCED to normal form.

  ------  4187/107934. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(a (^z.z))))
  3. ==[ beta  ]==> (((^y.y)(a (^z.z)))(((^y.y)(a (^z.z)))((^y.y)(a (^z.z)))))
  4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a (^x1.x1)))((^y1.y1)(a (^z1.z1)))))
  5. ==[ beta  ]==> ((a (^y.y))(((^z.z)(a (^x1.x1)))((^y1.y1)(a (^z1.z1)))))
  6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a (^z.z)))((^x1.x1)(a (^y1.y1)))))
  7. ==[ beta  ]==> ((a (^x.x))((a (^z.z))((^x1.x1)(a (^y1.y1)))))
  8. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z)(a (^x1.x1)))))
  9. ==[ beta  ]==> ((a (^x.x))((a (^y.y))(a (^x1.x1))))
 10. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  4188/107937. ------  

  1. ==[ start ]==> ((a (a (a a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))(^x.(a (^y.y))))

     REDUCED to normal form.

  ------  4189/108036. ------  

  1. ==[ start ]==> (((a (a a)) a)(^b.b))
  2. ==[ alpha ]==> (((a (a a)) a)(^x.x))

     REDUCED to normal form.

  ------  4190/108081. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.b))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.b))
  3. ==[ beta  ]==> ((^y.y)(^x1.b))
  4. ==[ alpha ]==> ((^x.x)(^y.b))
  5. ==[ beta  ]==> (^y.b)
  6. ==[ alpha ]==> (^x.b)

     REDUCED to normal form.

  ------  4191/108090. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^c.a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.a))

     REDUCED to normal form.

  ------  4192/108117. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^b.a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.a))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(^x1.a))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a))

     REDUCED to normal form.

  ------  4193/108135. ------  

  1. ==[ start ]==> (((^a.(a a))(a a))(^a.a))
  2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.y))
  3. ==[ beta  ]==> (((a a)(a a))(^y.y))
  4. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  4194/108147. ------  

  1. ==[ start ]==> ((a a)((^a.(a a))(a a)))
  2. ==[ alpha ]==> ((a a)((^x.(x x))(a a)))
  3. ==[ beta  ]==> ((a a)((a a)(a a)))

     REDUCED to normal form.

  ------  4195/108165. ------  

  1. ==[ start ]==> (((^a.a) a)(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> (a (((^y.y) a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> (a (((^x.x) a)(^y.(^z.z))))
  5. ==[ beta  ]==> (a (a (^y.(^z.z))))
  6. ==[ alpha ]==> (a (a (^x.(^y.y))))

     REDUCED to normal form.

  ------  4196/108174. ------  

  1. ==[ start ]==> ((a (a a))((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a a))((^x.a)(a (^y.y))))
  3. ==[ beta  ]==> ((a (a a)) a)

     REDUCED to normal form.

  ------  4197/108192. ------  

  1. ==[ start ]==> (((a a) a)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  4198/108201. ------  

  1. ==[ start ]==> ((a b)((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) a)))
  3. ==[ beta  ]==> ((a b)(^y.y))
  4. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  4199/108219. ------  

  1. ==[ start ]==> (((a a)(^a.a))((a a)(^a.(a a))))
  2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y y))))

     REDUCED to normal form.

  ------  4200/108246. ------  

  1. ==[ start ]==> (((^a.a) b)((a (a a)) a))
  2. ==[ alpha ]==> (((^x.x) b)((a (a a)) a))
  3. ==[ beta  ]==> (b ((a (a a)) a))

     REDUCED to normal form.

  ------  4201/108255. ------  

  1. ==[ start ]==> (((a a)(a a))((^a.(a a))(^a.a)))
  2. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.y)))
  3. ==[ beta  ]==> (((a a)(a a))((^y.y)(^y.y)))
  4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y)))
  5. ==[ beta  ]==> (((a a)(a a))(^y.y))
  6. ==[ alpha ]==> (((a a)(a a))(^x.x))

     REDUCED to normal form.

  ------  4202/108273. ------  

  1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a) b))
  2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a) b))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a) b))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a) b))
  5. ==[ beta  ]==> (((^y.y) a) b)
  6. ==[ alpha ]==> (((^x.x) a) b)
  7. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  4203/108282. ------  

  1. ==[ start ]==> ((a (a (^a.a)))((^b.a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a (^x.x))) a)

     REDUCED to normal form.

  ------  4204/108300. ------  

  1. ==[ start ]==> (((a a) b)((a (^a.a)) c))
  2. ==[ alpha ]==> (((a a) b)((a (^x.x)) c))

     REDUCED to normal form.

  ------  4205/108318. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b ((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b ((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(b ((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(b ((^y.y) a)))
  5. ==[ beta  ]==> (b ((^y.y) a))
  6. ==[ alpha ]==> (b ((^x.x) a))
  7. ==[ beta  ]==> (b a)

     REDUCED to normal form.

  ------  4206/108345. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (a (a a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (a (a a))))
  3. ==[ beta  ]==> ((a (^y.y))(a (a (a a))))
  4. ==[ alpha ]==> ((a (^x.x))(a (a (a a))))

     REDUCED to normal form.

  ------  4207/108354. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(a a)) a))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z)) a))
  3. ==[ beta  ]==> (((a a)(^x.(^y.y)))(a a))

     REDUCED to normal form.

  ------  4208/108372. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) a)(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) a)(a a)))
  3. ==[ beta  ]==> ((^y.y)(((^z.z) a)(a a)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a)))
  5. ==[ beta  ]==> (((^y.y) a)(a a))
  6. ==[ alpha ]==> (((^x.x) a)(a a))
  7. ==[ beta  ]==> (a (a a))

     REDUCED to normal form.

  ------  4209/108381. ------  

  1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.a) b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) b))
  3. ==[ beta  ]==> (((a (^x.x))(^y.y)) a)

     REDUCED to normal form.

  ------  4210/108399. ------  

  1. ==[ start ]==> ((a (^b.a))((a (^a.a))(a (^a.a))))
  2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(a (^z.z))))

     REDUCED to normal form.

  ------  4211/108417. ------  

  1. ==[ start ]==> (((a a)(a (^a.a)))(b (^b.a)))
  2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.a)))

     REDUCED to normal form.

  ------  4212/108444. ------  

  1. ==[ start ]==> (((a (^a.a))(a a))(a (^a.(a a))))
  2. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.(y y))))

     REDUCED to normal form.

  ------  4213/108471. ------  

  1. ==[ start ]==> ((a ((^a.a) a))((^b.a)(a a)))
  2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(a a)))
  3. ==[ beta  ]==> ((a a)((^y.a)(a a)))
  4. ==[ alpha ]==> ((a a)((^x.a)(a a)))
  5. ==[ beta  ]==> ((a a) a)

     REDUCED to normal form.

  ------  4214/108480. ------  

  1. ==[ start ]==> (((^a.a)(^b.a))(c b))
  2. ==[ alpha ]==> (((^x.x)(^y.a))(c b))
  3. ==[ beta  ]==> ((^y.a)(c b))
  4. ==[ alpha ]==> ((^x.a)(c b))
  5. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4215/108507. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b c))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b c))
  3. ==[ beta  ]==> ((^y.y)(b c))
  4. ==[ alpha ]==> ((^x.x)(b c))
  5. ==[ beta  ]==> (b c)

     REDUCED to normal form.

  ------  4216/108516. ------  

  1. ==[ start ]==> (((a (^a.a)) b)((a a)(^b.a)))
  2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.a)))

     REDUCED to normal form.

  ------  4217/108543. ------  

  1. ==[ start ]==> ((((^a.a) a) a)(((^a.a) a) a))
  2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) a) a))
  3. ==[ beta  ]==> ((a a)(((^y.y) a) a))
  4. ==[ alpha ]==> ((a a)(((^x.x) a) a))
  5. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  4218/108570. ------  

  1. ==[ start ]==> (((a a)(^b.a))((a (^a.a)) b))
  2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y)) b))

     REDUCED to normal form.

  ------  4219/108588. ------  

  1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (a (^a.a))))
  2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)(b (a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)(b (a (^y.y))))
  5. ==[ beta  ]==> (b (a (^y.y)))
  6. ==[ alpha ]==> (b (a (^x.x)))

     REDUCED to normal form.

  ------  4220/108624. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a) a))
  3. ==[ beta  ]==> ((a (^y.y))((^z.a) a))
  4. ==[ alpha ]==> ((a (^x.x))((^y.a) a))
  5. ==[ beta  ]==> ((a (^x.x)) a)

     REDUCED to normal form.

  ------  4221/108642. ------  

  1. ==[ start ]==> ((a (^a.(a a)))((a (^a.a))(a a)))
  2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(a a)))

     REDUCED to normal form.

  ------  4222/108660. ------  

  1. ==[ start ]==> (((a a)((^a.a) a))(b (^a.(^a.a))))
  2. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.(^z.z))))
  3. ==[ beta  ]==> (((a a) a)(b (^y.(^z.z))))
  4. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y))))

     REDUCED to normal form.

  ------  4223/108687. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (^b.a)))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.a)))

     REDUCED to normal form.

  ------  4224/108714. ------  

  1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))(a a)))
  3. ==[ beta  ]==> ((a (a a))((^y.(^z.z))(a a)))
  4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a a)))
  5. ==[ beta  ]==> ((a (a a))(^y.y))
  6. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  4225/108732. ------  

  1. ==[ start ]==> (((^a.(a a)) a)((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a a)((a a)(^y.(^z.z))))
  4. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y))))

     REDUCED to normal form.

  ------  4226/108741. ------  

  1. ==[ start ]==> ((a (a (a a)))((^a.a)(a (^a.a))))
  2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a (^y.y))))
  3. ==[ beta  ]==> ((a (a (a a)))(a (^y.y)))
  4. ==[ alpha ]==> ((a (a (a a)))(a (^x.x)))

     REDUCED to normal form.

  ------  4227/108777. ------  

  1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b (a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(b (a a)))
  3. ==[ beta  ]==> ((^y.y)(b (a a)))
  4. ==[ alpha ]==> ((^x.x)(b (a a)))
  5. ==[ beta  ]==> (b (a a))

     REDUCED to normal form.

  ------  4228/108813. ------  

  1. ==[ start ]==> ((((^a.a) a) b)((^a.(^a.a)) a))
  2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z)) a))
  3. ==[ beta  ]==> ((a b)((^y.(^z.z)) a))
  4. ==[ alpha ]==> ((a b)((^x.(^y.y)) a))
  5. ==[ beta  ]==> ((a b)(^y.y))
  6. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  4229/108831. ------  

  1. ==[ start ]==> (((^a.(a a))(^a.a))((a a)(a a)))
  2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(a a)))
  3. ==[ beta  ]==> (((^y.y)(^y.y))((a a)(a a)))
  4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a a)))
  5. ==[ beta  ]==> ((^y.y)((a a)(a a)))
  6. ==[ alpha ]==> ((^x.x)((a a)(a a)))
  7. ==[ beta  ]==> ((a a)(a a))

     REDUCED to normal form.

  ------  4230/108840. ------  

  1. ==[ start ]==> (((a (a a)) a)((^a.a) b))
  2. ==[ alpha ]==> (((a (a a)) a)((^x.x) b))
  3. ==[ beta  ]==> (((a (a a)) a) b)

     REDUCED to normal form.

  ------  4231/108858. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(b a))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(b a))
  3. ==[ beta  ]==> ((a (a a))(b a))

     REDUCED to normal form.

  ------  4232/108867. ------  

  1. ==[ start ]==> (((a a)(^a.(a a)))((a a)(^a.a)))
  2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.y)))

     REDUCED to normal form.

  ------  4233/108885. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a b))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a b))
  3. ==[ beta  ]==> ((^y.y)(a b))
  4. ==[ alpha ]==> ((^x.x)(a b))
  5. ==[ beta  ]==> (a b)

     REDUCED to normal form.

  ------  4234/108894. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))((a a) a))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a) a))

     REDUCED to normal form.

  ------  4235/108921. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.a) a))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1) a))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))((^x1.x1) a))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a))
  5. ==[ beta  ]==> ((a (^x.(^y.y))) a)

     REDUCED to normal form.

  ------  4236/108939. ------  

  1. ==[ start ]==> (((^a.(a a))(a a))(a a))
  2. ==[ alpha ]==> (((^x.(x x))(a a))(a a))
  3. ==[ beta  ]==> (((a a)(a a))(a a))

     REDUCED to normal form.

  ------  4237/108947. ------  

  1. ==[ start ]==> (^a.((a (a a))(^a.a)))
  2. ==[ alpha ]==> (^x.((x (x x))(^y.y)))

     REDUCED to normal form.

  ------  4238/108948. ------  

  1. ==[ start ]==> (a ((a (a a))(^a.a)))
  2. ==[ alpha ]==> (a ((a (a a))(^x.x)))

     REDUCED to normal form.

  ------  4239/109041. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (a a))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4240/109746. ------  

  1. ==[ start ]==> (((^a.(a a))(a a)) b)
  2. ==[ alpha ]==> (((^x.(x x))(a a)) b)
  3. ==[ beta  ]==> (((a a)(a a)) b)

     REDUCED to normal form.

  ------  4241/109755. ------  

  1. ==[ start ]==> (((a (a a))(^a.a)) a)
  2. ==[ alpha ]==> (((a (a a))(^x.x)) a)

     REDUCED to normal form.

  ------  4242/109761. ------  

  1. ==[ start ]==> ((^a.a)((a (a a))(^a.a)))
  2. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y)))
  3. ==[ beta  ]==> ((a (a a))(^y.y))
  4. ==[ alpha ]==> ((a (a a))(^x.x))

     REDUCED to normal form.

  ------  4243/109770. ------  

  1. ==[ start ]==> ((^a.(^a.a))((^a.(a a))(a a)))
  2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a a)))
  3. ==[ beta  ]==> (^y.y)
  4. ==[ alpha ]==> (^x.x)

     REDUCED to normal form.

  ------  4244/109788. ------  

  1. ==[ start ]==> ((^a.(a a))(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((((^y.y) a)(^z.(^x1.x1)))(((^y.y) a)(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1))))
  5. ==[ beta  ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1))))
  6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1))))
  7. ==[ beta  ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1))))
  8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1))))

     REDUCED to normal form.

  ------  4245/109815. ------  

  1. ==[ start ]==> ((^a.b)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.a)))
  3. ==[ beta  ]==> b

     REDUCED to normal form.

  ------  4246/109851. ------  

  1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(a (a a))))
  2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a (a a))))
  3. ==[ beta  ]==> (^y.(^z.z))
  4. ==[ alpha ]==> (^x.(^y.y))

     REDUCED to normal form.

  ------  4247/109854. ------  

  1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(a (a a))))
  2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a a))))

     REDUCED to normal form.

  ------  4248/109896. ------  

  1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a) b))
  2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a) b))
  3. ==[ beta  ]==> ((((^z.z) a) b)(^y.y))
  4. ==[ alpha ]==> ((((^x.x) a) b)(^y.y))
  5. ==[ beta  ]==> ((a b)(^y.y))
  6. ==[ alpha ]==> ((a b)(^x.x))

     REDUCED to normal form.

  ------  4249/109962. ------  

  1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^a.(a a))))
  2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(x1 x1))))
  3. ==[ beta  ]==> ((a (^y.y))(^z.(^x1.(x1 x1))))
  4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z))))

     REDUCED to normal form.

  ------  4250/109971. ------  

  1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(a (a a))))
  2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (z z))))

     REDUCED to normal form.

  ------  4251/110013. ------  

  1. ==[ start ]==> ((^a.(^b.a))(c (^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(^y.x))(c (^z.(^x1.x1))))
  3. ==[ beta  ]==> (^y.(c (^z.(^x1.x1))))
  4. ==[ alpha ]==> (^x.(c (^y.(^z.z))))

     REDUCED to normal form.

  ------  4252/110052. ------  

  1. ==[ start ]==> (((^a.(^a.a)) b)(^c.((^a.a) a)))
  2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.((^x1.x1) a)))
  3. ==[ beta  ]==> ((^y.y)(^z.((^x1.x1) a)))
  4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a)))
  5. ==[ beta  ]==> (^y.((^z.z) a))
  6. ==[ alpha ]==> (^x.((^y.y) a))
  7. ==[ beta  ]==> (^x.a)

     REDUCED to normal form.

  ------  4253/110085. ------  

  1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) a)(^a.a)))
  2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) a)(^x1.x1)))
  3. ==[ eta   ]==> ((^y.y)(((^z.z) a)(^x1.x1)))
  4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z)))
  5. ==[ beta  ]==> (((^y.y) a)(^z.z))
  6. ==[ alpha ]==> (((^x.x) a)(^y.y))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4254/110241. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.((^a.a) a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((^x1.x1) z)))
  3. ==[ eta   ]==> ((((^x.x) a)(^y.y))(^x1.x1))
  4. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.z))
  5. ==[ beta  ]==> ((a (^y.y))(^z.z))
  6. ==[ alpha ]==> ((a (^x.x))(^y.y))

     REDUCED to normal form.

  ------  4255/110304. ------  

  1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.c))
  2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.c))

     REDUCED to normal form.

  ------  4256/110355. ------  

  1. ==[ start ]==> ((^a.(a (a a)))((a a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(^y.(^z.z))))
  3. ==[ beta  ]==> (((a a)(^y.(^z.z)))(((a a)(^y.(^z.z)))((a a)(^y.(^z.z)))))
  4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))))

     REDUCED to normal form.

  ------  4257/110367. ------  

  1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.(y y))(^z.(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.(x x))(^y.(a (^z.z))))
  5. ==[ beta  ]==> ((^y.(a (^z.z)))(^y.(a (^z.z))))
  6. ==[ alpha ]==> ((^x.(a (^y.y)))(^z.(a (^x1.x1))))
  7. ==[ beta  ]==> (a (^y.y))
  8. ==[ alpha ]==> (a (^x.x))

     REDUCED to normal form.

  ------  4258/110430. ------  

  1. ==[ start ]==> ((((^a.a) a) b)(^a.(a (^a.a))))
  2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(y (^z.z))))
  3. ==[ beta  ]==> ((a b)(^y.(y (^z.z))))
  4. ==[ alpha ]==> ((a b)(^x.(x (^y.y))))

     REDUCED to normal form.

  ------  4259/110475. ------  

  1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(^a.(^a.a))))
  2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.(^x1.x1))))
  3. ==[ beta  ]==> ((a (a a))(^y.(^z.(^x1.x1))))
  4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z))))

     REDUCED to normal form.

  ------  4260/110502. ------  

  1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.(a a)))
  2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(a a)))
  3. ==[ beta  ]==> ((^y.y)(^x1.(a a)))
  4. ==[ alpha ]==> ((^x.x)(^y.(a a)))
  5. ==[ beta  ]==> (^y.(a a))
  6. ==[ alpha ]==> (^x.(a a))

     REDUCED to normal form.

  ------  4261/110511. ------  

  1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.b))
  2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.b))

     REDUCED to normal form.

  ------  4262/110538. ------  

  1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(a a)))
  2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(x1 x1)))
  3. ==[ beta  ]==> ((a (^y.(^z.z)))(^x1.(x1 x1)))
  4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z)))

     REDUCED to normal form.

  ------  4263/110556. ------  

  1. ==[ start ]==> (((^a.(a a))(a a))(^a.(^a.a)))
  2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(^z.z)))
  3. ==[ beta  ]==> (((a a)(a a))(^y.(^z.z)))
  4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y)))

     REDUCED to normal form.

  ------  4264/110565. ------  

  1. ==[ start ]==> (((a (a a))(^a.a))(^a.a))
  2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y))

     REDUCED to normal form.

  ------  4265/110577. ------  

  1. ==[ start ]==> ((a a)((a (a a))(^a.a)))
  2. ==[ alpha ]==> ((a a)((a (a a))(^x.x)))

     REDUCED to normal form.

  ------  4266/110586. ------  

  1. ==[ start ]==> ((a (^a.a))((^a.(a a))(a a)))
  2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a a)))
  3. ==[ beta  ]==> ((a (^x.x))((a a)(a a)))

     REDUCED to normal form.

  ------  4267/110604. ------  

  1. ==[ start ]==> ((a (a a))(((^a.a) a)(^a.(^a.a))))
  2. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.(^z.z))))
  3. ==[ beta  ]==> ((a (a a))(a (^y.(^z.z))))
  4. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y))))

     REDUCED to normal form.

  ------  4268/110613. ------  

  1. ==[ start ]==> (((^a.a)(^a.a))((^b.a)(a (^a.a))))
  2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.x1))))
  3. ==[ beta  ]==> ((^y.y)((^z.a)(a (^x1.x1))))
  4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z))))
  5. ==[ beta  ]==> ((^y.a)(a (^z.z)))
  6. ==[ alpha ]==> ((^x.a)(a (^y.y)))
  7. ==[ beta  ]==> a

     REDUCED to normal form.

  ------  4269/110631. ------  

  1. ==[ start ]==> ((a b)((a (^a.a))(^b.a)))
  2. ==[ alpha ]==> ((a b)((a (^x.x))(^y.a)))

     REDUCED to normal form.

  ------  4270/110640. ------  

  1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))((^a.a) a)))
  2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1) a)))
  3. ==[ beta  ]==> ((a a)((^y.(^z.z))((^