Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 175001/19985592. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 175002/19985619. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175003/19985646. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 175004/19986033. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(b (a a))) REDUCED to normal form. ------ 175005/19986123. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b) c)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b) c)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175006/19986312. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175007/19986348. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((b c)((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> ((b c)((^x.b)(a (^y.y)))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 175008/19986375. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 175009/19986420. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 175010/19986483. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 175011/19986501. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.(a a)))) REDUCED to normal form. ------ 175012/19986510. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 175013/19986582. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 175014/19986591. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 175015/19986618. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 175016/19986699. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 175017/19986726. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.a))(^y.(a a))) REDUCED to normal form. ------ 175018/19986816. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y) a)) 7. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 175019/19986843. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 175020/19986870. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a b)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a b)(a (^y.y))) 10. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 175021/19986897. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 175022/19986924. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(a b))) 5. ==[ beta ]==> ((b a)((a a)(a b))) REDUCED to normal form. ------ 175023/19987365. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) b)) 3. ==[ beta ]==> (b ((^x1.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175024/19987590. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (a ((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> (a ((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> (a (((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> (a (((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> (a (a ((^y.y) a))) 10. ==[ alpha ]==> (a (a ((^x.x) a))) 11. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 175025/19987608. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 9. ==[ beta ]==> (a (^y.(y y))) 10. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 175026/19987635. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 175027/19987689. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a) a)) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a) a)) 7. ==[ beta ]==> ((b b)(((a a) a) a)) REDUCED to normal form. ------ 175028/19987698. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.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. ------ 175029/19987725. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175030/19987779. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 175031/19987806. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175032/19987833. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 175033/19987878. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175034/19987941. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.(y y)))) REDUCED to normal form. ------ 175035/19988013. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 175036/19988247. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (a (a a)))) REDUCED to normal form. ------ 175037/19988301. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(a a))) REDUCED to normal form. ------ 175038/19988328. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))(a (a (^y.y)))) 6. ==[ alpha ]==> ((b (a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 175039/19988355. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a (^x.x)) a)) REDUCED to normal form. ------ 175040/19988427. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 175041/19988445. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((^z.z) a)(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175042/19988832. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.z))) 5. ==[ beta ]==> (b ((^y.a)(^z.z))) 6. ==[ alpha ]==> (b ((^x.a)(^y.y))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175043/19988850. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) b)) 5. ==[ beta ]==> ((^y.y)((a (^z.z)) b)) 6. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 7. ==[ beta ]==> ((a (^y.y)) b) 8. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175044/19988859. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 175045/19988886. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.a)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 175046/19988904. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 175047/19988994. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 175048/19989021. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 175049/19989039. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y)) a)) 3. ==[ beta ]==> (b ((a (^y.y)) a)) 4. ==[ alpha ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 175050/19989102. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (^z.z))) REDUCED to normal form. ------ 175051/19989147. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((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. ------ 175052/19989183. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175053/19989210. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 175054/19993146. ------ 1. ==[ start ]==> ((^a.(b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((a a)(a a)))) 3. ==[ eta ]==> (b (^y.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 175055/20000238. ------ 1. ==[ start ]==> ((^a.b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175056/20000508. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175057/20000778. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1)))(((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((a a)(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((a a)(((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a a)((a a)((^x1.(a a))(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a))(^y.(^z.z))))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 175058/20000979. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 175059/20001003. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175060/20002074. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((^y.a)(^z.a)) b) 4. ==[ alpha ]==> (((^x.a)(^y.a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175061/20002461. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.((((a a) a)((a a)(^z.z)))(((a a) a)((a a)(^z.z))))) 4. ==[ alpha ]==> (^x.((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^z.z))))) REDUCED to normal form. ------ 175062/20002986. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175063/20003382. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 175064/20004099. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)((a a)(a a)))) 3. ==[ eta ]==> (b ((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 175065/20004102. ------ 1. ==[ start ]==> ((a (b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 175066/20004462. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((y y)(y y)))) 3. ==[ beta ]==> (((a b)(a b))(^y.((y y)(y y)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((x x)(x x)))) REDUCED to normal form. ------ 175067/20004648. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a) a)(a b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 175068/20004936. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^x1.(a a))((^y1.y1)(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(a a))((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((a a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175069/20005539. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175070/20005776. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 175071/20005854. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175072/20006667. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175073/20006853. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((^y.(y y))(a b))((^y.(y y))(a b)))(((^y.(y y))(a b))((^y.(y y))(a b)))) 4. ==[ alpha ]==> ((((^x.(x x))(a b))((^y.(y y))(a b)))(((^z.(z z))(a b))((^x1.(x1 x1))(a b)))) 5. ==[ beta ]==> ((((a b)(a b))((^y.(y y))(a b)))(((^z.(z z))(a b))((^x1.(x1 x1))(a b)))) 6. ==[ alpha ]==> ((((a b)(a b))((^x.(x x))(a b)))(((^y.(y y))(a b))((^z.(z z))(a b)))) 7. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((^y.(y y))(a b))((^z.(z z))(a b)))) 8. ==[ alpha ]==> ((((a b)(a b))((a b)(a b)))(((^x.(x x))(a b))((^y.(y y))(a b)))) 9. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((^y.(y y))(a b)))) 10. ==[ alpha ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((^x.(x x))(a b)))) 11. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((a b)(a b)))) REDUCED to normal form. ------ 175074/20007216. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(b y))) 3. ==[ eta ]==> (((^x.x)((a a)(a a))) b) 4. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 175075/20007720. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 175076/20007933. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175077/20008854. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 175078/20009043. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(a y))) 3. ==[ eta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 175079/20010042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175080/20010312. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175081/20010336. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> (((^z.(z z))(a a))(((^z.(z z))(a a))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.(y y))(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(((^y.(y y))(a a))(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.(x x))(a a))(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(^y.y))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 175082/20010807. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^z1.z1)) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 175083/20010942. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.c)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.c)) 3. ==[ beta ]==> (b (^y.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 175084/20011086. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.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)) REDUCED to normal form. ------ 175085/20011113. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 175086/20011161. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (a (((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (a (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175087/20011188. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) 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. ------ 175088/20011197. ------ 1. ==[ start ]==> ((a b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.x)((^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. ------ 175089/20011242. ------ 1. ==[ start ]==> (((^a.a) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x) b)((b a)(^y.b))) 3. ==[ beta ]==> (b ((b a)(^y.b))) 4. ==[ alpha ]==> (b ((b a)(^x.b))) REDUCED to normal form. ------ 175090/20011269. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 175091/20011296. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 175092/20011350. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175093/20011377. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 175094/20011413. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 175095/20011440. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 175096/20011467. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175097/20011512. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a (^y.y))) a)) REDUCED to normal form. ------ 175098/20011539. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a a)((^y.y) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 175099/20011566. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y)) c)) REDUCED to normal form. ------ 175100/20011737. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 175101/20011935. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(a (a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a a))(a (a (a (^y.y))))) 4. ==[ alpha ]==> (((a a)(a a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 175102/20011944. ------ 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))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 175103/20011962. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175104/20012097. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175105/20012124. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(a b)) 6. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 175106/20012178. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a b)((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 175107/20012232. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 11. ==[ beta ]==> (a (^y.(^z.z))) 12. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175108/20012259. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 175109/20012313. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 175110/20012466. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (a a))) REDUCED to normal form. ------ 175111/20012493. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175112/20012646. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175113/20012673. ------ 1. ==[ start ]==> ((((a a) a) a)((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 175114/20012781. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z) a)) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y) a)) 5. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 175115/20012808. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175116/20012871. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(y y))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(x x))) REDUCED to normal form. ------ 175117/20012898. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 175118/20012979. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 175119/20013006. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 175120/20013033. ------ 1. ==[ start ]==> ((a (a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(^y.a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 175121/20013204. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b (^z.z))(a a))) 3. ==[ beta ]==> (b ((b (^z.z))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 175122/20013231. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((a b)(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> ((a b)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 175123/20013240. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 175124/20013258. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175125/20013312. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((b a)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.x))) REDUCED to normal form. ------ 175126/20013393. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 175127/20013420. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 175128/20013591. ------ 1. ==[ start ]==> (((^a.b) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) b)((b (^y.y))(^z.z))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175129/20013807. ------ 1. ==[ start ]==> (((a b) b)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 175130/20013861. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175131/20013888. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 175132/20013969. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z)) a)) 5. ==[ beta ]==> ((^y.(y y))((b (^z.z)) a)) 6. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) a)) 7. ==[ beta ]==> (((b (^y.y)) a)((b (^y.y)) a)) 8. ==[ alpha ]==> (((b (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 175133/20013996. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a)) b)) REDUCED to normal form. ------ 175134/20014023. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 175135/20014113. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 175136/20014140. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 175137/20014167. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 175138/20014248. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 175139/20014275. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.y))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 175140/20014338. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 175141/20014473. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175142/20014554. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 175143/20014581. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175144/20014635. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 175145/20014725. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 175146/20014752. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 175147/20014779. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 175148/20014869. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))((a a) a))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))((a a) a))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 175149/20014896. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.b)(a b))) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 175150/20014950. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 175151/20014977. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))(b a))) 5. ==[ beta ]==> (((a b) a)((b a)(b a))) REDUCED to normal form. ------ 175152/20015004. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 175153/20015031. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 175154/20015058. ------ 1. ==[ start ]==> ((a (b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> ((a (b a))((a a)(a a))) REDUCED to normal form. ------ 175155/20015418. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(a ((a a)(a a)))) REDUCED to normal form. ------ 175156/20015427. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 175157/20015481. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175158/20015499. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a)((^y.y) a))) 3. ==[ beta ]==> (b ((b a)((^y.y) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 175159/20015607. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(a b))) REDUCED to normal form. ------ 175160/20015706. ------ 1. ==[ start ]==> (((a (a a))(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175161/20015733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(b (^z.z))) 3. ==[ beta ]==> (((^y.y)((a a) a))(b (^z.z))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(b (^y.y))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 175162/20015787. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(a a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 175163/20015814. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 175164/20015886. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175165/20015895. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 175166/20016363. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c (b a))) 3. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 175167/20016426. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 175168/20016471. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175169/20016498. ------ 1. ==[ start ]==> ((a (^b.b))(((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)(^y.y)) a)) REDUCED to normal form. ------ 175170/20016678. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (^d.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c (^z.a))) 3. ==[ beta ]==> (((a b)(^y.y))(c (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(c (^y.a))) REDUCED to normal form. ------ 175171/20016705. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175172/20016732. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(a (^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 175173/20016777. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175174/20016813. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 175175/20017101. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z)) c)) REDUCED to normal form. ------ 175176/20017308. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(b (b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 175177/20017344. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175178/20017416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175179/20017623. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175180/20017704. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 175181/20017785. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 175182/20017812. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a b)(a b))) REDUCED to normal form. ------ 175183/20018172. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(a (b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(a (b a))) 3. ==[ beta ]==> (((a a)(a a))(a (b a))) REDUCED to normal form. ------ 175184/20018199. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(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. ------ 175185/20018208. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^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. ------ 175186/20018235. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a)) c)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 175187/20018253. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)((^y.y) a))) 3. ==[ beta ]==> (((b a)(b a))((a b)((^y.y) a))) 4. ==[ alpha ]==> (((b a)(b a))((a b)((^x.x) a))) 5. ==[ beta ]==> (((b a)(b a))((a b) a)) REDUCED to normal form. ------ 175188/20018334. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (a a))((a a) a))) 3. ==[ beta ]==> (b ((a (a a))((a a) a))) REDUCED to normal form. ------ 175189/20018451. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 175190/20018478. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175191/20018505. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 175192/20018568. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 175193/20018595. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175194/20018622. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(a b))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 175195/20018649. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175196/20018676. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 175197/20018703. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 175198/20018730. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 175199/20018757. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 175200/20018811. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 175201/20018838. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 175202/20018865. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 175203/20018892. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 175204/20018982. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175205/20019063. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a (a a))(^y.y))) 6. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 175206/20019207. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b c)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175207/20019234. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 175208/20019342. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 175209/20019369. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 175210/20019450. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a) c)) REDUCED to normal form. ------ 175211/20019612. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175212/20019783. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (^z.b))) 3. ==[ beta ]==> (((^y.y)(b a))(b (^z.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (^y.b))) 5. ==[ beta ]==> ((b a)(b (^y.b))) 6. ==[ alpha ]==> ((b a)(b (^x.b))) REDUCED to normal form. ------ 175213/20019810. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 175214/20019837. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b)(a a))) 3. ==[ beta ]==> (((a b)(a a))((^y.b)(a a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.b)(a a))) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 175215/20019864. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 175216/20019891. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 175217/20019945. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 175218/20019972. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))((a a) a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))((a a) a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175219/20019999. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a b)) REDUCED to normal form. ------ 175220/20020143. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(c ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(c ((^y.y)(^z.z)))) 7. ==[ beta ]==> (c ((^y.y)(^z.z))) 8. ==[ alpha ]==> (c ((^x.x)(^y.y))) 9. ==[ beta ]==> (c (^y.y)) 10. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 175221/20020224. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(a a))) 3. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 175222/20020332. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175223/20020449. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (a a))(^z.a))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))(^y.a))) 5. ==[ beta ]==> (a ((a (a a))(^y.a))) 6. ==[ alpha ]==> (a ((a (a a))(^x.a))) REDUCED to normal form. ------ 175224/20020557. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a) a)) REDUCED to normal form. ------ 175225/20020584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1)) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175226/20020638. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a d)) REDUCED to normal form. ------ 175227/20020737. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175228/20020746. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 175229/20020773. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y)) c)) 5. ==[ beta ]==> ((b (^x.(x x)))(c c)) REDUCED to normal form. ------ 175230/20020890. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175231/20020917. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 175232/20020944. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 175233/20020971. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 175234/20020998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175235/20021025. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 175236/20021052. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 175237/20021079. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.a))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 175238/20021106. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 175239/20021268. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(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. ------ 175240/20021286. ------ 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 ]==> ((a (^y.y))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 175241/20021295. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(a a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a a)(a a))) REDUCED to normal form. ------ 175242/20021691. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a) a)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a) a)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) a)) 5. ==[ beta ]==> (b (((^y.y) a) a)) 6. ==[ alpha ]==> (b (((^x.x) a) a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175243/20021718. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y)) b)) REDUCED to normal form. ------ 175244/20021736. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (a (^z.z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (a (^z.z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 175245/20021763. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(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. ------ 175246/20021817. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(a (^x.x)))) REDUCED to normal form. ------ 175247/20021853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 7. ==[ beta ]==> ((a (^y.y))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 175248/20021880. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175249/20021898. ------ 1. ==[ start ]==> (((^a.b)(b a))(a c)) 2. ==[ alpha ]==> (((^x.b)(b a))(a c)) 3. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 175250/20021961. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 175251/20022006. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 175252/20022042. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 175253/20022069. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 175254/20022095. ------ 1. ==[ start ]==> (^a.((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (^x.((b (^y.y))(^z.x))) REDUCED to normal form. ------ 175255/20022096. ------ 1. ==[ start ]==> (a ((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (a ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175256/20026014. ------ 1. ==[ start ]==> ((^a.(b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(a a)))) 3. ==[ eta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 175257/20033061. ------ 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)) REDUCED to normal form. ------ 175258/20033088. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(^y.(y y)))(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 175259/20033115. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175260/20033151. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175261/20033196. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^z.z))(^x1.(a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 175262/20033313. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175263/20033424. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(a (a (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^y1.(a (a (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 175264/20033556. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.b)(^b.(^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. ------ 175265/20033856. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 175266/20033865. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 175267/20034438. ------ 1. ==[ start ]==> ((^a.((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((b a)(^y.a))) 3. ==[ beta ]==> ((((b a)(^y.a))((b a)(^y.a)))((b a)(^y.a))) 4. ==[ alpha ]==> ((((b a)(^x.a))((b a)(^y.a)))((b a)(^z.a))) REDUCED to normal form. ------ 175268/20034693. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)(^y.((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((a a)(^x.((^y.(^z.z)) a))) 9. ==[ beta ]==> ((a a)(^x.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175269/20034771. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 175270/20035107. ------ 1. ==[ start ]==> ((((a a) a) b)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((((a a) a) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 175271/20035545. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((((a a)(a a))(^z.(^x1.x1)))(((a a)(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175272/20036976. ------ 1. ==[ start ]==> ((^a.(b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((a a)(^y.(a a)))) 3. ==[ eta ]==> (b ((a a)(^y.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 175273/20036979. ------ 1. ==[ start ]==> ((a (b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 175274/20037339. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 175275/20037348. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((y y)(y y)))) REDUCED to normal form. ------ 175276/20037813. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^x1.x1)(a a))(^y1.(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175277/20038347. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^z.b)) REDUCED to normal form. ------ 175278/20038731. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175279/20039238. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(b a))) REDUCED to normal form. ------ 175280/20039265. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 175281/20039730. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (a a))(^y.b))) 3. ==[ beta ]==> ((((a (a a))(^y.b))((a (a a))(^y.b)))(((a (a a))(^y.b))((a (a a))(^y.b)))) 4. ==[ alpha ]==> ((((a (a a))(^x.b))((a (a a))(^y.b)))(((a (a a))(^z.b))((a (a a))(^x1.b)))) REDUCED to normal form. ------ 175282/20041533. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 175283/20041971. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a) b)) 3. ==[ eta ]==> ((^y.(^z.z))(((a a) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175284/20042469. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((a a) a))) 7. ==[ beta ]==> ((b b)(^y.((a a) a))) 8. ==[ alpha ]==> ((b b)(^x.((a a) a))) REDUCED to normal form. ------ 175285/20043213. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^z.z))(((a (a a))(^z.z))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a (a a))(^y.y))(^z.z))) REDUCED to normal form. ------ 175286/20043684. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 175287/20043819. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (^z.z)))) 3. ==[ beta ]==> (b (^y.(a (^z.z)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 175288/20043882. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 175289/20043927. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 175290/20043963. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 175291/20043990. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 175292/20044029. ------ 1. ==[ start ]==> ((a a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175293/20044056. ------ 1. ==[ start ]==> ((a (a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175294/20044083. ------ 1. ==[ start ]==> ((a b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 175295/20044092. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175296/20044119. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175297/20044137. ------ 1. ==[ start ]==> (((a a)(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a a))((b a)(^x.b))) REDUCED to normal form. ------ 175298/20044164. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 175299/20044200. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175300/20044227. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(b a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175301/20044281. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 175302/20044362. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 175303/20044389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a (^z1.z1))))) 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. ------ 175304/20044524. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.b)(^b.(^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. ------ 175305/20044632. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a a)((^x1.(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 175306/20044713. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 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. ------ 175307/20044776. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(c (b (^z.z)))) REDUCED to normal form. ------ 175308/20044803. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 175309/20044821. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 175310/20044830. ------ 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. ------ 175311/20044938. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> ((b b)(b (a (a a)))) REDUCED to normal form. ------ 175312/20045073. ------ 1. ==[ start ]==> (((a (a a)) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 175313/20045100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(b a))) 5. ==[ beta ]==> (a (((a a) a)(b a))) REDUCED to normal form. ------ 175314/20045127. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175315/20045154. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (a a)) b)) REDUCED to normal form. ------ 175316/20045181. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 175317/20045208. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 175318/20045235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 8. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175319/20045271. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175320/20045298. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175321/20045325. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^y.a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(^y.a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 175322/20045352. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 175323/20045379. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175324/20045406. ------ 1. ==[ start ]==> ((a ((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((a ((a a) a))((b a)(^x.a))) REDUCED to normal form. ------ 175325/20045442. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175326/20045496. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (a ((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175327/20045577. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (((a a) a)(b ((^y.y) b))) 8. ==[ alpha ]==> (((a a) a)(b ((^x.x) b))) 9. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 175328/20045604. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((a a)(a a))) 6. ==[ alpha ]==> ((^x.a)((a a)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175329/20045658. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)((^y.y)((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((a a)((^x.x)((^y.(^z.z)) a))) 9. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 10. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175330/20045739. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 175331/20045928. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.b)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175332/20046009. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(a a)))) IRREDUCIBLE: cycle. ------ 175333/20046072. ------ 1. ==[ start ]==> ((((a a) a) b)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a) b)(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)(a (^x.x))) REDUCED to normal form. ------ 175334/20046099. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b) a)((b (^x.x))(a a))) REDUCED to normal form. ------ 175335/20046126. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 175336/20046180. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 175337/20046207. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((b a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)(^y.y))) REDUCED to normal form. ------ 175338/20046234. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.a)(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175339/20046261. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 175340/20046288. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 175341/20046486. ------ 1. ==[ start ]==> (((a b)(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175342/20046513. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 175343/20046522. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175344/20046549. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 175345/20046684. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175346/20046738. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(b a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(b a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175347/20046765. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175348/20046819. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175349/20046900. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175350/20047368. ------ 1. ==[ start ]==> (((a b) c)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) c)(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175351/20047395. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (((a a) b)((a a)((a a) a))) REDUCED to normal form. ------ 175352/20047422. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(a b))) REDUCED to normal form. ------ 175353/20047476. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.z))) REDUCED to normal form. ------ 175354/20047503. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (a a))(b a))) 3. ==[ beta ]==> ((a (^y.b))((a (a a))(b a))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))(b a))) REDUCED to normal form. ------ 175355/20047557. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175356/20047584. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 175357/20047701. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 175358/20047728. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175359/20047755. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((a (a b))((a a)(^y.a))) 6. ==[ alpha ]==> ((a (a b))((a a)(^x.a))) REDUCED to normal form. ------ 175360/20047782. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a b)(^x.b))) REDUCED to normal form. ------ 175361/20047809. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(a a)))) 7. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(a a)))) 8. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(a a)))) 9. ==[ beta ]==> (((a a) a)(^y.(a a))) 10. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 175362/20047890. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175363/20047917. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 175364/20047944. ------ 1. ==[ start ]==> ((a (b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 175365/20048034. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175366/20048115. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175367/20048250. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175368/20048286. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> ((a (^y.(a a)))(b ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(b b)) REDUCED to normal form. ------ 175369/20048304. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(a a))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(a a))) REDUCED to normal form. ------ 175370/20048313. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(a ((a a)(a a)))) REDUCED to normal form. ------ 175371/20048367. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 175372/20048394. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((b a) a)) REDUCED to normal form. ------ 175373/20048421. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 175374/20048448. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 175375/20048673. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> (((a b)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a b)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 175376/20048700. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175377/20048727. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 175378/20048781. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175379/20048790. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175380/20048871. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175381/20048952. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175382/20049114. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175383/20049258. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (b a))) REDUCED to normal form. ------ 175384/20049285. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 175385/20049312. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a b)) REDUCED to normal form. ------ 175386/20049366. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a)(a (^x1.x1)))) REDUCED to normal form. ------ 175387/20049672. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175388/20049699. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 175389/20049708. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^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. ------ 175390/20049735. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175391/20049870. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175392/20050032. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175393/20050059. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175394/20050113. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 175395/20050176. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 175396/20050203. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (b a))) REDUCED to normal form. ------ 175397/20050230. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 175398/20050257. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a)(a a))) REDUCED to normal form. ------ 175399/20050311. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) a)) REDUCED to normal form. ------ 175400/20050338. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 175401/20050536. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((b a)(^x.x))) REDUCED to normal form. ------ 175402/20050563. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175403/20050590. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.a))) REDUCED to normal form. ------ 175404/20050644. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175405/20050671. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((b (a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b (a a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((b (a a))(^y.a)) 8. ==[ alpha ]==> ((b (a a))(^x.a)) REDUCED to normal form. ------ 175406/20050698. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.b))) REDUCED to normal form. ------ 175407/20050734. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175408/20050869. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175409/20050977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175410/20051013. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((b b)(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b b)(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((b b)(c (a a))) REDUCED to normal form. ------ 175411/20051040. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(b ((a a)(^x.x)))) REDUCED to normal form. ------ 175412/20051094. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 175413/20051121. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 175414/20051202. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175415/20051229. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a))((a a) a))) REDUCED to normal form. ------ 175416/20051283. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 175417/20051427. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 175418/20051454. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 175419/20051508. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> (((a (a a))(b a))(a (^y.b))) 4. ==[ alpha ]==> (((a (a a))(b a))(a (^x.b))) REDUCED to normal form. ------ 175420/20051535. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 175421/20051589. ------ 1. ==[ start ]==> (((a b)(a b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 175422/20051616. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a)) b)) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a)) b)) 5. ==[ beta ]==> (((a a)((a a) a))((a a) b)) REDUCED to normal form. ------ 175423/20051643. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b) c)) REDUCED to normal form. ------ 175424/20052165. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 175425/20052192. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^y.y)(^z.z))) 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. ------ 175426/20052246. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 175427/20052327. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175428/20052435. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175429/20052471. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (a b))) 3. ==[ beta ]==> ((b (^y.a))(b (a b))) 4. ==[ alpha ]==> ((b (^x.a))(b (a b))) REDUCED to normal form. ------ 175430/20052498. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 175431/20052561. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a) c)) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 175432/20052723. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)(^y.y))) 3. ==[ beta ]==> (((a b)(a a))((a b)(^y.y))) 4. ==[ alpha ]==> (((a b)(a a))((a b)(^x.x))) REDUCED to normal form. ------ 175433/20052750. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 175434/20052777. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.a)) REDUCED to normal form. ------ 175435/20052831. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175436/20052858. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.a))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 175437/20052885. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 175438/20052939. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((a a) a) b)) 3. ==[ beta ]==> ((a (^y.y))(((a a) a) b)) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a) b)) REDUCED to normal form. ------ 175439/20053029. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 175440/20053218. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175441/20053353. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 9. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 10. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175442/20053380. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (a a)))) 5. ==[ beta ]==> ((^y.a)(a (a a))) 6. ==[ alpha ]==> ((^x.a)(a (a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175443/20053434. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)((a a) a))) 7. ==[ beta ]==> ((b b)((^y.y)((a a) a))) 8. ==[ alpha ]==> ((b b)((^x.x)((a a) a))) 9. ==[ beta ]==> ((b b)((a a) a)) REDUCED to normal form. ------ 175444/20053515. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175445/20053524. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d ((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(d a)) REDUCED to normal form. ------ 175446/20053551. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (a (a a)))) REDUCED to normal form. ------ 175447/20053578. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.z))) REDUCED to normal form. ------ 175448/20053632. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 175449/20053659. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 175450/20053686. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 175451/20053740. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175452/20053776. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175453/20053803. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175454/20053830. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.a))) REDUCED to normal form. ------ 175455/20053857. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 175456/20053884. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175457/20053911. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y)) a)) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) a)) 5. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 175458/20053938. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 175459/20054046. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 175460/20054073. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y)) b)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y)) b)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x)) b)) 5. ==[ beta ]==> ((b (a (a a)))(b b)) REDUCED to normal form. ------ 175461/20054100. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a) c)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a) c)) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 175462/20054181. ------ 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. ------ 175463/20054190. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))(a a))) 5. ==[ beta ]==> (((^z.(z z))(a a))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(a a))(^y.y)) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 175464/20054595. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 7. ==[ beta ]==> ((^y.a)(^z.z)) 8. ==[ alpha ]==> ((^x.a)(^y.y)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 175465/20054622. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175466/20054631. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (a (^z.z)))) REDUCED to normal form. ------ 175467/20054649. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 175468/20054703. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 175469/20054739. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c a)) 3. ==[ beta ]==> (((^y.y)(^z.z))(c a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c a)) 5. ==[ beta ]==> ((^y.y)(c a)) 6. ==[ alpha ]==> ((^x.x)(c a)) 7. ==[ beta ]==> (c a) REDUCED to normal form. ------ 175470/20054766. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 175471/20054784. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^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. ------ 175472/20054847. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (a (^z.z)))) REDUCED to normal form. ------ 175473/20054892. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 175474/20054928. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 175475/20054955. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 175476/20065974. ------ 1. ==[ start ]==> ((^a.(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175477/20066217. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^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 ]==> (^x.((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175478/20066337. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 175479/20066769. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175480/20066784. ------ 1. ==[ start ]==> ((^a.(^b.(^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. ------ 175481/20066910. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175482/20067606. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 175483/20067675. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a)) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 175484/20068794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(y (^z.z)))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1)))) 9. ==[ beta ]==> ((^z.(z (^x1.x1)))(^y.y)) 10. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 11. ==[ beta ]==> ((^z.z)(^y.y)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175485/20070252. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 175486/20071251. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 175487/20072169. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 175488/20072448. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(b a))) REDUCED to normal form. ------ 175489/20073714. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c (a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c (a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175490/20074437. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 175491/20075373. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.a))) 7. ==[ beta ]==> ((b b)(^y.(^z.a))) 8. ==[ alpha ]==> ((b b)(^x.(^y.a))) REDUCED to normal form. ------ 175492/20075382. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 175493/20075985. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175494/20076111. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^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. ------ 175495/20076516. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 5. ==[ beta ]==> (b (^y.((^z.z) a))) 6. ==[ alpha ]==> (b (^x.((^y.y) a))) 7. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 175496/20076678. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 175497/20076723. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175498/20076786. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175499/20076831. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 175500/20076867. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 175501/20076894. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 175502/20076951. ------ 1. ==[ start ]==> ((a (^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 175503/20076978. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 175504/20077005. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 175505/20077014. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 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. ------ 175506/20077041. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175507/20077086. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175508/20077095. ------ 1. ==[ start ]==> (((a a) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 175509/20077122. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 175510/20077149. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 175511/20077167. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175512/20077194. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 175513/20077230. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 175514/20077302. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(y1 (^z1.z1))))) 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. ------ 175515/20077311. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (a (^y.y)))) REDUCED to normal form. ------ 175516/20077338. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a a)((^z.z)(^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. ------ 175517/20077356. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (a (((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175518/20077383. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 175519/20077608. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 175520/20077635. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(^a.a))(^b.b))) 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. ------ 175521/20077743. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 175522/20077761. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 175523/20077779. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 175524/20077806. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 175525/20077833. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 175526/20077860. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(b (a (a a)))) REDUCED to normal form. ------ 175527/20077887. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 175528/20078355. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 175529/20078409. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175530/20078445. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(b a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(b a))) 5. ==[ beta ]==> (b ((^y.a)(b a))) 6. ==[ alpha ]==> (b ((^x.a)(b a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175531/20078472. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 175532/20078490. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 175533/20078526. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 175534/20078553. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175535/20078580. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 175536/20078652. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a)) c)) REDUCED to normal form. ------ 175537/20078823. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175538/20079237. ------ 1. ==[ start ]==> (((a a)(a b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 175539/20079264. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(b a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(b a))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(b a)) REDUCED to normal form. ------ 175540/20079291. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 175541/20079318. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(a ((^x.x) b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a b)) REDUCED to normal form. ------ 175542/20079345. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> (a ((a (^y.y))((a a)(a a)))) 8. ==[ alpha ]==> (a ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 175543/20079372. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 175544/20079435. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175545/20079462. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 175546/20079516. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((b a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(^y.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 175547/20079597. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (b ((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 175548/20079606. ------ 1. ==[ start ]==> (((a b) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 175549/20079660. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175550/20079678. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175551/20079687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 175552/20079741. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175553/20079768. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(b (^z.z)))) 7. ==[ beta ]==> (((^y.y)(b (^z.z)))((^y.y)(b (^z.z)))) 8. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.z)(b (^x1.x1)))) 9. ==[ beta ]==> ((b (^y.y))((^z.z)(b (^x1.x1)))) 10. ==[ alpha ]==> ((b (^x.x))((^y.y)(b (^z.z)))) 11. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 12. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 175554/20079813. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 175555/20079822. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175556/20079849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 175557/20080038. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))(^d.a))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 175558/20080470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(c (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(c (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175559/20080497. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.(a a)))) REDUCED to normal form. ------ 175560/20080578. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 175561/20080947. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1))) c)) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1))) c)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 175562/20081091. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 175563/20081199. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175564/20081226. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(a a))) REDUCED to normal form. ------ 175565/20081298. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175566/20081424. ------ 1. ==[ start ]==> (((a a)(b a))(((a a) a)(a b))) REDUCED to normal form. ------ 175567/20081451. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 175568/20081478. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (a a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 175569/20081505. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a (a a))(a b))(a (b a))) REDUCED to normal form. ------ 175570/20081532. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 175571/20081559. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a) b)) REDUCED to normal form. ------ 175572/20081703. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175573/20081784. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a a)(((^z.z)(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 175574/20081865. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175575/20081973. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((b a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175576/20082090. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 175577/20082117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175578/20082198. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175579/20082225. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 175580/20082270. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175581/20082315. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 175582/20082342. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a)(a (a a)))) REDUCED to normal form. ------ 175583/20082369. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a b)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 175584/20082396. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175585/20082423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> ((a b)((^y.y)(a b))) 8. ==[ alpha ]==> ((a b)((^x.x)(a b))) 9. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 175586/20082450. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (a a))(a a))) REDUCED to normal form. ------ 175587/20082477. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> (((a b)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 175588/20082504. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.y))(b a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.y))(b a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))(b a))) REDUCED to normal form. ------ 175589/20082531. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 175590/20082576. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175591/20082621. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 175592/20082648. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(a a))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(z z))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(y y))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 175593/20082783. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 175594/20082891. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175595/20082927. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175596/20082954. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 175597/20082981. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 175598/20083062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175599/20083089. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 175600/20083116. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 175601/20083143. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175602/20083287. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(((a a) a)(^y.y))) 6. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 175603/20083314. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 175604/20083341. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))(a b))) 3. ==[ beta ]==> ((a (b a))((a (a a))(a b))) REDUCED to normal form. ------ 175605/20083368. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 175606/20083395. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)((a (^y.y))((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 175607/20083422. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a a)(b a))) REDUCED to normal form. ------ 175608/20083647. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(a a))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 175609/20083782. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (b (((^z.z)(a a)) c)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) c)) 5. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 175610/20083926. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 175611/20084052. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a)) c)) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a)) c)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a)) c)) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 175612/20084196. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (^x1.(a a)))) REDUCED to normal form. ------ 175613/20084277. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175614/20084304. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 175615/20084691. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c (a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c (a b))) REDUCED to normal form. ------ 175616/20084781. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175617/20085006. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a))(a a))) 3. ==[ beta ]==> ((b c)((^y.(a a))(a a))) 4. ==[ alpha ]==> ((b c)((^x.(a a))(a a))) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 175618/20085033. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 175619/20085078. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 175620/20085105. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((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. ------ 175621/20085141. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 175622/20085159. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) REDUCED to normal form. ------ 175623/20085168. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 175624/20085240. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 175625/20085249. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 175626/20085276. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 175627/20085357. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 175628/20085384. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 175629/20085411. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 175630/20085474. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 175631/20085501. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y) a)) 7. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 175632/20085528. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((a b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 175633/20085555. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 175634/20085582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((b a)((a (^y.y))((a a) a))) 6. ==[ alpha ]==> ((b a)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 175635/20085609. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(a b))) REDUCED to normal form. ------ 175636/20086023. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b) a)) 3. ==[ beta ]==> (b ((^x1.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175637/20086248. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 175638/20086266. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (a a))(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 175639/20086293. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 175640/20086347. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(^y.a))) 7. ==[ beta ]==> ((b b)((a a)(^y.a))) 8. ==[ alpha ]==> ((b b)((a a)(^x.a))) REDUCED to normal form. ------ 175641/20086356. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a a) a)) REDUCED to normal form. ------ 175642/20086428. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a)) c)) 3. ==[ beta ]==> (b ((a (a a)) c)) REDUCED to normal form. ------ 175643/20086437. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 175644/20086464. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 175645/20086491. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 175646/20086653. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175647/20086770. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c d)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c d)) 3. ==[ beta ]==> (((a (a a)) b)(c d)) REDUCED to normal form. ------ 175648/20086905. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(c a)) REDUCED to normal form. ------ 175649/20086959. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.x1))) REDUCED to normal form. ------ 175650/20086986. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))(a a))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))(a a))) REDUCED to normal form. ------ 175651/20087013. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (a (^x.x)))) REDUCED to normal form. ------ 175652/20087067. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(a (a a)))) 5. ==[ beta ]==> ((a a)((a a)(a (a a)))) REDUCED to normal form. ------ 175653/20087085. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(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. ------ 175654/20087103. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(^z.z))) 5. ==[ beta ]==> (((a (a a))(^z.z))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 175655/20087490. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z) a))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175656/20087508. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) 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. ------ 175657/20087517. ------ 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 (^x.x))) a) a) REDUCED to normal form. ------ 175658/20087535. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 175659/20087544. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 175660/20087616. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y)) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 175661/20087652. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.a))) 5. ==[ beta ]==> ((^y.y)(a (^z.a))) 6. ==[ alpha ]==> ((^x.x)(a (^y.a))) 7. ==[ beta ]==> (a (^y.a)) 8. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 175662/20087679. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 175663/20087697. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((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. ------ 175664/20087760. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175665/20087805. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 175666/20087841. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175667/20087868. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175668/20088735. ------ 1. ==[ start ]==> ((^a.(^b.(^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. ------ 175669/20098068. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))((^z.(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175670/20098950. ------ 1. ==[ start ]==> ((^a.b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175671/20099220. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)(b (^x1.x1)))) 3. ==[ eta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175672/20099268. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175673/20099715. ------ 1. ==[ start ]==> ((^a.(^b.(^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. ------ 175674/20099718. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 175675/20100141. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175676/20100273. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3))))((^y3.(^z3.(^x4.x4)))((^y4.y4)(^z4.z4)))) 5. ==[ beta ]==> (((^y.(^z.z))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3))))((^y3.(^z3.(^x4.x4)))((^y4.y4)(^z4.z4)))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2))))((^y2.(^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 7. ==[ beta ]==> ((^y.y)((^y2.(^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175677/20100786. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.z))) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175678/20100960. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.b)(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (b (^z.(^x1.x1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175679/20101173. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.(((a b)((^z.z)(a a)))((a b)((^z.z)(a a))))) 4. ==[ alpha ]==> (^x.(((a b)((^y.y)(a a)))((a b)((^z.z)(a a))))) 5. ==[ beta ]==> (^x.(((a b)(a a))((a b)((^z.z)(a a))))) 6. ==[ alpha ]==> (^x.(((a b)(a a))((a b)((^y.y)(a a))))) 7. ==[ beta ]==> (^x.(((a b)(a a))((a b)(a a)))) REDUCED to normal form. ------ 175680/20102055. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((^z.a)(^x1.x1))((^z.a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)(^y.y))((^z.a)(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> ((a ((^z.a)(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((a ((^x.a)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((a a)(^z.z)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175681/20102472. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (b (^z.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 175682/20102811. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ eta ]==> (b ((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175683/20103360. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a b)((a a) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 175684/20103543. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.(x x)))) REDUCED to normal form. ------ 175685/20104251. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175686/20105406. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175687/20105565. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))(((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a) a)))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a) a))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a)))) 11. ==[ beta ]==> (((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a))) 12. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a))) 13. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 15. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 16. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175688/20105955. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(b x1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.z) b)) b) 4. ==[ beta ]==> ((^y.y) b) 5. ==[ alpha ]==> ((^x.x) b) 6. ==[ beta ]==> b REDUCED to normal form. ------ 175689/20106459. ------ 1. ==[ start ]==> (((a b)(a b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 175690/20106645. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175691/20107593. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 175692/20107806. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b)(^y1.y1))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175693/20107980. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> (b (^x1.(x1 b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 175694/20108313. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 175695/20108493. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.((z1 z1) z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((z1 z1) z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z) z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175696/20108625. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 175697/20108781. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 175698/20108916. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 175699/20109048. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^z.(^x1.x1)))((a (^z.(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 175700/20109051. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 175701/20109447. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a))) 5. ==[ beta ]==> (b (^y.(^z.a))) 6. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 175702/20109609. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.c)) 5. ==[ beta ]==> ((^y.y)(^z.c)) 6. ==[ alpha ]==> ((^x.x)(^y.c)) 7. ==[ beta ]==> (^y.c) 8. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 175703/20109717. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.b)) REDUCED to normal form. ------ 175704/20109798. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(^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))) REDUCED to normal form. ------ 175705/20109900. ------ 1. ==[ start ]==> (((^a.a) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.a))) 3. ==[ beta ]==> (a ((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (a ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175706/20109927. ------ 1. ==[ start ]==> (((a a) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175707/20109936. ------ 1. ==[ start ]==> ((a b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(a (a a)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 175708/20109954. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 175709/20109981. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 175710/20109990. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175711/20110008. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 175712/20110035. ------ 1. ==[ start ]==> (((a a) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 175713/20110116. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175714/20110152. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175715/20110170. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 175716/20110179. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 175717/20110206. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 175718/20110251. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 175719/20110278. ------ 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. ------ 175720/20110305. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 175721/20110332. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1)) c)) REDUCED to normal form. ------ 175722/20110395. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.b)(^b.(^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. ------ 175723/20110674. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a a))(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a)(a a))(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 175724/20110701. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 175725/20110791. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a)) d)) 3. ==[ beta ]==> ((b b)((^y.(a a)) d)) 4. ==[ alpha ]==> ((b b)((^x.(a a)) d)) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 175726/20110836. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175727/20110863. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 175728/20110917. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 175729/20110971. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(b a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 175730/20110998. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175731/20111052. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 175732/20111124. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 175733/20111232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 175734/20111259. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 175735/20111412. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175736/20111466. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 175737/20111547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175738/20111574. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 175739/20111637. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 175740/20111664. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 175741/20111745. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 175742/20111772. ------ 1. ==[ start ]==> ((a (a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 175743/20111943. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 175744/20111970. ------ 1. ==[ start ]==> (((^a.a)(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a b))((b (^y.y))(a a))) 3. ==[ beta ]==> ((a b)((b (^y.y))(a a))) 4. ==[ alpha ]==> ((a b)((b (^x.x))(a a))) REDUCED to normal form. ------ 175745/20111997. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 175746/20112051. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 175747/20112132. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 175748/20112159. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))((a b)(a a))) REDUCED to normal form. ------ 175749/20112546. ------ 1. ==[ start ]==> (((a b) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)((a b)(^x.(a a)))) REDUCED to normal form. ------ 175750/20112627. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175751/20112681. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 175752/20112735. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b (^y.y)) a)) REDUCED to normal form. ------ 175753/20112762. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(a a)) b)) REDUCED to normal form. ------ 175754/20112789. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) b) c)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b) c)) 5. ==[ beta ]==> (((a a)(^x.x))(b c)) REDUCED to normal form. ------ 175755/20112825. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175756/20112906. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 175757/20112933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.b)(^z.(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(a a)))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 175758/20113014. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175759/20113041. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 175760/20113077. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 175761/20113212. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 175762/20113221. ------ 1. ==[ start ]==> (((a b) c)((^d.a) e)) 2. ==[ alpha ]==> (((a b) c)((^x.a) e)) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 175763/20113293. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(a b))) REDUCED to normal form. ------ 175764/20113320. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 175765/20113374. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (a a))(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (a a))(b a))) REDUCED to normal form. ------ 175766/20113455. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 175767/20113491. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 175768/20113518. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 175769/20113554. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 175770/20113608. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 175771/20113635. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a a)) REDUCED to normal form. ------ 175772/20113662. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(a b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a b))) 7. ==[ beta ]==> ((^y.y)((^z.b)(a b))) 8. ==[ alpha ]==> ((^x.x)((^y.b)(a b))) 9. ==[ beta ]==> ((^y.b)(a b)) 10. ==[ alpha ]==> ((^x.b)(a b)) 11. ==[ beta ]==> b REDUCED to normal form. ------ 175773/20113716. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 175774/20113743. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((b a)(b a))) REDUCED to normal form. ------ 175775/20113770. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 175776/20113797. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 175777/20114157. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b)(a b))(b ((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a b))(b ((^x.x) b))) 5. ==[ beta ]==> (((a b)(a b))(b b)) REDUCED to normal form. ------ 175778/20114220. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 175779/20114238. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 175780/20114247. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 175781/20114346. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)((a a) a))) REDUCED to normal form. ------ 175782/20114499. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 175783/20114526. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.(a a)))) REDUCED to normal form. ------ 175784/20114553. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(a a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 175785/20114580. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175786/20114625. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175787/20114922. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a) c)) REDUCED to normal form. ------ 175788/20115210. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175789/20115219. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175790/20115237. ------ 1. ==[ start ]==> ((a (^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(a (^y.y)))) REDUCED to normal form. ------ 175791/20115471. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175792/20115516. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175793/20115525. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 175794/20115840. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a) b)) REDUCED to normal form. ------ 175795/20115867. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((b a)(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 175796/20116047. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c ((a a)(^y.y)))) 3. ==[ beta ]==> (b (c ((a a)(^y.y)))) 4. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 175797/20116110. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175798/20116155. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175799/20116389. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175800/20116497. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 175801/20116524. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 175802/20116551. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 175803/20116911. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 175804/20116938. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(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. ------ 175805/20116992. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((b a)(b a))((a a)(a (^y.y)))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 175806/20117073. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175807/20117181. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175808/20117217. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 175809/20117244. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 175810/20117280. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 175811/20117307. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 175812/20117334. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 175813/20117361. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))((a a) a))) 3. ==[ beta ]==> (((a (a a))(b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175814/20117388. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a b))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 175815/20117415. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 175816/20117442. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.y))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.x))) REDUCED to normal form. ------ 175817/20117496. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 175818/20117577. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175819/20117631. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.b))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 175820/20117721. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175821/20117802. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (b ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 175822/20117910. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175823/20117946. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((b c)(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> ((b c)((a a)(^y.y))) 6. ==[ alpha ]==> ((b c)((a a)(^x.x))) REDUCED to normal form. ------ 175824/20117973. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175825/20118081. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 175826/20118108. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 175827/20118189. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b) b)) REDUCED to normal form. ------ 175828/20118216. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a) c)) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a) c)) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a) c)) REDUCED to normal form. ------ 175829/20118522. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (^z.a))) 3. ==[ beta ]==> (((^y.y)(b a))(c (^z.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (^y.a))) 5. ==[ beta ]==> ((b a)(c (^y.a))) 6. ==[ alpha ]==> ((b a)(c (^x.a))) REDUCED to normal form. ------ 175830/20118549. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.b))) REDUCED to normal form. ------ 175831/20118576. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a (^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 175832/20118603. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)(a b))((^y.b)(a a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.b)(a a))) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 175833/20118684. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 175834/20118711. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 175835/20118738. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175836/20118792. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.z))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175837/20118963. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 175838/20119071. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175839/20119188. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175840/20119296. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 175841/20119323. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175842/20119377. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a)) c)) REDUCED to normal form. ------ 175843/20119476. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(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. ------ 175844/20119485. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 175845/20119512. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175846/20119539. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y)) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(c c)) REDUCED to normal form. ------ 175847/20119611. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 175848/20119656. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 175849/20119683. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 175850/20119710. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 175851/20119737. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175852/20119764. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 175853/20119791. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 175854/20119818. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 175855/20119845. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 175856/20119899. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175857/20120007. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(y y)))) 5. ==[ beta ]==> ((a a)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 175858/20120034. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 175859/20120430. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)(^z.a))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 175860/20120457. ------ 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 (^x.x))) a)(a a)) REDUCED to normal form. ------ 175861/20120484. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z)) b)) REDUCED to normal form. ------ 175862/20120502. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(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. ------ 175863/20120556. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(a a))) REDUCED to normal form. ------ 175864/20120592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) c)) 5. ==[ beta ]==> ((^y.y)((^z.z) c)) 6. ==[ alpha ]==> ((^x.x)((^y.y) c)) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 175865/20120619. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 175866/20120637. ------ 1. ==[ start ]==> (((^a.b)(b a))(b b)) 2. ==[ alpha ]==> (((^x.b)(b a))(b b)) 3. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 175867/20120700. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a) b)) REDUCED to normal form. ------ 175868/20120745. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((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. ------ 175869/20120781. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 175870/20120808. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a) a)) REDUCED to normal form. ------ 175871/20120861. ------ 1. ==[ start ]==> (^a.(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.(^z.z)) x)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^x.((^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. ------ 175872/20120862. ------ 1. ==[ start ]==> (a (((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^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. ------ 175873/20121684. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^b.(^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. ------ 175874/20131848. ------ 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. ------ 175875/20131854. ------ 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)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175876/20131881. ------ 1. ==[ start ]==> ((^a.(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(^z.a))) 3. ==[ beta ]==> (((b (^y.y))(^z.a))((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (((b (^x.x))(^y.a))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 175877/20131908. ------ 1. ==[ start ]==> ((^a.b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175878/20131944. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175879/20131989. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> (((b a)(^z.b))(^y.y)) 4. ==[ alpha ]==> (((b a)(^x.b))(^y.y)) REDUCED to normal form. ------ 175880/20132106. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 175881/20132673. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175882/20132676. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 175883/20133231. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^y.(^z.z)))(^x1.(^y1.y1))))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2))))((a (^z2.(^x3.x3)))(^y3.(^z3.z3)))) REDUCED to normal form. ------ 175884/20133927. ------ 1. ==[ start ]==> (((a b) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 175885/20134305. ------ 1. ==[ start ]==> (((^a.b) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 175886/20134338. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((b (^z.z))(^x1.x1))((b (^z.z))(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((b (^y.y))(^z.z))((b (^x1.x1))(^y1.y1)))) 5. ==[ beta ]==> (((b (^y.y))(^z.z))((b (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (((b (^x.x))(^y.y))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 175887/20135439. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 175888/20135769. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))(^z.z))) 3. ==[ eta ]==> (b ((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 175889/20136606. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x1.x1))(^y1.(y1 y1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175890/20137524. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175891/20138085. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 175892/20138922. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(b z))) 3. ==[ eta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 175893/20139165. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 175894/20139417. ------ 1. ==[ start ]==> (((a b)(a b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175895/20140764. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b) a)) 3. ==[ eta ]==> ((^y.(^z.z))((a b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175896/20140938. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (b (^x1.(^y1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 175897/20141451. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175898/20141460. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((y1 y1) y1))) REDUCED to normal form. ------ 175899/20141583. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 175900/20141739. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175901/20142018. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175902/20142423. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^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 ]==> (^x.a) REDUCED to normal form. ------ 175903/20142567. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 7. ==[ beta ]==> (^y.(a (^z.z))) 8. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 175904/20142783. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 175905/20142837. ------ 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. ------ 175906/20142849. ------ 1. ==[ start ]==> ((a a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^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. ------ 175907/20142876. ------ 1. ==[ start ]==> ((a (a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175908/20142903. ------ 1. ==[ start ]==> ((a b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175909/20142939. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 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. ------ 175910/20142984. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b a)(^y.b))) REDUCED to normal form. ------ 175911/20143047. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 175912/20143074. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175913/20143101. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 175914/20143119. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175915/20143182. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 175916/20143209. ------ 1. ==[ start ]==> (((^a.(^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)) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175917/20143263. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (a ((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.z))) 7. ==[ beta ]==> (a ((^z.z)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 175918/20143479. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175919/20143560. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(^a.a))(^b.b))) 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. ------ 175920/20143650. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.y))) REDUCED to normal form. ------ 175921/20143668. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 175922/20143686. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a a)(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 175923/20143758. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((b b)(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> ((b b)(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> ((b b)(((a a)(a a)) a)) REDUCED to normal form. ------ 175924/20143893. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a)) b)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a (a a)) b)((a a)(a a))) REDUCED to normal form. ------ 175925/20143920. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) a)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) a)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> (a ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 175926/20143947. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 175927/20143974. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175928/20144001. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.a))((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (^x.a))((a (a a)) b)) REDUCED to normal form. ------ 175929/20144028. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 175930/20144055. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(b (^z.z)))) 7. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 175931/20144118. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 175932/20144145. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 175933/20144172. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 175934/20144199. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(b (^y.(y y)))) 8. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 175935/20144226. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175936/20144316. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (a ((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 175937/20144397. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 175938/20144424. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 7. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 8. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 9. ==[ beta ]==> (b ((^y.y) b)) 10. ==[ alpha ]==> (b ((^x.x) b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175939/20144478. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(b (^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(b (^z.z)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175940/20144748. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175941/20144829. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.x1))) IRREDUCIBLE: cycle. ------ 175942/20144892. ------ 1. ==[ start ]==> ((((a a) a) b)(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(b (b (^x.x)))) REDUCED to normal form. ------ 175943/20144919. ------ 1. ==[ start ]==> (((a b) a)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a b) a)(a (^y.y))) 4. ==[ alpha ]==> (((a b) a)(a (^x.x))) REDUCED to normal form. ------ 175944/20144946. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y))(a a))) REDUCED to normal form. ------ 175945/20145000. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b ((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 175946/20145027. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 175947/20145054. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175948/20145081. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 175949/20145108. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)(a b))) REDUCED to normal form. ------ 175950/20145297. ------ 1. ==[ start ]==> (((^a.b) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((a a)(b (^y.y)))) 3. ==[ beta ]==> (b ((a a)(b (^y.y)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 175951/20145333. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b (^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175952/20145369. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175953/20145423. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175954/20145504. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (b ((^x1.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175955/20145585. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175956/20145639. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) b))) 9. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) b))) 10. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 11. ==[ beta ]==> ((^y.a)((^z.z) b)) 12. ==[ alpha ]==> ((^x.a)((^y.y) b)) 13. ==[ beta ]==> a REDUCED to normal form. ------ 175957/20146044. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175958/20146188. ------ 1. ==[ start ]==> (((a b) c)((b a)(a (a a)))) REDUCED to normal form. ------ 175959/20146215. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b)(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175960/20146242. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)((a a) a))) REDUCED to normal form. ------ 175961/20146296. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 175962/20146323. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 175963/20146377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175964/20146404. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 175965/20146422. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 175966/20146431. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 175967/20146521. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 175968/20146548. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 175969/20146575. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 175970/20146629. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.b))) 7. ==[ beta ]==> ((^y.y)((a b)(^z.b))) 8. ==[ alpha ]==> ((^x.x)((a b)(^y.b))) 9. ==[ beta ]==> ((a b)(^y.b)) 10. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 175971/20146656. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 175972/20146683. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 175973/20146737. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175974/20146764. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 175975/20146854. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175976/20146935. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175977/20147043. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175978/20147106. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 175979/20147124. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 175980/20147133. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b ((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))(b b)) REDUCED to normal form. ------ 175981/20147187. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 175982/20147214. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 175983/20147241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.a))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.a))((b a) a)) REDUCED to normal form. ------ 175984/20147268. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 175985/20147520. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.z))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.y))) 7. ==[ beta ]==> (((a a) a)(b (^y.y))) 8. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 175986/20147547. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 175987/20147601. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 175988/20147691. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(a b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(a b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(a b))) 5. ==[ beta ]==> ((a a)((^z.a)(a b))) 6. ==[ alpha ]==> ((a a)((^x.a)(a b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 175989/20147772. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (b ((^x1.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175990/20147880. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175991/20147934. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175992/20147988. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)(^x1.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)(^z.a))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.a))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 175993/20148069. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175994/20148132. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 175995/20148186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(a a))) REDUCED to normal form. ------ 175996/20148249. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 175997/20148492. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 175998/20148519. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 175999/20148690. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 176000/20148798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.z2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.z2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176001/20148852. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176002/20148879. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176003/20149014. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^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. ------ 176004/20149023. ------ 1. ==[ start ]==> (((a b)(^c.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 176005/20149050. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (b a))) REDUCED to normal form. ------ 176006/20149077. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176007/20149131. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1))(a (^z1.z1)))) REDUCED to normal form. ------ 176008/20149158. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 176009/20149383. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 176010/20149410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176011/20149464. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 176012/20149491. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 176013/20149554. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a b))) 5. ==[ beta ]==> ((^y.(y y))(a b)) 6. ==[ alpha ]==> ((^x.(x x))(a b)) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 176014/20149689. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176015/20149797. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176016/20149914. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (b a))) REDUCED to normal form. ------ 176017/20149941. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(a a))) REDUCED to normal form. ------ 176018/20150022. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 176019/20150049. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 8. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 176020/20150103. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (a b))) REDUCED to normal form. ------ 176021/20150148. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176022/20150157. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 176023/20150247. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a b)(^x.a))) REDUCED to normal form. ------ 176024/20150274. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 176025/20150301. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 176026/20150328. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))(^x.a))) REDUCED to normal form. ------ 176027/20150355. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.b))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.b))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.b))) REDUCED to normal form. ------ 176028/20150382. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 176029/20150409. ------ 1. ==[ start ]==> (((a b)(a b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176030/20150436. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a)(^y.y)) a)) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 176031/20150463. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a)) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a) b)) REDUCED to normal form. ------ 176032/20150877. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b (^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176033/20150985. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 176034/20151012. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176035/20151066. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 176036/20151147. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176037/20151255. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176038/20151291. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c ((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(c ((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(c ((a a) a))) REDUCED to normal form. ------ 176039/20151318. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (a b))) REDUCED to normal form. ------ 176040/20151381. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b) b)) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 176041/20151570. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b)(^y.y))) 3. ==[ beta ]==> (((a a)(a b))((a b)(^y.y))) 4. ==[ alpha ]==> (((a a)(a b))((a b)(^x.x))) REDUCED to normal form. ------ 176042/20151597. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 176043/20151651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 176044/20151678. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176045/20151759. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b) a)) 3. ==[ beta ]==> ((a (^y.y))((a b) a)) 4. ==[ alpha ]==> ((a (^x.x))((a b) a)) REDUCED to normal form. ------ 176046/20151849. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 9. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 176047/20151930. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (b ((^x.x)(^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 176048/20152173. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 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. ------ 176049/20152200. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 7. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176050/20152254. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 176051/20152335. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176052/20152398. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (a (a a)))) REDUCED to normal form. ------ 176053/20152452. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((a a) a))) REDUCED to normal form. ------ 176054/20152479. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 176055/20152506. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 176056/20152560. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (a a)))) 7. ==[ beta ]==> ((a (^y.y))(a (a a))) 8. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 176057/20152578. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176058/20152623. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 176059/20152650. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176060/20152677. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.a))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.a))) REDUCED to normal form. ------ 176061/20152704. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 176062/20152731. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176063/20152758. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z) a)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 176064/20152785. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a)) b)) 5. ==[ beta ]==> (((a a)(a a))((a (a a)) b)) REDUCED to normal form. ------ 176065/20152812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a c)) REDUCED to normal form. ------ 176066/20152893. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 176067/20152920. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y)) b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x)) b)) 5. ==[ beta ]==> ((((a a)(a a)) a)(b b)) REDUCED to normal form. ------ 176068/20152992. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 176069/20153010. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176070/20153397. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b c)) 3. ==[ beta ]==> (((^y.y) b)(b c)) 4. ==[ alpha ]==> (((^x.x) b)(b c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 176071/20153415. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 176072/20153442. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 176073/20153469. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 176074/20153559. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 176075/20153604. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^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. ------ 176076/20153667. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (a a))) REDUCED to normal form. ------ 176077/20153712. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 176078/20153748. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 176079/20153775. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a b)) REDUCED to normal form. ------ 176080/20153829. ------ 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. ------ 176081/20164824. ------ 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. ------ 176082/20164848. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176083/20164929. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176084/20165091. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176085/20165238. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 176086/20165679. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 176087/20165784. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176088/20166507. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176089/20166549. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z)) b)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 176090/20167299. ------ 1. ==[ start ]==> (((a b)(a a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 176091/20167695. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 176092/20169486. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a b)(a (a a)))(^x.b)) REDUCED to normal form. ------ 176093/20170194. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176094/20170476. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^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. ------ 176095/20171070. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 176096/20171349. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(b a))) REDUCED to normal form. ------ 176097/20172906. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176098/20173536. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(a b))) 3. ==[ beta ]==> (((a b)(a a))(^y.(a b))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(a b))) REDUCED to normal form. ------ 176099/20174283. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176100/20174445. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.a))) REDUCED to normal form. ------ 176101/20174886. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 176102/20174991. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(a (a a)))(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(a (a a)))(^x.x))) REDUCED to normal form. ------ 176103/20175417. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^y.a)) REDUCED to normal form. ------ 176104/20175579. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.x1))) REDUCED to normal form. ------ 176105/20175741. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176106/20175768. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 176107/20175822. ------ 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. ------ 176108/20175852. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.x))((^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. ------ 176109/20175879. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 176110/20175906. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 176111/20175933. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176112/20175942. ------ 1. ==[ start ]==> (((^a.a) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176113/20175969. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176114/20175987. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176115/20176014. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 176116/20176050. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176117/20176077. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 176118/20176095. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176119/20176131. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176120/20176212. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 176121/20176239. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 176122/20176257. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((^y.y) a)((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y))) a)) 5. ==[ beta ]==> (a ((a (a (^y.y))) a)) 6. ==[ alpha ]==> (a ((a (a (^x.x))) a)) REDUCED to normal form. ------ 176123/20176266. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.a))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 176124/20176284. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 176125/20176563. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176126/20176590. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 176127/20176680. ------ 1. ==[ start ]==> (((a a)(a (a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(a (a (a (^x.x))))) REDUCED to normal form. ------ 176128/20176707. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 176129/20176734. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 176130/20176761. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a a))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 176131/20176788. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(b (a (a a)))) REDUCED to normal form. ------ 176132/20177085. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176133/20177256. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 176134/20177310. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (a (((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> (a ((a a)(^y.(a a)))) 8. ==[ alpha ]==> (a ((a a)(^x.(a a)))) REDUCED to normal form. ------ 176135/20177346. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176136/20177391. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176137/20177418. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 176138/20177427. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((^y1.y1) b)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b ((^y1.y1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.x1) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b b)) REDUCED to normal form. ------ 176139/20177454. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 176140/20177481. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 176141/20177508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176142/20177553. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y)) b)) REDUCED to normal form. ------ 176143/20177724. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176144/20178138. ------ 1. ==[ start ]==> (((a a)(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a)(a b))((a b)(a a))) REDUCED to normal form. ------ 176145/20178165. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 176146/20178192. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(b a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(b a))) 9. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 176147/20178219. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 176148/20178246. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> (a (((^y.y) a)((^z.z) b))) 8. ==[ alpha ]==> (a (((^x.x) a)((^y.y) b))) 9. ==[ beta ]==> (a (a ((^y.y) b))) 10. ==[ alpha ]==> (a (a ((^x.x) b))) 11. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 176149/20178273. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 176150/20178300. ------ 1. ==[ start ]==> (((a b)(a a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 176151/20178336. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))((b (^y.y))(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176152/20178363. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 176153/20178417. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 176154/20178498. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 176155/20178507. ------ 1. ==[ start ]==> (((a b) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(a b))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 176156/20178534. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 176157/20178561. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 176158/20178588. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 176159/20178633. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 11. ==[ beta ]==> (((^y.y) a)(^z.z)) 12. ==[ alpha ]==> (((^x.x) a)(^y.y)) 13. ==[ beta ]==> (a (^y.y)) 14. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 176160/20178642. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 176161/20178669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))((^y.(^z.z))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176162/20178696. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 176163/20178714. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b (^z.z)) a)) 3. ==[ beta ]==> (b ((b (^z.z)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 176164/20178939. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^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. ------ 176165/20179425. ------ 1. ==[ start ]==> (((a b)(^b.a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.(a a)))) REDUCED to normal form. ------ 176166/20179848. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b) b)) 5. ==[ beta ]==> (b (((^z.z) b) b)) 6. ==[ alpha ]==> (b (((^x.x) b) b)) 7. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 176167/20179992. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 176168/20180100. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 176169/20180127. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 176170/20180199. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y) b)) 3. ==[ beta ]==> (b ((^y.y) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176171/20180325. ------ 1. ==[ start ]==> (((a a)(b a))((a b)((a a) a))) REDUCED to normal form. ------ 176172/20180352. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 176173/20180379. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (a a))((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 10. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 11. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 176174/20180406. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 176175/20180433. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a a) a)(((^y.y) a)(b a))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) a)(b a))) 7. ==[ beta ]==> (((a a) a)(a (b a))) REDUCED to normal form. ------ 176176/20180460. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176177/20180487. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a a)((^x.x) b))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a) b)) REDUCED to normal form. ------ 176178/20180604. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176179/20180685. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a) a)(^z.b))) 5. ==[ beta ]==> ((a a)(((a a) a)(^z.b))) 6. ==[ alpha ]==> ((a a)(((a a) a)(^x.b))) REDUCED to normal form. ------ 176180/20180874. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176181/20180883. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 176182/20180901. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a) c)) REDUCED to normal form. ------ 176183/20180991. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 176184/20181018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((^y.b)((^z.a)(^x1.b))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(^z.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176185/20181072. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176186/20181126. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 176187/20181171. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 176188/20181198. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176189/20181216. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a)(a (^z.z)))) REDUCED to normal form. ------ 176190/20181243. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 176191/20181270. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 176192/20181297. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a a))((a b)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a a))((a b)(^x.x))) REDUCED to normal form. ------ 176193/20181324. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a) a)((a a) a))) 5. ==[ beta ]==> ((a b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 176194/20181351. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(a b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(a b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a b)) REDUCED to normal form. ------ 176195/20181378. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 176196/20181405. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a ((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a)(a (a a)))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 176197/20181432. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.z))(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(b a))) REDUCED to normal form. ------ 176198/20181477. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(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. ------ 176199/20181522. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176200/20181549. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 176201/20181684. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 176202/20181792. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176203/20181801. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 176204/20181846. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z)) c)) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y)) c)) 5. ==[ beta ]==> (b (((a a)(^y.y)) c)) 6. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 176205/20181855. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^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. ------ 176206/20181882. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 176207/20181963. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176208/20181990. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 176209/20182017. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 176210/20182071. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176211/20182188. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(a (a a)))) 3. ==[ beta ]==> (((a a) b)((a b)(a (a a)))) REDUCED to normal form. ------ 176212/20182215. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 176213/20182242. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((a (b a))((^y.y)((a a) a))) 6. ==[ alpha ]==> ((a (b a))((^x.x)((a a) a))) 7. ==[ beta ]==> ((a (b a))((a a) a)) REDUCED to normal form. ------ 176214/20182269. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (a a))(a b))) REDUCED to normal form. ------ 176215/20182296. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)(a ((^y.y)(a a)))) 10. ==[ alpha ]==> ((a a)(a ((^x.x)(a a)))) 11. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 176216/20182323. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176217/20182350. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(b a))) REDUCED to normal form. ------ 176218/20182548. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.b))) 5. ==[ beta ]==> ((a (a a))(^y.b)) 6. ==[ alpha ]==> ((a (a a))(^x.b)) REDUCED to normal form. ------ 176219/20182683. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (b (((a a)(^z.z)) b)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) b)) REDUCED to normal form. ------ 176220/20182827. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((b b)((^y.b)(^y.b))) 6. ==[ alpha ]==> ((b b)((^x.b)(^y.b))) 7. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 176221/20182854. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 176222/20182953. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y)) b)) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 176223/20183151. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 176224/20183763. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a) d)) 3. ==[ beta ]==> (b ((^z.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176225/20183907. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176226/20183934. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 176227/20183979. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 176228/20184006. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z z))) 7. ==[ beta ]==> ((^y.y)(^z.(z z))) 8. ==[ alpha ]==> ((^x.x)(^y.(y y))) 9. ==[ beta ]==> (^y.(y y)) 10. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 176229/20184042. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> ((a (^x.x))(^z.z)) 12. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 176230/20184069. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 176231/20184141. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (b (((^z.z)(a a)) a)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) a)) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 176232/20184150. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 176233/20184177. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 176234/20184258. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 176235/20184285. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 176236/20184312. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176237/20184375. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 176238/20184402. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 176239/20184429. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a b)((^y.y)((^z.z) a))) 8. ==[ alpha ]==> ((a b)((^x.x)((^y.y) a))) 9. ==[ beta ]==> ((a b)((^y.y) a)) 10. ==[ alpha ]==> ((a b)((^x.x) a)) 11. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 176240/20184456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(a (a a)))) REDUCED to normal form. ------ 176241/20184483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b a)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b a)(a (^y.y))) 10. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 176242/20184510. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 176243/20184537. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)(a b))) 3. ==[ beta ]==> (((a b)(a a))((a a)(a b))) REDUCED to normal form. ------ 176244/20185167. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176245/20185194. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.a))) 5. ==[ beta ]==> ((a (a a))(^y.a)) 6. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 176246/20185248. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((a (^y.y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176247/20185257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.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. ------ 176248/20185284. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176249/20185329. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) b)) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176250/20185338. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176251/20185365. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 176252/20185392. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 176253/20185446. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.a)) REDUCED to normal form. ------ 176254/20185590. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176255/20185860. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b (a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a (a a)))) REDUCED to normal form. ------ 176256/20185887. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))(a (^y.y))) 6. ==[ alpha ]==> ((b (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 176257/20185914. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))(a a))) REDUCED to normal form. ------ 176258/20185968. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z) a))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y) a))) 7. ==[ beta ]==> ((a a)((a (^x.x)) a)) REDUCED to normal form. ------ 176259/20185986. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 176260/20185995. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(a (a a)))) REDUCED to normal form. ------ 176261/20186391. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176262/20186409. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(^x1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 176263/20186418. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z) a)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y) a)) 5. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 176264/20186436. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 176265/20186445. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 176266/20186463. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((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. ------ 176267/20186517. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 176268/20186553. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 176269/20186580. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.a))) REDUCED to normal form. ------ 176270/20186598. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((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. ------ 176271/20186661. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 176272/20186706. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 176273/20186742. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176274/20186769. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 176275/20186823. ------ 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. ------ 176276/20186840. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(x x))) 3. ==[ beta ]==> (^x.((x x)(^z.z))) 4. ==[ alpha ]==> (^x.((x x)(^y.y))) REDUCED to normal form. ------ 176277/20186841. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (a ((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (a ((a a)(^y.y))) 4. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 176278/20195754. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(a x1))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.(a x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a z))) 5. ==[ eta ]==> ((^x.(^y.y)) a) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176279/20197845. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a)) a) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a)) a) 3. ==[ beta ]==> (((a a)(^y.y)) a) 4. ==[ alpha ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 176280/20197851. ------ 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 ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176281/20197986. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((^z.(^x1.(^y1.y1)))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 176282/20198175. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z z))((a a)(a a)))) 3. ==[ eta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 176283/20198670. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176284/20198691. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 176285/20199123. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176286/20199228. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(a (a a)))((^y.y)(a (a a))))((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(a (a a)))((^y.y)(a (a a))))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (a a))((^y.y)(a (a a))))((^z.z)(a (a a)))) 6. ==[ alpha ]==> (((a (a a))((^x.x)(a (a a))))((^y.y)(a (a a)))) 7. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(a (a a)))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(a (a a)))) 9. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 176287/20199741. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^z.(a a))) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a))) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176288/20199942. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.x)(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. ------ 176289/20200128. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))(a b))(((^z.z)(a a))(a b)))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))(a b))(((^z.z)(a a))(a b)))) 5. ==[ beta ]==> (^x.(((a a)(a b))(((^z.z)(a a))(a b)))) 6. ==[ alpha ]==> (^x.(((a a)(a b))(((^y.y)(a a))(a b)))) 7. ==[ beta ]==> (^x.(((a a)(a b))((a a)(a b)))) REDUCED to normal form. ------ 176290/20200707. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176291/20201010. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^z.(z z))(^x1.(^y1.(^z1.z1))))((^z.(z z))(^x1.(^y1.(^z1.z1)))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 5. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 6. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3)))))(^y3.y3)) 7. ==[ beta ]==> (((^y.(^z.z))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3)))))(^y3.y3)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1)))))(^x2.x2)) 9. ==[ beta ]==> ((^y.y)(^x2.x2)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176292/20201766. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ eta ]==> (b ((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176293/20202315. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176294/20203182. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^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. ------ 176295/20203206. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176296/20203497. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 176297/20203521. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176298/20204388. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176299/20205441. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 176300/20205600. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176301/20205693. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((x2 x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((x2 x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176302/20206575. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 176303/20206761. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)(a b))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176304/20206764. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(a z))) 3. ==[ eta ]==> ((a ((^x.(^y.y)) a)) a) 4. ==[ beta ]==> ((a (^y.y)) a) 5. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 176305/20206935. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((a a) a))) 3. ==[ beta ]==> (b (^x1.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 176306/20207580. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 176307/20207628. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 176308/20207763. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176309/20207898. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176310/20208003. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (^z.(z z)))) 3. ==[ beta ]==> ((b (^z.(z z)))((b (^z.(z z)))(^y.y))) 4. ==[ alpha ]==> ((b (^x.(x x)))((b (^y.(y y)))(^z.z))) REDUCED to normal form. ------ 176311/20208528. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.(x x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.y)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176312/20208591. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.c)) REDUCED to normal form. ------ 176313/20208717. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 176314/20208753. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.b)) 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)) REDUCED to normal form. ------ 176315/20208834. ------ 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. ------ 176316/20208852. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 176317/20208864. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a a)((^x.(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. ------ 176318/20208882. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (a (((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^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. ------ 176319/20208909. ------ 1. ==[ start ]==> (((a a) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a) a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176320/20208936. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 176321/20208963. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 176322/20208972. ------ 1. ==[ start ]==> (((a a)(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 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. ------ 176323/20208999. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176324/20209017. ------ 1. ==[ start ]==> (((a a) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((a a) b)((b a)(^x.b))) REDUCED to normal form. ------ 176325/20209044. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 176326/20209152. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 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. ------ 176327/20209161. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 176328/20209188. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 176329/20209260. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((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. ------ 176330/20209287. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a (^y.y))) a)) REDUCED to normal form. ------ 176331/20209314. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 176332/20209341. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b (^z.z)) c)) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 176333/20209404. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.b)(^b.(^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. ------ 176334/20209683. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176335/20209701. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 176336/20209818. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176337/20209845. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176338/20209899. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(a b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(a b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 7. ==[ beta ]==> (((a a)(^y.y))(a b)) 8. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 176339/20209953. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 176340/20209980. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 176341/20210034. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 176342/20210133. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 176343/20210241. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.b)(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. ------ 176344/20210367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 176345/20210448. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 176346/20210556. ------ 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) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y) a)) 5. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 176347/20210646. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(y y))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(x x))) REDUCED to normal form. ------ 176348/20210673. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 176349/20210754. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 176350/20210925. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b (b (^z.z)))) 3. ==[ beta ]==> (b (b (b (^z.z)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 176351/20210952. ------ 1. ==[ start ]==> (((^a.a)(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a b)(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a b)(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 176352/20210979. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 5. ==[ beta ]==> ((b (^y.y))(a a)) 6. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 176353/20211015. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176354/20211033. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b ((^y.y) a))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) a))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 176355/20211114. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 176356/20211141. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)(a b))) REDUCED to normal form. ------ 176357/20211528. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(a a))(^y.b))) 3. ==[ beta ]==> (((a b) b)((a a)(^y.b))) 4. ==[ alpha ]==> (((a b) b)((a a)(^x.b))) REDUCED to normal form. ------ 176358/20211555. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a a) a)((a b)(^y.(a a)))) 4. ==[ alpha ]==> (((a a) a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 176359/20211582. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 176360/20211663. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 176361/20211744. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 176362/20211771. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 176363/20211807. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 176364/20211834. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 176365/20211915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.b))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.b))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 176366/20211942. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 176367/20211969. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 176368/20212023. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176369/20212059. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(c ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y) b))) 5. ==[ beta ]==> (c ((^y.y) b)) 6. ==[ alpha ]==> (c ((^x.x) b)) 7. ==[ beta ]==> (c b) REDUCED to normal form. ------ 176370/20212194. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 176371/20212203. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a))) d)) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z))) d)) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 176372/20212275. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 176373/20212302. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a b)(a b))) 3. ==[ beta ]==> ((^y.y)((a b)(a b))) 4. ==[ alpha ]==> ((^x.x)((a b)(a b))) 5. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 176374/20212356. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(^y.y))) 8. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 176375/20212437. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 176376/20212500. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 176377/20212536. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 176378/20212563. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 176379/20212644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((a a) a))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))((a a) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a) a))) 9. ==[ beta ]==> ((^y.(a a))((a a) a)) 10. ==[ alpha ]==> ((^x.(a a))((a a) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176380/20212671. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 176381/20212698. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 176382/20212725. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 176383/20212752. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((b a)(b a))) REDUCED to normal form. ------ 176384/20212779. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 176385/20213139. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)(a b))(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b)(a b))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 176386/20213202. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176387/20213220. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (b (((^y.y) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 176388/20213229. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) b)) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 176389/20213256. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1))) c)) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 176390/20213328. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 176391/20213508. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 176392/20213562. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 176393/20213607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176394/20213904. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 176395/20213931. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a) c)) REDUCED to normal form. ------ 176396/20214192. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(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. ------ 176397/20214201. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 176398/20214219. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 176399/20214507. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(a (^z.z))) REDUCED to normal form. ------ 176400/20214534. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 176401/20214822. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 176402/20214849. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a) b)) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a) b)) 3. ==[ beta ]==> ((b a)((b a) b)) REDUCED to normal form. ------ 176403/20214876. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 176404/20215137. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((b a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176405/20215173. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 176406/20215344. ------ 1. ==[ start ]==> ((((a a) a)(a b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(c (^x.(^y.y)))) REDUCED to normal form. ------ 176407/20215398. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176408/20215479. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 176409/20215506. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((b (a a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(a (a a)))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 176410/20215920. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 176411/20215974. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 176412/20216055. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (((a a) a)(a (a a)))) REDUCED to normal form. ------ 176413/20216163. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176414/20216226. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 176415/20216262. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 176416/20216289. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 176417/20216343. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 176418/20216370. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 176419/20216397. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)(a b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)(a b))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 176420/20216424. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 176421/20216451. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 176422/20216532. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 176423/20216559. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 176424/20216586. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 176425/20216613. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 176426/20216703. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a ((a a)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176427/20216784. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (b (((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x) a))) 5. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 176428/20216892. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176429/20216955. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.x))) REDUCED to normal form. ------ 176430/20217063. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 176431/20217171. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 176432/20217198. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b) b)) 3. ==[ beta ]==> (((a a)(^y.b))((a b) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((a b) b)) REDUCED to normal form. ------ 176433/20217558. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b (^y.b))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.b))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.b))) REDUCED to normal form. ------ 176434/20217585. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a (^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 176435/20217612. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 176436/20217666. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 176437/20217693. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(a (a a)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(a (a a)))) 7. ==[ beta ]==> ((b a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 176438/20217720. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 176439/20217774. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.z)(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a b))) 5. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 176440/20217945. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 176441/20218053. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176442/20218170. ------ 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) 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. ------ 176443/20218278. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176444/20218359. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 176445/20218386. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a)) c)) REDUCED to normal form. ------ 176446/20218458. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b ((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176447/20218494. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a) a)) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 176448/20218521. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 176449/20218593. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 176450/20218611. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 176451/20218638. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.a))) REDUCED to normal form. ------ 176452/20218665. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176453/20218692. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176454/20218719. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 176455/20218746. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 176456/20218773. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 176457/20218800. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 176458/20218827. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 176459/20218881. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 176460/20218908. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 176461/20219016. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.(y y)))) REDUCED to normal form. ------ 176462/20219025. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a a)(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(a (a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 176463/20219412. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176464/20219430. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b c)) 3. ==[ beta ]==> (((^z.z)(^y.y))(b c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b c)) 5. ==[ beta ]==> ((^y.y)(b c)) 6. ==[ alpha ]==> ((^x.x)(b c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176465/20219439. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(^y.a))) REDUCED to normal form. ------ 176466/20219466. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 176467/20219538. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a ((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a ((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 176468/20219574. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 176469/20219619. ------ 1. ==[ start ]==> (((^a.b)(b a))(c a)) 2. ==[ alpha ]==> (((^x.b)(b a))(c a)) 3. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 176470/20219682. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z)) a)) REDUCED to normal form. ------ 176471/20219727. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 176472/20219763. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 176473/20219790. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 176474/20219844. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^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. ------ 176475/20219862. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a a)) 3. ==[ beta ]==> (((a a)(^y.y))(a a)) 4. ==[ alpha ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 176476/20219870. ------ 1. ==[ start ]==> (^a.((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (^x.((x (x (^y.y)))(^z.z))) REDUCED to normal form. ------ 176477/20219871. ------ 1. ==[ start ]==> (a ((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (a ((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 176478/20230875. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a)) b) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a)) b) 3. ==[ beta ]==> (((a a)(^y.y)) b) 4. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 176479/20230884. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a)) a) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 176480/20230890. ------ 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. ------ 176481/20230899. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176482/20230917. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.(^y1.y1)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 7. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 8. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176483/20230944. ------ 1. ==[ start ]==> ((^a.b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 176484/20231142. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.b)(b a))) 3. ==[ beta ]==> (^y.((^z.b)(b a))) 4. ==[ alpha ]==> (^x.((^y.b)(b a))) 5. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 176485/20231307. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (a (^y.(a (a (^z.z))))) 6. ==[ alpha ]==> (a (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 176486/20232267. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((((^y.y) b)(^z.(z z)))(((^y.y) b)(^z.(z z))))(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (((((^x.x) b)(^y.(y y)))(((^z.z) b)(^x1.(x1 x1))))(((^y1.y1) b)(^z1.(z1 z1)))) 5. ==[ beta ]==> (((b (^y.(y y)))(((^z.z) b)(^x1.(x1 x1))))(((^y1.y1) b)(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((b (^x.(x x)))(((^y.y) b)(^z.(z z))))(((^x1.x1) b)(^y1.(y1 y1)))) 7. ==[ beta ]==> (((b (^x.(x x)))(b (^z.(z z))))(((^x1.x1) b)(^y1.(y1 y1)))) 8. ==[ alpha ]==> (((b (^x.(x x)))(b (^y.(y y))))(((^z.z) b)(^x1.(x1 x1)))) 9. ==[ beta ]==> (((b (^x.(x x)))(b (^y.(y y))))(b (^x1.(x1 x1)))) 10. ==[ alpha ]==> (((b (^x.(x x)))(b (^y.(y y))))(b (^z.(z z)))) REDUCED to normal form. ------ 176487/20232990. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 176488/20233764. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 176489/20234805. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b (((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176490/20235231. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 176491/20235642. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((b a)(^x1.a))) 3. ==[ beta ]==> (((b a)(^x1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((b a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 176492/20236221. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^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. ------ 176493/20236230. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^x1.b)) REDUCED to normal form. ------ 176494/20236527. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176495/20236560. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176496/20236842. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176497/20237559. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((((a a) a)(^y.(^z.z)))(((a a) a)(^y.(^z.z))))((((a a) a)(^y.(^z.z)))(((a a) a)(^y.(^z.z))))) 4. ==[ alpha ]==> (((((a a) a)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1))))((((a a) a)(^y1.(^z1.z1)))(((a a) a)(^x2.(^y2.y2))))) REDUCED to normal form. ------ 176498/20237985. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(^z.(^x1.x1)))) b) 4. ==[ beta ]==> ((a (^y.(^z.(^x1.x1)))) b) 5. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 176499/20238228. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 176500/20238732. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176501/20238957. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((b c)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((b c)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((b c)(^x.(a a))) REDUCED to normal form. ------ 176502/20239191. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 176503/20239800. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)(^x1.b))) 3. ==[ eta ]==> ((^y.(^z.z))((a a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176504/20240523. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((z z) z))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((z z) z))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((y y) y))) REDUCED to normal form. ------ 176505/20240802. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176506/20241486. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^y.a)) REDUCED to normal form. ------ 176507/20241567. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.a))) REDUCED to normal form. ------ 176508/20241648. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.y))) 3. ==[ beta ]==> (b (^y.(^z.y))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 176509/20241711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.c)) REDUCED to normal form. ------ 176510/20241756. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 176511/20241792. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 176512/20241873. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(y1 y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176513/20241891. ------ 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)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176514/20241900. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 176515/20241912. ------ 1. ==[ start ]==> ((a a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 176516/20241921. ------ 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))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176517/20241939. ------ 1. ==[ start ]==> ((a (a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(^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. ------ 176518/20241966. ------ 1. ==[ start ]==> ((a b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a b)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176519/20242020. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 176520/20242056. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176521/20242137. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176522/20242164. ------ 1. ==[ start ]==> ((a (^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.b)(b a))) 3. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 176523/20242182. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176524/20242209. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 176525/20242245. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 176526/20242272. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176527/20242326. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (a ((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> (a ((^x.x)(a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 176528/20242353. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.z1))) 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 ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176529/20242542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176530/20242650. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 176531/20242776. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (((a (^x.x)) a)(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 176532/20242821. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b b)((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176533/20242956. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 176534/20242983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (a (((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 176535/20243010. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 176536/20243037. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a) a)(b a))) REDUCED to normal form. ------ 176537/20243064. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (^x.a))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176538/20243091. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 176539/20243118. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> (((^y.y) a)((a a)(a a))) 8. ==[ alpha ]==> (((^x.x) a)((a a)(a a))) 9. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 176540/20243208. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176541/20243235. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176542/20243262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^y.a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(^y.a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 176543/20243289. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a) a))(b (^y.(y y)))) 4. ==[ alpha ]==> ((a ((a a) a))(b (^x.(x x)))) REDUCED to normal form. ------ 176544/20243325. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176545/20243379. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 176546/20243487. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176547/20243541. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)((a a)(a a)))) 7. ==[ beta ]==> ((a a)((^y.a)((a a)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)((a a)(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 176548/20243640. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x)) b)) REDUCED to normal form. ------ 176549/20243811. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176550/20243892. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) IRREDUCIBLE: cycle. ------ 176551/20243955. ------ 1. ==[ start ]==> ((((a a) a) b)(c ((a a)(a a)))) REDUCED to normal form. ------ 176552/20243982. ------ 1. ==[ start ]==> (((a b) a)(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(b (b (^x.x)))) REDUCED to normal form. ------ 176553/20244009. ------ 1. ==[ start ]==> (((a a)(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 176554/20244063. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 176555/20244090. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b ((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 176556/20244117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176557/20244144. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 176558/20244171. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 176559/20244360. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 176560/20244486. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 176561/20244567. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176562/20244621. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)((^y.b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176563/20244648. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176564/20244702. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 11. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 12. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 13. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 14. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176565/20244783. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 176566/20244855. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b) c)) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b) c)) 5. ==[ beta ]==> (((a a)(a a))(b c)) REDUCED to normal form. ------ 176567/20245107. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^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. ------ 176568/20245251. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> (((a b) c)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 176569/20245278. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b a)(a (a a)))) 3. ==[ beta ]==> (((a a) b)((b a)(a (a a)))) REDUCED to normal form. ------ 176570/20245305. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 176571/20245359. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)(a b))) REDUCED to normal form. ------ 176572/20245386. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.b))(((a a) a)(a a))) REDUCED to normal form. ------ 176573/20245440. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176574/20245467. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 176575/20245485. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c (^z.z))) 3. ==[ beta ]==> (b (c (^z.z))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 176576/20245494. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.a))((a (^y.y)) b)) REDUCED to normal form. ------ 176577/20245521. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 176578/20245584. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 176579/20245611. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 176580/20245638. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((a (a b))((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((a (a b))((b a)(^x.(x x)))) REDUCED to normal form. ------ 176581/20245665. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176582/20245719. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a b)(^x.b))) REDUCED to normal form. ------ 176583/20245746. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 176584/20245827. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176585/20245917. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (b ((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176586/20246106. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((b a)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((b a)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 176587/20246133. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^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. ------ 176588/20246187. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 176589/20246196. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 176590/20246250. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 176591/20246277. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b (a a))) REDUCED to normal form. ------ 176592/20246304. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 176593/20246331. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a) a)) REDUCED to normal form. ------ 176594/20246610. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176595/20246664. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a)(^z.a))) REDUCED to normal form. ------ 176596/20246754. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.b)((a a) a))) 5. ==[ beta ]==> ((a a)((^z.b)((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.b)((a a) a))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176597/20246835. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176598/20246943. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176599/20246970. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176600/20247051. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 176601/20247132. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176602/20247195. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(c (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(c (b a))) REDUCED to normal form. ------ 176603/20247240. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 176604/20247249. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a b)) REDUCED to normal form. ------ 176605/20247285. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 176606/20247546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176607/20247582. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 176608/20247591. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176609/20247753. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176610/20247861. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176611/20247996. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 176612/20248077. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176613/20248086. ------ 1. ==[ start ]==> (((a b)(^c.a))(d ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(d (a a))) REDUCED to normal form. ------ 176614/20248113. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((a a)(^z.z)))) REDUCED to normal form. ------ 176615/20248140. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (b a))) REDUCED to normal form. ------ 176616/20248194. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a)(a a))) REDUCED to normal form. ------ 176617/20248221. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 176618/20248473. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a)(^y.y))) REDUCED to normal form. ------ 176619/20248527. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.a))) REDUCED to normal form. ------ 176620/20248554. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((b (a a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((b (a a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 176621/20248581. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 176622/20248617. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176623/20248860. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176624/20248941. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 176625/20248968. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 176626/20248977. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 176627/20249004. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(a (b a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (b a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (b a))) REDUCED to normal form. ------ 176628/20249085. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a b) a)) REDUCED to normal form. ------ 176629/20249112. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 176630/20249166. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))((a a) a))) REDUCED to normal form. ------ 176631/20249220. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 176632/20249247. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 176633/20249310. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176634/20249337. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.a))) REDUCED to normal form. ------ 176635/20249364. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 176636/20249391. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.y))) REDUCED to normal form. ------ 176637/20249445. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (^y.b))) 6. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.b))) REDUCED to normal form. ------ 176638/20249472. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 176639/20249526. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 176640/20249580. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b) c)) REDUCED to normal form. ------ 176641/20249976. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((b c)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((b c)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((b c)((a a)(a a))) REDUCED to normal form. ------ 176642/20250048. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 176643/20250129. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^z1.z1)(^x2.x2))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)((^x2.x2)(^y2.y2)))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.x2))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 176644/20250210. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (b ((^y.y)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176645/20250318. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176646/20250444. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 176647/20250471. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 176648/20250498. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a) c)) 5. ==[ beta ]==> ((a b)((^y.a) c)) 6. ==[ alpha ]==> ((a b)((^x.a) c)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 176649/20250660. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b)(^y.y))) REDUCED to normal form. ------ 176650/20250714. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.a)) REDUCED to normal form. ------ 176651/20250741. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (a a))(^y.(y y)))) 5. ==[ beta ]==> ((b a)((a (a a))(^y.(y y)))) 6. ==[ alpha ]==> ((b a)((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 176652/20250768. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176653/20250822. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 176654/20250912. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.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. ------ 176655/20250993. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176656/20251263. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 176657/20251317. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(a (a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(a (a a)))) 7. ==[ beta ]==> ((b b)((^y.a)(a (a a)))) 8. ==[ alpha ]==> ((b b)((^x.a)(a (a a)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 176658/20251398. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176659/20251506. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176660/20251515. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.y1))) REDUCED to normal form. ------ 176661/20251542. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a ((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(a ((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a ((a a) a))) REDUCED to normal form. ------ 176662/20251569. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 176663/20251623. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((^y.y) a)((^z.z) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176664/20251713. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176665/20251740. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176666/20251767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 176667/20251794. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 176668/20251821. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 176669/20251848. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z)) a)) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y)) a)) 7. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 176670/20251875. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a)) b)) REDUCED to normal form. ------ 176671/20251983. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 176672/20252037. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a) c)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a) c)) 5. ==[ beta ]==> ((a a)((^y.a) c)) 6. ==[ alpha ]==> ((a a)((^x.a) c)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 176673/20252055. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 176674/20252073. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(z z)))) 5. ==[ beta ]==> ((b (^z.(z z)))(^y.y)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176675/20252460. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c b)) 3. ==[ beta ]==> (((^y.y) b)(c b)) 4. ==[ alpha ]==> (((^x.x) b)(c b)) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 176676/20252478. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 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. ------ 176677/20252487. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b c)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b c)) REDUCED to normal form. ------ 176678/20252505. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 176679/20252532. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 176680/20252586. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.a)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 176681/20252622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a))) 7. ==[ beta ]==> ((a (^y.y))(a a)) 8. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 176682/20252649. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 176683/20252667. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (^y.a))) 3. ==[ beta ]==> (b (a (^y.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 176684/20252730. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a c)) REDUCED to normal form. ------ 176685/20252775. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 176686/20252811. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 176687/20252838. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 176688/20252892. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176689/20252910. ------ 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)(^y.y))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 176690/20252919. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 176691/20263941. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a)) b) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y)) b) REDUCED to normal form. ------ 176692/20263965. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176693/20264046. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176694/20264382. ------ 1. ==[ start ]==> (((a a)(^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 176695/20264451. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z)) c)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 176696/20264823. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 176697/20264901. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176698/20265651. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176699/20265666. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 176700/20266440. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(b (^z.z)))((a a)(b (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(((a a)(b (^y.y)))((a a)(b (^z.z))))) 5. ==[ beta ]==> (((a a)(b (^y.y)))((a a)(b (^z.z)))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 176701/20266830. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176702/20266839. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 176703/20268297. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 176704/20269296. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 176705/20269311. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.b) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176706/20269917. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 176707/20272023. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(a a)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(a a)))) REDUCED to normal form. ------ 176708/20272050. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176709/20272257. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 176710/20272266. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 176711/20272491. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 176712/20272680. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(a b))) 3. ==[ beta ]==> (((a a)(a b))(^y.(a b))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(a b))) REDUCED to normal form. ------ 176713/20273265. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.b))) 5. ==[ beta ]==> (a (^y.(^z.b))) 6. ==[ alpha ]==> (a (^x.(^y.b))) REDUCED to normal form. ------ 176714/20273589. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 176715/20273733. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176716/20274030. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^x.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 176717/20274108. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^z.z))((^x1.x1) a))(((a (^z.z))((^x1.x1) a))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a (^z.z))((^x1.x1) a))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x)) a)(((a (^z.z))((^x1.x1) a))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y))((^z.z) a))(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x)) a)(((a (^y.y)) a)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y)) a)(^z.z))) REDUCED to normal form. ------ 176718/20274561. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 176719/20274714. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.c)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.c)) 3. ==[ beta ]==> (b (^y.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 176720/20274777. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 176721/20274885. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176722/20274939. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^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. ------ 176723/20274957. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.a)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 176724/20274966. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 176725/20274980. ------ 1. ==[ start ]==> (^a.(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176726/20274981. ------ 1. ==[ start ]==> (a (^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176727/20274996. ------ 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. ------ 176728/20275005. ------ 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 ((a a)(^y.y))) 6. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 176729/20275023. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176730/20275050. ------ 1. ==[ start ]==> (((^a.a)(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176731/20275077. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 176732/20275086. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176733/20275113. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 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. ------ 176734/20275140. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 176735/20275158. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 176736/20275185. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 176737/20275221. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 176738/20275275. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176739/20275320. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((^y.a)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((^x.a)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 176740/20275356. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 176741/20275383. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176742/20275401. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> (a ((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> (a ((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 176743/20275410. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(^x.a))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 176744/20275428. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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) REDUCED to normal form. ------ 176745/20275437. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^z1.z1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 176746/20275482. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y)) c)) REDUCED to normal form. ------ 176747/20275653. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 176748/20275734. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 176749/20275824. ------ 1. ==[ start ]==> (((a a)(a (a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 176750/20275851. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (a (a (^y.y))))) REDUCED to normal form. ------ 176751/20275878. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 176752/20275905. ------ 1. ==[ start ]==> (((a (a a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176753/20275932. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 176754/20275941. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) d)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) d)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176755/20276229. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 176756/20276256. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)(^y.y))) REDUCED to normal form. ------ 176757/20276400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 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))) REDUCED to normal form. ------ 176758/20276454. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> (a (((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 176759/20276490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176760/20276517. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 176761/20276562. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 9. ==[ beta ]==> (^y.(^z.(^x1.x1))) 10. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176762/20276571. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 176763/20276598. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(x x)))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.(x x)))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.(x x)))(b b)) REDUCED to normal form. ------ 176764/20276625. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 176765/20276652. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176766/20276679. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 176767/20276697. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (^x.b))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a (^x.b))((^z.z) a)) 4. ==[ alpha ]==> ((a (^x.b))((^y.y) a)) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 176768/20276868. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176769/20277030. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 176770/20277282. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 176771/20277309. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a b)(a a))) REDUCED to normal form. ------ 176772/20277336. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 176773/20277363. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(b a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(b a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 176774/20277390. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((^y.y) a)((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((^x.x) a)((a (a a))(a (^y.(^z.z))))) 7. ==[ beta ]==> (a ((a (a a))(a (^y.(^z.z))))) 8. ==[ alpha ]==> (a ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 176775/20277417. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a b)) REDUCED to normal form. ------ 176776/20277435. ------ 1. ==[ start ]==> (((^a.b) b)(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 176777/20277444. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 176778/20277471. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a a))((a a)(b (^y.y)))) 4. ==[ alpha ]==> ((a (a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 176779/20277507. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 176780/20277561. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 7. ==[ beta ]==> (((^y.y) b)(^z.a)) 8. ==[ alpha ]==> (((^x.x) b)(^y.a)) 9. ==[ beta ]==> (b (^y.a)) 10. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 176781/20277642. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 176782/20277651. ------ 1. ==[ start ]==> (((a b) b)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 176783/20277678. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(a b))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(a b))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 176784/20277696. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a a)((a b)(^y.(a a)))) 6. ==[ alpha ]==> ((a a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 176785/20277705. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 176786/20277723. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((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. ------ 176787/20277732. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 176788/20277777. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 11. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176789/20277786. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 176790/20277813. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)((^z.z) b))) 7. ==[ beta ]==> (((^y.a)((^z.z) b))((^y.a)((^z.z) b))) 8. ==[ alpha ]==> (((^x.a)((^y.y) b))((^z.a)((^x1.x1) b))) 9. ==[ beta ]==> (a ((^z.a)((^x1.x1) b))) 10. ==[ alpha ]==> (a ((^x.a)((^y.y) b))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176791/20277840. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 176792/20277867. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176793/20278083. ------ 1. ==[ start ]==> (((^a.b) c)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176794/20278317. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z) c)) 3. ==[ beta ]==> (b ((^z.z) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176795/20278569. ------ 1. ==[ start ]==> (((a b)(^b.a))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 176796/20278596. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 176797/20278992. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(a a)) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(a a)) a)) 5. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 176798/20279136. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 176799/20279271. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 176800/20279325. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 176801/20279343. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (b ((^y.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176802/20279469. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(b a))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(b a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 176803/20279496. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 176804/20279523. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a) a)(a b))) 5. ==[ beta ]==> ((a (a a))(((a a) a)(a b))) REDUCED to normal form. ------ 176805/20279550. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(a b))((^y.y)(a a))) 6. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(a a))) 7. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 176806/20279577. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) a)((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 176807/20279604. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (b a))) REDUCED to normal form. ------ 176808/20279631. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 176809/20279658. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a a)((^y.y) b))) 5. ==[ beta ]==> (((a a) a)((a a)((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)((a a)((^x.x) b))) 7. ==[ beta ]==> (((a a) a)((a a) b)) REDUCED to normal form. ------ 176810/20279730. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176811/20279748. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(^x1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176812/20279829. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)(^z.a))) 5. ==[ beta ]==> ((a a)((a b)(^z.a))) 6. ==[ alpha ]==> ((a a)((a b)(^x.a))) REDUCED to normal form. ------ 176813/20279910. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176814/20280018. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) b) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176815/20280027. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 176816/20280045. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 176817/20280054. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 176818/20280072. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 176819/20280135. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 176820/20280162. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((^y.b)((^z.b)(^x1.a))) 6. ==[ alpha ]==> ((^x.b)((^y.b)(^z.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176821/20280216. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176822/20280324. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 176823/20280342. ------ 1. ==[ start ]==> ((a (^b.b))((^b.b) a)) 2. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 176824/20280360. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 176825/20280387. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a)(a (^y.y)))) REDUCED to normal form. ------ 176826/20280414. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 176827/20280441. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a a))((a a)(a (a a)))) REDUCED to normal form. ------ 176828/20280468. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((a b)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)((a b)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)((a b)(^y.y))) 8. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 176829/20280495. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 176830/20280522. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(a b))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a b))) 7. ==[ beta ]==> (((a b)(^x.x))(a b)) REDUCED to normal form. ------ 176831/20280549. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a (a a))(a a))) REDUCED to normal form. ------ 176832/20280576. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(a ((a a)(^y.y)))) REDUCED to normal form. ------ 176833/20280621. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176834/20280630. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176835/20280666. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((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)) REDUCED to normal form. ------ 176836/20280693. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176837/20280828. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (b ((^y.y)(^z.b))) 6. ==[ alpha ]==> (b ((^x.x)(^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 176838/20280936. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176839/20280945. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176840/20280972. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176841/20280990. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a) b)) 3. ==[ beta ]==> (((^y.y) b)((b a) b)) 4. ==[ alpha ]==> (((^x.x) b)((b a) b)) 5. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 176842/20281107. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176843/20281134. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 176844/20281161. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 176845/20281188. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 176846/20281260. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176847/20281332. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a) b)((a a)((^y.y) a))) 6. ==[ alpha ]==> (((a a) b)((a a)((^x.x) a))) 7. ==[ beta ]==> (((a a) b)((a a) a)) REDUCED to normal form. ------ 176848/20281359. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(a (a a)))) REDUCED to normal form. ------ 176849/20281386. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (b a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((a (b a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 176850/20281413. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 176851/20281440. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (a a))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (a a))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a b))) 7. ==[ beta ]==> ((a a)((a (a a))(a b))) REDUCED to normal form. ------ 176852/20281467. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a b))(a (a a))) REDUCED to normal form. ------ 176853/20281494. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176854/20281521. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a a)(b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a a)(b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)(b a))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(b a))) REDUCED to normal form. ------ 176855/20281692. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 176856/20281827. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((b a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((b a) a)) 3. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 176857/20281971. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 176858/20281998. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.b)(^y.b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(^y.b))) 5. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 176859/20282052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.a))(^c.(^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. ------ 176860/20282295. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (^x1.(a a)))) REDUCED to normal form. ------ 176861/20282322. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176862/20282907. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b) c)) 3. ==[ beta ]==> (b ((^z.b) c)) 4. ==[ alpha ]==> (b ((^x.b) c)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176863/20283051. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b (^y.(a a)))) 3. ==[ beta ]==> ((b c)(b (^y.(a a)))) 4. ==[ alpha ]==> ((b c)(b (^x.(a a)))) REDUCED to normal form. ------ 176864/20283078. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176865/20283123. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 176866/20283150. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.a))) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 176867/20283186. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 176868/20283204. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 176869/20283213. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 10. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 176870/20283285. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (b ((a a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 176871/20283294. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(a a))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 176872/20283321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 176873/20283402. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 176874/20283429. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.a))(^z.z)) 8. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 176875/20283456. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 176876/20283519. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (a a))) REDUCED to normal form. ------ 176877/20283546. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b)(a a))) REDUCED to normal form. ------ 176878/20283573. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> ((a b)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 176879/20283600. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z) a)) 7. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 176880/20283627. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((b a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 176881/20283654. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 176882/20283681. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)(a a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (((a b)(a a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 176883/20283708. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a)(a b))) 3. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 176884/20283987. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) c)) 7. ==[ beta ]==> (((^y.y)(^z.z)) c) 8. ==[ alpha ]==> (((^x.x)(^y.y)) c) 9. ==[ beta ]==> ((^y.y) c) 10. ==[ alpha ]==> ((^x.x) c) 11. ==[ beta ]==> c REDUCED to normal form. ------ 176885/20284176. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176886/20284293. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a (^z.b))) 3. ==[ beta ]==> (((^y.y) a)(a (^z.b))) 4. ==[ alpha ]==> (((^x.x) a)(a (^y.b))) 5. ==[ beta ]==> (a (a (^y.b))) 6. ==[ alpha ]==> (a (a (^x.b))) REDUCED to normal form. ------ 176887/20284311. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(^z.z))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 176888/20284338. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176889/20284392. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(^z.(z z)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(^z.(z z)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.(y y)))) 9. ==[ beta ]==> ((b b)(a (^y.(y y)))) 10. ==[ alpha ]==> ((b b)(a (^x.(x x)))) REDUCED to normal form. ------ 176890/20284401. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 176891/20284428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176892/20284473. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a) a)) 3. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 176893/20284482. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 176894/20284509. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 176895/20284536. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 176896/20284590. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 176897/20284617. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.a)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.a)) REDUCED to normal form. ------ 176898/20284734. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 176899/20284761. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 176900/20284869. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c d)) REDUCED to normal form. ------ 176901/20285031. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 176902/20285058. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.x))) REDUCED to normal form. ------ 176903/20285112. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 176904/20285139. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a (^y.y)) a)) REDUCED to normal form. ------ 176905/20285535. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(a a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(a a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(a a))) 5. ==[ beta ]==> (b ((^y.a)(a a))) 6. ==[ alpha ]==> (b ((^x.a)(a a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176906/20285553. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176907/20285562. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 176908/20285580. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)(^z.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 176909/20285589. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1) a)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z) a)) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 176910/20285607. ------ 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)(((^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. ------ 176911/20285697. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.z))) 5. ==[ beta ]==> ((^y.y)(c (^z.z))) 6. ==[ alpha ]==> ((^x.x)(c (^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 176912/20285724. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 176913/20285742. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y) c)) 3. ==[ beta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176914/20285805. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 176915/20285850. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((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. ------ 176916/20285886. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176917/20285913. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176918/20285967. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176919/20285985. ------ 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)(^y.y))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 176920/20285994. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 176921/20286009. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) a) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176922/20286011. ------ 1. ==[ start ]==> (^a.(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(x (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176923/20286012. ------ 1. ==[ start ]==> (a (a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176924/20286015. ------ 1. ==[ start ]==> ((^a.a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176925/20291370. ------ 1. ==[ start ]==> ((^a.(^b.b))(^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. ------ 176926/20291685. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176927/20297040. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176928/20297043. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 176929/20297049. ------ 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. ------ 176930/20297052. ------ 1. ==[ start ]==> ((a a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176931/20297076. ------ 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 (^z.z)))(a a))((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z (^x1.x1)))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176932/20297184. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)((^x1.x1)(^y1.y1)))(^y.y)) 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. ------ 176933/20297373. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176934/20297475. ------ 1. ==[ start ]==> (((a a)(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176935/20297868. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c (b (^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176936/20297916. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176937/20298348. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 176938/20298939. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.b)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.b)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176939/20299167. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(^y.y))((a a) a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^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. ------ 176940/20299326. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (^y.((((a a)(^z.z))((a a) a))(((a a)(^z.z))((a a) a)))) 4. ==[ alpha ]==> (^x.((((a a)(^y.y))((a a) a))(((a a)(^z.z))((a a) a)))) REDUCED to normal form. ------ 176941/20299545. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(b (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176942/20299932. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176943/20300964. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))(b a))) 3. ==[ eta ]==> (b ((^y.(y y))(b a))) 4. ==[ alpha ]==> (b ((^x.(x x))(b a))) 5. ==[ beta ]==> (b ((b a)(b a))) REDUCED to normal form. ------ 176944/20301408. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((y y)(y y)))) 3. ==[ beta ]==> (b (^y.((y y)(y y)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 176945/20301513. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176946/20301801. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176947/20302404. ------ 1. ==[ start ]==> ((^a.(^b.b))(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. ------ 176948/20302407. ------ 1. ==[ start ]==> ((a (^b.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 176949/20302719. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(a (^z.z))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176950/20302722. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.z))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 176951/20303010. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 176952/20303325. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(y1 (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176953/20303613. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176954/20303718. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((^y.b)(a (a a)))((^y.b)(a (a a))))(((^y.b)(a (a a)))((^y.b)(a (a a))))) 4. ==[ alpha ]==> ((((^x.b)(a (a a)))((^y.b)(a (a a))))(((^z.b)(a (a a)))((^x1.b)(a (a a))))) 5. ==[ beta ]==> ((b ((^y.b)(a (a a))))(((^z.b)(a (a a)))((^x1.b)(a (a a))))) 6. ==[ alpha ]==> ((b ((^x.b)(a (a a))))(((^y.b)(a (a a)))((^z.b)(a (a a))))) 7. ==[ beta ]==> ((b b)(((^y.b)(a (a a)))((^z.b)(a (a a))))) 8. ==[ alpha ]==> ((b b)(((^x.b)(a (a a)))((^y.b)(a (a a))))) 9. ==[ beta ]==> ((b b)(b ((^y.b)(a (a a))))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(a (a a))))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 176955/20304162. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(b y))) 3. ==[ eta ]==> (((^x.(x x))(b a)) b) 4. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 176956/20304666. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 176957/20304798. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176958/20305359. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 176959/20305584. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 176960/20305800. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 176961/20305959. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))((a a) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176962/20306778. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 176963/20306988. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^x.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 176964/20307123. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176965/20307807. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (^z.z)))) 3. ==[ beta ]==> (b (^y.(a (^z.z)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 176966/20307870. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176967/20307978. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176968/20308050. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(z z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 176969/20308059. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.a)) REDUCED to normal form. ------ 176970/20308074. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176971/20308077. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 176972/20308089. ------ 1. ==[ start ]==> ((a a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176973/20308107. ------ 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. ------ 176974/20308116. ------ 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))((a a)(^y.y))) 4. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 176975/20308134. ------ 1. ==[ start ]==> (((a a) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(^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. ------ 176976/20308161. ------ 1. ==[ start ]==> (((a a)(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 176977/20308188. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 176978/20308215. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 176979/20308224. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 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. ------ 176980/20308242. ------ 1. ==[ start ]==> (((a a) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 176981/20308269. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b a)(^y.b))) REDUCED to normal form. ------ 176982/20308296. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 176983/20308359. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 176984/20308377. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176985/20308413. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176986/20308512. ------ 1. ==[ start ]==> (((a a)(^b.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 176987/20308539. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a (^x1.x1))) a)) REDUCED to normal form. ------ 176988/20308566. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 176989/20308656. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.b)(^b.(^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. ------ 176990/20308908. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(c (b (^z.z)))) REDUCED to normal form. ------ 176991/20308953. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (^z.z)))) REDUCED to normal form. ------ 176992/20309043. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176993/20309070. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 176994/20309124. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 176995/20309178. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 176996/20309205. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 176997/20309259. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176998/20309385. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 176999/20309592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> (b ((a a)(^y.(a a)))) 8. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 177000/20309619. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 177001/20309673. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177002/20309700. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 177003/20309727. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 177004/20309898. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(y y))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(x x))) REDUCED to normal form. ------ 177005/20309925. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177006/20309979. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 177007/20310150. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 177008/20310177. ------ 1. ==[ start ]==> (((^a.a)(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(b (b (^y.y)))) 3. ==[ beta ]==> ((a b)(b (b (^y.y)))) 4. ==[ alpha ]==> ((a b)(b (b (^x.x)))) REDUCED to normal form. ------ 177009/20310204. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(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. ------ 177010/20310258. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 177011/20310339. ------ 1. ==[ start ]==> (((^a.b)(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b ((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 177012/20310366. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 177013/20310546. ------ 1. ==[ start ]==> (((a b)(a a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(c (^x.(a a)))) REDUCED to normal form. ------ 177014/20310582. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.(a a))((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))((a a)(b (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177015/20310753. ------ 1. ==[ start ]==> (((a b) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 177016/20310780. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.b))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.b))) REDUCED to normal form. ------ 177017/20310807. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 177018/20310834. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177019/20310888. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177020/20310915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.z))) 7. ==[ beta ]==> ((((^y.y) a)(^z.z))(((^y.y) a)(^z.z))) 8. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1))) 9. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 11. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 12. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 177021/20310942. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 177022/20310996. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b (^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 177023/20311059. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.a)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 177024/20311086. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177025/20311167. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 177026/20311194. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) b) REDUCED to normal form. ------ 177027/20311419. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 177028/20311428. ------ 1. ==[ start ]==> (((a b) c)((^b.b) c)) 2. ==[ alpha ]==> (((a b) c)((^x.x) c)) 3. ==[ beta ]==> (((a b) c) c) REDUCED to normal form. ------ 177029/20311500. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 177030/20311527. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177031/20311581. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)(a a))) REDUCED to normal form. ------ 177032/20311662. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 177033/20311788. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 177034/20311815. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 177035/20311896. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a a)) REDUCED to normal form. ------ 177036/20311923. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)(a b))) 3. ==[ beta ]==> (((a b) a)((^y.b)(a b))) 4. ==[ alpha ]==> (((a b) a)((^x.b)(a b))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 177037/20311977. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 177038/20312004. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))(b a))) 3. ==[ beta ]==> ((a (b a))((b a)(b a))) REDUCED to normal form. ------ 177039/20312445. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(a ((a a)(a a)))) 3. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 177040/20312454. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 177041/20312481. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z) b)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 177042/20312553. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 177043/20312733. ------ 1. ==[ start ]==> (((a b)(a (a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177044/20312760. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(b (^z.z))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b (^z.z))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.y))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 177045/20312832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177046/20312841. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 177047/20313129. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b a)) REDUCED to normal form. ------ 177048/20313156. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.(^y1.y1))) b)) REDUCED to normal form. ------ 177049/20313417. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177050/20313444. ------ 1. ==[ start ]==> ((a (^b.b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) b))) 3. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 177051/20313732. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177052/20313759. ------ 1. ==[ start ]==> ((a ((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(a (^y.y))) 3. ==[ beta ]==> ((a b)(a (^y.y))) 4. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 177053/20314047. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177054/20314074. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177055/20314101. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((b a) b)) REDUCED to normal form. ------ 177056/20314362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(a (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177057/20314371. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 177058/20314596. ------ 1. ==[ start ]==> (((a b)((a a) a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 177059/20314650. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177060/20314731. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 177061/20314758. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 177062/20315145. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y)(a a)))) 5. ==[ beta ]==> (c ((^y.y)(a a))) 6. ==[ alpha ]==> (c ((^x.x)(a a))) 7. ==[ beta ]==> (c (a a)) REDUCED to normal form. ------ 177063/20315199. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(a (b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(a (b a))) 3. ==[ beta ]==> (((b a)(b a))(a (b a))) REDUCED to normal form. ------ 177064/20315262. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 177065/20315280. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)((^y.y) a))) 3. ==[ beta ]==> (b ((a b)((^y.y) a))) 4. ==[ alpha ]==> (b ((a b)((^x.x) a))) 5. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 177066/20315388. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177067/20315514. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 177068/20315541. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 177069/20315568. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 177070/20315595. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177071/20315622. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177072/20315649. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(a b))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 177073/20315676. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 177074/20315703. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 177075/20315757. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 177076/20315784. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 177077/20315838. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 177078/20315928. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b ((^x2.x2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((^x2.x2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177079/20316009. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b)(a (^z.z)))) 3. ==[ beta ]==> (b ((a b)(a (^z.z)))) 4. ==[ alpha ]==> (b ((a b)(a (^x.x)))) REDUCED to normal form. ------ 177080/20316117. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177081/20316288. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 177082/20316315. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177083/20316396. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 177084/20316423. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.b))((a a) a)) REDUCED to normal form. ------ 177085/20316621. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 177086/20316783. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (^y.a))) 3. ==[ beta ]==> (((a b)(a a))(c (^y.a))) 4. ==[ alpha ]==> (((a b)(a a))(c (^x.a))) REDUCED to normal form. ------ 177087/20316810. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b (^y.b))) 3. ==[ beta ]==> (((a a)(a b))(b (^y.b))) 4. ==[ alpha ]==> (((a a)(a b))(b (^x.b))) REDUCED to normal form. ------ 177088/20316837. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.(a a)))) REDUCED to normal form. ------ 177089/20316918. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 177090/20316945. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 177091/20316999. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177092/20317170. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (c ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 177093/20317278. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177094/20317503. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 177095/20317530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177096/20317584. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 177097/20317611. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 177098/20317638. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a)) c)) REDUCED to normal form. ------ 177099/20317746. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 177100/20317818. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 177101/20317863. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 177102/20317917. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 177103/20317944. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (^x1.x1))(a (^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 177104/20317971. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 177105/20317998. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 177106/20318025. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177107/20318052. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 177108/20318106. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 177109/20318133. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 177110/20318160. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 177111/20318232. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) c)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177112/20318250. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^z.z))((^x1.x1) a))(^y.y)) 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. ------ 177113/20318637. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 177114/20318664. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177115/20318682. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b c)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b c)) 3. ==[ beta ]==> ((a (a (^y.y)))(b c)) 4. ==[ alpha ]==> ((a (a (^x.x)))(b c)) REDUCED to normal form. ------ 177116/20318691. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.a))) REDUCED to normal form. ------ 177117/20318763. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 177118/20318799. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.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) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177119/20318826. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177120/20318844. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((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. ------ 177121/20318907. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177122/20318952. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(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. ------ 177123/20318988. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177124/20319015. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) b) REDUCED to normal form. ------ 177125/20319069. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a) a)) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177126/20319087. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (a a))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 177127/20319096. ------ 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)))(^y.y)) a) REDUCED to normal form. ------ 177128/20319111. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) b) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177129/20319114. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 177130/20319135. ------ 1. ==[ start ]==> ((^a.(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177131/20320836. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177132/20324481. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177133/20330151. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177134/20330154. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 177135/20330178. ------ 1. ==[ start ]==> ((^a.(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177136/20330181. ------ 1. ==[ start ]==> ((a (^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177137/20330196. ------ 1. ==[ start ]==> ((^a.(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a (^y.y)))(^z.z))((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 177138/20330223. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177139/20330304. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^z.z) b)(^x1.(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177140/20330421. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (^x.((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 177141/20330493. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ eta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 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. ------ 177142/20330613. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 177143/20331546. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (((((a a)(a a))(^y.a))(((a a)(a a))(^y.a)))(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (((((a a)(a a))(^x.a))(((a a)(a a))(^y.a)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 177144/20331879. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177145/20331882. ------ 1. ==[ start ]==> ((a (^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 177146/20334177. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.((a a)(a a)))) 5. ==[ beta ]==> (b (^z.((a a)(a a)))) 6. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 177147/20334528. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 177148/20334537. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 177149/20334921. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 177150/20335203. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^z1.z1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.y1)) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177151/20335524. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177152/20335527. ------ 1. ==[ start ]==> ((a (^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177153/20335851. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^a.(^b.b))) 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. ------ 177154/20336445. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177155/20336454. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 (^z1.(^x2.x2))))) REDUCED to normal form. ------ 177156/20336838. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((((a b)(^y.(y y)))((a b)(^y.(y y))))(((a b)(^y.(y y)))((a b)(^y.(y y))))) 4. ==[ alpha ]==> ((((a b)(^x.(x x)))((a b)(^y.(y y))))(((a b)(^z.(z z)))((a b)(^x1.(x1 x1))))) REDUCED to normal form. ------ 177157/20337012. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(z a))) 3. ==[ beta ]==> (b (^z.(z a))) 4. ==[ alpha ]==> (b (^x.(x a))) REDUCED to normal form. ------ 177158/20338263. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^x.(a a))) REDUCED to normal form. ------ 177159/20339496. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.b))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 7. ==[ beta ]==> (^y.(^z.b)) 8. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 177160/20339658. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((a a) a))) 3. ==[ beta ]==> (b (^z.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 177161/20339829. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((y y) y))) REDUCED to normal form. ------ 177162/20340321. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a) c)) 3. ==[ beta ]==> (((^z.a) c)(((^z.a) c)(^y.y))) 4. ==[ alpha ]==> (((^x.a) c)(((^y.a) c)(^z.z))) 5. ==[ beta ]==> (a (((^y.a) c)(^z.z))) 6. ==[ alpha ]==> (a (((^x.a) c)(^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 177163/20340792. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^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. ------ 177164/20340882. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.z))(^y1.y1)) 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. ------ 177165/20341071. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 177166/20341152. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177167/20341170. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^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. ------ 177168/20341179. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 177169/20341194. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177170/20341197. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 177171/20341227. ------ 1. ==[ start ]==> ((a (^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177172/20341245. ------ 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. ------ 177173/20341254. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(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 ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177174/20341272. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 177175/20341326. ------ 1. ==[ start ]==> (((a a)(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 177176/20341353. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177177/20341362. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177178/20341389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177179/20341470. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 177180/20341515. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177181/20341542. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177182/20341551. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177183/20341578. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 177184/20341632. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177185/20341659. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (a (^y1.y1))))) 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. ------ 177186/20341731. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b (^y.y)) c)) 3. ==[ beta ]==> (((a a) a)((b (^y.y)) c)) 4. ==[ alpha ]==> (((a a) a)((b (^x.x)) c)) REDUCED to normal form. ------ 177187/20341902. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177188/20342109. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 177189/20342127. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((b b)(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a)(a a))) 5. ==[ beta ]==> ((b b)((^y.y)(a a))) 6. ==[ alpha ]==> ((b b)((^x.x)(a a))) 7. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 177190/20342262. ------ 1. ==[ start ]==> (((a (a a)) b)((b a)((a a) a))) REDUCED to normal form. ------ 177191/20342289. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (a (((a a)(^y.y))(a b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 177192/20342316. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 177193/20342343. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 177194/20342370. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)(b a))) REDUCED to normal form. ------ 177195/20342397. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 177196/20342424. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) b))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 7. ==[ beta ]==> ((a (a a))((^y.y) b)) 8. ==[ alpha ]==> ((a (a a))((^x.x) b)) 9. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 177197/20342541. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177198/20342568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177199/20342595. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a) a))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 177200/20342631. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(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. ------ 177201/20342766. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177202/20342847. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) b))) 8. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) b))) 9. ==[ beta ]==> ((a a)(((^y.y) b)((^y.y) b))) 10. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) b))) 11. ==[ beta ]==> ((a a)(b ((^y.y) b))) 12. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 13. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 177203/20342928. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 177204/20342946. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y) a)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x) a)) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 177205/20342973. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z)) b)) REDUCED to normal form. ------ 177206/20343117. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177207/20343279. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177208/20343288. ------ 1. ==[ start ]==> (((a b) a)(c ((a a)(a a)))) REDUCED to normal form. ------ 177209/20343315. ------ 1. ==[ start ]==> (((a a)(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(b (b (^y.y)))) REDUCED to normal form. ------ 177210/20343369. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 177211/20343396. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 177212/20343423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.a)(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177213/20343450. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 177214/20343477. ------ 1. ==[ start ]==> (((a b)(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x))((b a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 177215/20343666. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 177216/20343792. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177217/20343927. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 177218/20343954. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177219/20344008. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(b a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(b a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(b a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(b a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 11. ==[ beta ]==> ((^y.(^z.z))(b a)) 12. ==[ alpha ]==> ((^x.(^y.y))(b a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177220/20344089. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177221/20344161. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 177222/20344188. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b) c)) 3. ==[ beta ]==> (((a (^x.x))(a b))(b c)) REDUCED to normal form. ------ 177223/20344413. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177224/20344557. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> (((a b) c)(b (a (^y.y)))) 4. ==[ alpha ]==> (((a b) c)(b (a (^x.x)))) REDUCED to normal form. ------ 177225/20344584. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a a) b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177226/20344611. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(a (a a)))) REDUCED to normal form. ------ 177227/20344665. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 177228/20344692. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)(a b))) 3. ==[ beta ]==> ((a (^y.b))((a b)(a b))) 4. ==[ alpha ]==> ((a (^x.b))((a b)(a b))) REDUCED to normal form. ------ 177229/20344746. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177230/20344773. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (a a))(b a))) REDUCED to normal form. ------ 177231/20344800. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.a))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 177232/20344827. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 177233/20344854. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)((a a)(a a)))) REDUCED to normal form. ------ 177234/20344890. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 177235/20344917. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177236/20344944. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 177237/20344971. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 177238/20344998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177239/20345052. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a b)(^y.b))) 3. ==[ beta ]==> (((a b) a)((a b)(^y.b))) 4. ==[ alpha ]==> (((a b) a)((a b)(^x.b))) REDUCED to normal form. ------ 177240/20345079. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 177241/20345223. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> (b ((^z.z)((a a)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 177242/20345304. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177243/20345412. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((b a)((^y.b)(^z.b))) 4. ==[ alpha ]==> ((b a)((^x.b)(^y.b))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 177244/20345556. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 177245/20345574. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 177246/20345583. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 177247/20345610. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a)(^x.a))(b (a a))) REDUCED to normal form. ------ 177248/20345637. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) REDUCED to normal form. ------ 177249/20345970. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177250/20345979. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177251/20346060. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^z.(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 177252/20346141. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177253/20346249. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1)((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177254/20346276. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 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. ------ 177255/20346303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177256/20346438. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177257/20346546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177258/20346555. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 177259/20346573. ------ 1. ==[ start ]==> ((a (^b.b))((^a.a)(^b.b))) 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. ------ 177260/20346591. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z) a)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 177261/20346618. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 177262/20346852. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177263/20346897. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(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. ------ 177264/20346924. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.(^y2.y2)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177265/20347059. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((a a) a))) 3. ==[ beta ]==> (b ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177266/20347167. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177267/20347221. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177268/20347302. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 177269/20347383. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177270/20347491. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177271/20347500. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 177272/20347527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a)(a a))) 3. ==[ beta ]==> ((b (^y.y))((b a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((b a)(a a))) REDUCED to normal form. ------ 177273/20347563. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 177274/20347833. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177275/20347860. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((b (a a))((a a)(^y.a))) 6. ==[ alpha ]==> ((b (a a))((a a)(^x.a))) REDUCED to normal form. ------ 177276/20347887. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a b)(^x.(x x)))) REDUCED to normal form. ------ 177277/20347923. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177278/20348058. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(b a))) 3. ==[ beta ]==> (b ((^z.z)(b a))) 4. ==[ alpha ]==> (b ((^x.x)(b a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 177279/20348166. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177280/20348247. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 177281/20348274. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177282/20348283. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(c (a a))) REDUCED to normal form. ------ 177283/20348310. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b ((a a)(^x1.x1)))) REDUCED to normal form. ------ 177284/20348391. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 177285/20348418. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.b))((a b) a)) REDUCED to normal form. ------ 177286/20348472. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 177287/20348526. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (a b))) REDUCED to normal form. ------ 177288/20348553. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 177289/20348580. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 177290/20348616. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 177291/20348643. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177292/20348670. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b)(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.a))) REDUCED to normal form. ------ 177293/20348697. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 177294/20348724. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177295/20348778. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.b))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.b))) REDUCED to normal form. ------ 177296/20348805. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 177297/20348886. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a) b)) REDUCED to normal form. ------ 177298/20348913. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b) c)) 3. ==[ beta ]==> ((b (a (^y.y)))((a b) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b) c)) REDUCED to normal form. ------ 177299/20349057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177300/20349282. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))(a b))) 3. ==[ beta ]==> ((b c)((a (^y.y))(a b))) 4. ==[ alpha ]==> ((b c)((a (^x.x))(a b))) REDUCED to normal form. ------ 177301/20349309. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(a a))) REDUCED to normal form. ------ 177302/20349354. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(a a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 177303/20349381. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((^y.b)(a (^z.z))) 6. ==[ alpha ]==> ((^x.b)(a (^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177304/20349435. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 177305/20349516. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177306/20349777. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 177307/20349804. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b) b)) 5. ==[ beta ]==> ((a b)((^y.b) b)) 6. ==[ alpha ]==> ((a b)((^x.b) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 177308/20350020. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177309/20350047. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.a))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.a))) 9. ==[ beta ]==> ((b a)(^y.a)) 10. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 177310/20350074. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 177311/20350218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177312/20350299. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177313/20350524. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((a a)((a a) a))) 5. ==[ beta ]==> (a ((a a)((a a) a))) REDUCED to normal form. ------ 177314/20350542. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a (^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(a (^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.b))) 5. ==[ beta ]==> ((^y.y)(a (^z.b))) 6. ==[ alpha ]==> ((^x.x)(a (^y.b))) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 177315/20350569. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 177316/20350623. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))((^z.z) a))) 7. ==[ beta ]==> ((b b)((^y.(y y))((^z.z) a))) 8. ==[ alpha ]==> ((b b)((^x.(x x))((^y.y) a))) 9. ==[ beta ]==> ((b b)(((^y.y) a)((^y.y) a))) 10. ==[ alpha ]==> ((b b)(((^x.x) a)((^y.y) a))) 11. ==[ beta ]==> ((b b)(a ((^y.y) a))) 12. ==[ alpha ]==> ((b b)(a ((^x.x) a))) 13. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 177317/20350704. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.z)((a a) a))) 3. ==[ beta ]==> (b ((^z.z)((a a) a))) 4. ==[ alpha ]==> (b ((^x.x)((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 177318/20350812. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a)(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177319/20350821. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (a (a a)))) REDUCED to normal form. ------ 177320/20350848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 177321/20350875. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((a a) a))) REDUCED to normal form. ------ 177322/20350929. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 177323/20351046. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a)) b)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 177324/20351073. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177325/20351100. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(b a))(a (^y.a))) 4. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.a))) REDUCED to normal form. ------ 177326/20351127. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 177327/20351154. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 177328/20351181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 177329/20351343. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y)) b)) 5. ==[ beta ]==> ((a a)((^y.(y y)) b)) 6. ==[ alpha ]==> ((a a)((^x.(x x)) b)) 7. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 177330/20351361. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 177331/20351370. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a) c)) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 177332/20351784. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 7. ==[ beta ]==> ((^y.a)(a a)) 8. ==[ alpha ]==> ((^x.a)(a a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177333/20351811. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177334/20351820. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b c)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b c)) REDUCED to normal form. ------ 177335/20351838. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^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. ------ 177336/20351892. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 177337/20351928. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z) 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. ------ 177338/20351955. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 177339/20351973. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (^y.(^z.z)))) 3. ==[ beta ]==> (b (b (^y.(^z.z)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 177340/20352036. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b b)) REDUCED to normal form. ------ 177341/20352081. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 177342/20352117. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 177343/20352144. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 177344/20352198. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a b)) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177345/20352216. ------ 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 ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 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. ------ 177346/20352225. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (a a))) REDUCED to normal form. ------ 177347/20352240. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) c) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177348/20352243. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 177349/20352260. ------ 1. ==[ start ]==> (^a.((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.((x x)(x (x (^y.y))))) REDUCED to normal form. ------ 177350/20352261. ------ 1. ==[ start ]==> (a ((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (a ((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 177351/20357934. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177352/20363289. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177353/20363292. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) c) REDUCED to normal form. ------ 177354/20363310. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a)))) a) 2. ==[ alpha ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 177355/20363316. ------ 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. ------ 177356/20363337. ------ 1. ==[ start ]==> (((^a.a) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177357/20363406. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177358/20363568. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^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 ]==> (^x.((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177359/20363769. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) REDUCED to normal form. ------ 177360/20363811. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 177361/20364210. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 177362/20364261. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177363/20365800. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))((a a)(a a)))((a (^z.z))((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))((a a)(a a)))((a (^z.z))((a a)(a a))))) 5. ==[ beta ]==> (((a (^y.y))((a a)(a a)))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 177364/20366226. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177365/20367324. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (b (^z.(^x1.(a a)))) 6. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 177366/20367684. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177367/20368359. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 177368/20368692. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 177369/20368986. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177370/20368989. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177371/20369304. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177372/20369601. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) REDUCED to normal form. ------ 177373/20370159. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 177374/20371653. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 177375/20371878. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^y.(y y))) REDUCED to normal form. ------ 177376/20372805. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 177377/20372814. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 177378/20372976. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 177379/20373468. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((^z.z) a)(a (^x1.x1)))((((^z.z) a)(a (^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((((^z.z) a)(a (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a (a (^y.y)))((((^z.z) a)(a (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((((^y.y) a)(a (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a (a (^x.x)))((a (a (^z.z)))(^x1.x1))) 8. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 177380/20373867. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 5. ==[ beta ]==> (b (^y.(^z.(z z)))) 6. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 177381/20374029. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 177382/20374218. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177383/20374299. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177384/20374326. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 177385/20374341. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177386/20374344. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 177387/20374362. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 177388/20374374. ------ 1. ==[ start ]==> ((a a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 177389/20374392. ------ 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. ------ 177390/20374410. ------ 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. ------ 177391/20374419. ------ 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)((a a)(^y.y))) 4. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 177392/20374437. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 177393/20374464. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 177394/20374518. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177395/20374527. ------ 1. ==[ start ]==> (((a a) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 177396/20374554. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 177397/20374572. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 177398/20374599. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 177399/20374626. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177400/20374662. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177401/20374707. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177402/20374743. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 177403/20374770. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 177404/20374797. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 177405/20374815. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 (^y1.y1))))) 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. ------ 177406/20374824. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (a (^x1.x1)))) REDUCED to normal form. ------ 177407/20374851. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177408/20374869. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 177409/20374959. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.b)(^b.(^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. ------ 177410/20375040. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 177411/20375067. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 177412/20375121. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 177413/20375148. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177414/20375238. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 177415/20375265. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 177416/20375292. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a a))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 177417/20375319. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 177418/20375616. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 177419/20375643. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 177420/20375670. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a a)((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)((a a)((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 177421/20375787. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 177422/20375841. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)(^z.a))) 5. ==[ beta ]==> (a ((b a)(^z.a))) 6. ==[ alpha ]==> (a ((b a)(^x.a))) REDUCED to normal form. ------ 177423/20375877. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177424/20375904. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 177425/20375922. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 177426/20375958. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 177427/20375985. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177428/20376003. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (a a))(^z.z))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(^z.z))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(^y.y))) 7. ==[ beta ]==> ((a a)((a (a a))(^y.y))) 8. ==[ alpha ]==> ((a a)((a (a a))(^x.x))) REDUCED to normal form. ------ 177429/20376012. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.a))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.a))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a (a a))(^x.a))(b ((^y.y) b))) 7. ==[ beta ]==> (((a (a a))(^x.a))(b b)) REDUCED to normal form. ------ 177430/20376039. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177431/20376066. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177432/20376417. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a) b)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 177433/20376444. ------ 1. ==[ start ]==> (((a b) a)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 177434/20376669. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 177435/20376696. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a a)(a b))) REDUCED to normal form. ------ 177436/20376723. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a b)(a a))) REDUCED to normal form. ------ 177437/20376750. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 177438/20376777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> (a (((^y.y)(^z.z))(b a))) 8. ==[ alpha ]==> (a (((^x.x)(^y.y))(b a))) 9. ==[ beta ]==> (a ((^y.y)(b a))) 10. ==[ alpha ]==> (a ((^x.x)(b a))) 11. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 177439/20376804. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 177440/20376831. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a a))(a ((^x.x) b))) 5. ==[ beta ]==> (((a b)(a a))(a b)) REDUCED to normal form. ------ 177441/20376858. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 177442/20376948. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177443/20377029. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 177444/20377083. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.b))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.b))) 7. ==[ beta ]==> ((a a)((a a)(^y.b))) 8. ==[ alpha ]==> ((a a)((a a)(^x.b))) REDUCED to normal form. ------ 177445/20377092. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 177446/20377110. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 177447/20377119. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 177448/20377173. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177449/20377200. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((^y.(y y))(a (^z.(^x1.x1))))((^y.(y y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 9. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^z1.(^x2.x2)))(a (^z1.(^x2.x2))))) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))) REDUCED to normal form. ------ 177450/20377227. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 177451/20377245. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 177452/20377254. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177453/20377281. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 177454/20377470. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a))(^z.b))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177455/20377704. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177456/20378010. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(a a)))) REDUCED to normal form. ------ 177457/20378379. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(^z.(a a)))) 5. ==[ beta ]==> (b ((a a)(^z.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 177458/20378460. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 177459/20378523. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 177460/20378631. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177461/20378712. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177462/20378739. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(a a))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 177463/20378856. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 177464/20378883. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 177465/20378910. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a b)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a b)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)((a a) a))) 5. ==[ beta ]==> ((a (a a))((a b)((a a) a))) REDUCED to normal form. ------ 177466/20378937. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a) a)(a b))) REDUCED to normal form. ------ 177467/20378964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 10. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 11. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 177468/20378991. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 177469/20379018. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a (b a))) REDUCED to normal form. ------ 177470/20379045. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 177471/20379072. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a) b)) REDUCED to normal form. ------ 177472/20379117. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^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. ------ 177473/20379135. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177474/20379216. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 177475/20379297. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 177476/20379405. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177477/20379414. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 177478/20379432. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 177479/20379441. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177480/20379459. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((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) REDUCED to normal form. ------ 177481/20379522. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177482/20379549. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177483/20379603. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 177484/20379630. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177485/20379657. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 177486/20379711. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 177487/20379747. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a ((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 177488/20379774. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 177489/20379801. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 177490/20379828. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 177491/20379855. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> ((a b)((a a)(a (a a)))) REDUCED to normal form. ------ 177492/20379882. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.x))) REDUCED to normal form. ------ 177493/20379909. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177494/20379936. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(a b))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a b))) 7. ==[ beta ]==> (((a a)(a (a a)))(a b)) REDUCED to normal form. ------ 177495/20379963. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))(a a))) REDUCED to normal form. ------ 177496/20380008. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(c (^d.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(c (^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177497/20380017. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.z))(b a))) REDUCED to normal form. ------ 177498/20380044. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b)((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a b)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 177499/20380080. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.y)((a (^z1.(^x2.x2)))(^y2.y2))) 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)) REDUCED to normal form. ------ 177500/20380215. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a) a)(^z.a))) 3. ==[ beta ]==> (b (((a a) a)(^z.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 177501/20380332. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 177502/20380359. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 177503/20380377. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z))) a)) 5. ==[ beta ]==> (b ((a (^y.(^z.z))) a)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177504/20380386. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177505/20380404. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((b a) b)) 3. ==[ beta ]==> ((^y.y)((b a) b)) 4. ==[ alpha ]==> ((^x.x)((b a) b)) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 177506/20380494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177507/20380521. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 177508/20380548. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 177509/20380575. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 177510/20380602. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 177511/20380656. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 177512/20380719. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 177513/20380746. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 177514/20380773. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(a (a a)))) 3. ==[ beta ]==> ((a (b a))((a b)(a (a a)))) REDUCED to normal form. ------ 177515/20380800. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 177516/20380827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((a a) a))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((a a) a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((a a) a))) 9. ==[ beta ]==> ((a a)((^y.y)((a a) a))) 10. ==[ alpha ]==> ((a a)((^x.x)((a a) a))) 11. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177517/20380854. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))(a b))) REDUCED to normal form. ------ 177518/20380881. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)((a a) a))(a (a a))) REDUCED to normal form. ------ 177519/20380908. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 177520/20380935. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(b a))) REDUCED to normal form. ------ 177521/20381079. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.y1)))) 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. ------ 177522/20381358. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 177523/20381385. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 177524/20381439. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 177525/20381565. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(a a)) c)) 3. ==[ beta ]==> (b ((^y.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177526/20381709. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 177527/20381736. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177528/20382294. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177529/20382438. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (^y.b))) 3. ==[ beta ]==> ((b c)(c (^y.b))) 4. ==[ alpha ]==> ((b c)(c (^x.b))) REDUCED to normal form. ------ 177530/20382465. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b (^x.(a a)))) REDUCED to normal form. ------ 177531/20382510. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((b (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 177532/20382537. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((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. ------ 177533/20382573. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177534/20382591. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.(x2 x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.(z1 z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.(z1 z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(y1 y1))) REDUCED to normal form. ------ 177535/20382600. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177536/20382672. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 177537/20382681. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177538/20382708. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 177539/20382816. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 177540/20382843. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177541/20382906. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (a b))) REDUCED to normal form. ------ 177542/20382933. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 177543/20382960. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b)(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a b)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b)(a a))) 5. ==[ beta ]==> ((a b)((a b)(a a))) REDUCED to normal form. ------ 177544/20382987. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 177545/20383014. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b a)((^y.y)((^z.z) a))) 8. ==[ alpha ]==> ((b a)((^x.x)((^y.y) a))) 9. ==[ beta ]==> ((b a)((^y.y) a)) 10. ==[ alpha ]==> ((b a)((^x.x) a)) 11. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177546/20383041. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 177547/20383068. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a a))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a b)(a a))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a b)(a a))(a (^y.y))) 8. ==[ alpha ]==> (((a b)(a a))(a (^x.x))) REDUCED to normal form. ------ 177548/20383095. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)(a b))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a)(a b))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 177549/20383122. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)(a b))) REDUCED to normal form. ------ 177550/20383374. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a) b)) 5. ==[ beta ]==> ((^y.y)(((a a) a) b)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177551/20383563. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177552/20383680. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b (^z.a))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.a))) 4. ==[ alpha ]==> (((^x.x) a)(b (^y.a))) 5. ==[ beta ]==> (a (b (^y.a))) 6. ==[ alpha ]==> (a (b (^x.a))) REDUCED to normal form. ------ 177553/20383725. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^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. ------ 177554/20383779. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a))(^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a))(^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a))(^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a))(^y.a))) 7. ==[ beta ]==> ((b b)((a (a a))(^y.a))) 8. ==[ alpha ]==> ((b b)((a (a a))(^x.a))) REDUCED to normal form. ------ 177555/20383788. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 177556/20383815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177557/20383860. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)(^z.a))) 3. ==[ beta ]==> (b ((a a)(^z.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 177558/20383869. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 177559/20383896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 177560/20383923. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 177561/20383977. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 177562/20384004. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177563/20384031. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 177564/20384121. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 177565/20384148. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 177566/20384175. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.x))) REDUCED to normal form. ------ 177567/20384283. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c d)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c d)) REDUCED to normal form. ------ 177568/20384418. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c ((^y.y) a))) 3. ==[ beta ]==> ((b (a (a a)))(c ((^y.y) a))) 4. ==[ alpha ]==> ((b (a (a a)))(c ((^x.x) a))) 5. ==[ beta ]==> ((b (a (a a)))(c a)) REDUCED to normal form. ------ 177569/20384445. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (a (a a)))) REDUCED to normal form. ------ 177570/20384499. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a a))) 5. ==[ beta ]==> ((a a)((a (a a))(a a))) REDUCED to normal form. ------ 177571/20384526. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a (^y.y)))) REDUCED to normal form. ------ 177572/20384535. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a) c)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a) c)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a) c)) 5. ==[ beta ]==> (((^z.a) c)(^y.y)) 6. ==[ alpha ]==> (((^x.a) c)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177573/20384922. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a (^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.(y y)))) 5. ==[ beta ]==> (b (a (^y.(y y)))) 6. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 177574/20384940. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> (((^y.y) a)(^z.z)) 8. ==[ alpha ]==> (((^x.x) a)(^y.y)) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177575/20384949. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 177576/20384967. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177577/20384976. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 177578/20384994. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((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. ------ 177579/20385048. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y)) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 177580/20385084. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 177581/20385129. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((^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. ------ 177582/20385192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 177583/20385237. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((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. ------ 177584/20385273. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 177585/20385300. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 177586/20385354. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177587/20385372. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 177588/20385381. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 177589/20385399. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 177590/20385417. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 177591/20385425. ------ 1. ==[ start ]==> (^a.(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 177592/20385426. ------ 1. ==[ start ]==> (a (b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (a (b (^x.(x (^y.y))))) REDUCED to normal form. ------ 177593/20385456. ------ 1. ==[ start ]==> ((^a.(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177594/20396454. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177595/20396475. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a)))) b) 2. ==[ alpha ]==> (((a a)(a (a (^x.x)))) b) REDUCED to normal form. ------ 177596/20396490. ------ 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. ------ 177597/20396499. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177598/20396517. ------ 1. ==[ start ]==> ((^a.(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 177599/20396520. ------ 1. ==[ start ]==> ((a (a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177600/20396544. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177601/20397084. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.b)(^b.(^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. ------ 177602/20397384. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 177603/20397816. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 177604/20398221. ------ 1. ==[ start ]==> (((a a)((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)((a a) a))(^x.(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177605/20398767. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.(((b a)((^z.z)(^x1.x1)))((b a)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((b a)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1))))) 5. ==[ beta ]==> (^x.(((b a)(^z.z))((b a)((^x1.x1)(^y1.y1))))) 6. ==[ alpha ]==> (^x.(((b a)(^y.y))((b a)((^z.z)(^x1.x1))))) 7. ==[ beta ]==> (^x.(((b a)(^y.y))((b a)(^x1.x1)))) 8. ==[ alpha ]==> (^x.(((b a)(^y.y))((b a)(^z.z)))) REDUCED to normal form. ------ 177606/20399013. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 177607/20400405. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ eta ]==> (b ((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177608/20400954. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177609/20401242. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^x1.x1)(a a))(^y.(^z.z))) 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. ------ 177610/20401845. ------ 1. ==[ start ]==> ((^a.(^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177611/20401866. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 177612/20402160. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177613/20402172. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(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)))) REDUCED to normal form. ------ 177614/20402478. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177615/20403159. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((^y.(a a))((^z.z) a))((^y.(a a))((^z.z) a)))(((^y.(a a))((^z.z) a))((^y.(a a))((^z.z) a)))) 4. ==[ alpha ]==> ((((^x.(a a))((^y.y) a))((^z.(a a))((^x1.x1) a)))(((^y1.(a a))((^z1.z1) a))((^x2.(a a))((^y2.y2) a)))) 5. ==[ beta ]==> (((a a)((^z.(a a))((^x1.x1) a)))(((^y1.(a a))((^z1.z1) a))((^x2.(a a))((^y2.y2) a)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))((^y.y) a)))(((^z.(a a))((^x1.x1) a))((^y1.(a a))((^z1.z1) a)))) 7. ==[ beta ]==> (((a a)(a a))(((^z.(a a))((^x1.x1) a))((^y1.(a a))((^z1.z1) a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))((^y.y) a))((^z.(a a))((^x1.x1) a)))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^z.(a a))((^x1.x1) a)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))((^y.y) a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 177616/20404239. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177617/20404827. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177618/20405052. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177619/20405400. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177620/20405988. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 177621/20406219. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 177622/20406321. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.y))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.y))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.x))) REDUCED to normal form. ------ 177623/20406456. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 177624/20407203. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.c)) 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. ------ 177625/20407392. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 177626/20407491. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.b)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 177627/20407515. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177628/20407518. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 177629/20407536. ------ 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. ------ 177630/20407557. ------ 1. ==[ start ]==> ((a a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 177631/20407566. ------ 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. ------ 177632/20407584. ------ 1. ==[ start ]==> ((a (a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177633/20407602. ------ 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. ------ 177634/20407611. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> ((a b)((a a)(^y.y))) 4. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 177635/20407629. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177636/20407656. ------ 1. ==[ start ]==> (((^a.a) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 177637/20407683. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 177638/20407710. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 177639/20407764. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 177640/20407791. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177641/20407827. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 177642/20407854. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 177643/20407926. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 177644/20408007. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 177645/20408034. ------ 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)) REDUCED to normal form. ------ 177646/20408151. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.b)(^b.(^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. ------ 177647/20408448. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177648/20408466. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((b b)((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> ((b b)((^x.(x (^y.y))) a)) 5. ==[ beta ]==> ((b b)(a (^y.y))) 6. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 177649/20408511. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177650/20408538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 177651/20408592. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177652/20408646. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 7. ==[ beta ]==> (((a a)(^y.y))(a b)) 8. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 177653/20408673. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(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. ------ 177654/20408727. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 177655/20408880. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 177656/20409060. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (b (((a a)(^y.y))(^z.b))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 177657/20409087. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 177658/20409168. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177659/20409195. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (a a))(^y.y))) REDUCED to normal form. ------ 177660/20409285. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 177661/20409393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 177662/20409420. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177663/20409645. ------ 1. ==[ start ]==> (((^a.a)(a b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((a b)(c ((a a)(a a)))) REDUCED to normal form. ------ 177664/20409672. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(b (b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 177665/20409726. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b (^y.y))(a a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b (^y.y))(a a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x))(a a))) REDUCED to normal form. ------ 177666/20409762. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a)) c)) 5. ==[ beta ]==> ((^y.a)((^z.(a a)) c)) 6. ==[ alpha ]==> ((^x.a)((^y.(a a)) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177667/20409807. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 177668/20409834. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a)))((b a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.y))) REDUCED to normal form. ------ 177669/20410050. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177670/20410077. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 177671/20410221. ------ 1. ==[ start ]==> (((a b) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 177672/20410275. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 177673/20410302. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b)(^z.(a a)))) REDUCED to normal form. ------ 177674/20410383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))((a (a a))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))((a (a a))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a (a a))(^y.(^z.(^x1.x1))))((a (a a))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 177675/20410410. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 177676/20410437. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177677/20410527. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 177678/20410554. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.a)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.a)) REDUCED to normal form. ------ 177679/20410581. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177680/20410662. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 177681/20410689. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 177682/20410887. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 177683/20410896. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b) c)((^x.(a a)) b)) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 177684/20410923. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y) c)) 3. ==[ beta ]==> (((a a) b)((^y.y) c)) 4. ==[ alpha ]==> (((a a) b)((^x.x) c)) 5. ==[ beta ]==> (((a a) b) c) REDUCED to normal form. ------ 177685/20410968. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(a (a a)))) REDUCED to normal form. ------ 177686/20410995. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177687/20411049. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a b)(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(a b))) REDUCED to normal form. ------ 177688/20411130. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 177689/20411283. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((a (a b))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((a (a b))(a (^y.y))) 6. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 177690/20411310. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177691/20411391. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))((a a) a))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 177692/20411418. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(a b))) 5. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 177693/20411472. ------ 1. ==[ start ]==> ((a (b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 177694/20411913. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(b ((^y.y) b))) 3. ==[ beta ]==> (b (b ((^y.y) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 177695/20411949. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 177696/20411976. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 177697/20412021. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((b a) a)) REDUCED to normal form. ------ 177698/20412255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 177699/20412300. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177700/20412309. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b)(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. ------ 177701/20412597. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.z))) REDUCED to normal form. ------ 177702/20412624. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 177703/20412912. ------ 1. ==[ start ]==> ((a (^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 177704/20412930. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 177705/20413227. ------ 1. ==[ start ]==> ((a ((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177706/20413236. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((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. ------ 177707/20413542. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177708/20413569. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 177709/20413596. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a) b)) REDUCED to normal form. ------ 177710/20413830. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(b (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177711/20413866. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177712/20414199. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 177713/20414226. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 177714/20414667. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((b a)(b a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 177715/20414730. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177716/20414748. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (b ((a a)(a (^y.y)))) 6. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 177717/20414757. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 177718/20414856. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (a a))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177719/20414982. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 177720/20415009. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 177721/20415036. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 177722/20415090. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 177723/20415117. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))((a a) a))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177724/20415144. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)(a b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)(a b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)(a b))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 177725/20415171. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 177726/20415252. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 177727/20415279. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 177728/20415306. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 177729/20415477. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 177730/20415585. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177731/20415756. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 177732/20415783. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.(y1 y1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 177733/20415864. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 177734/20415891. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 177735/20416089. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 177736/20416116. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.(a a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(a a))) REDUCED to normal form. ------ 177737/20416278. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c (^y.a))) 3. ==[ beta ]==> (((a a)(a b))(c (^y.a))) 4. ==[ alpha ]==> (((a a)(a b))(c (^x.a))) REDUCED to normal form. ------ 177738/20416305. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.b))) REDUCED to normal form. ------ 177739/20416359. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 177740/20416386. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((b a)((^y.a)(a (^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.a)(a (^y.y)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177741/20416413. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177742/20416467. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177743/20416638. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (a (a a)))) 3. ==[ beta ]==> (b (d (a (a a)))) REDUCED to normal form. ------ 177744/20416746. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177745/20416881. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((a a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((a a) a))) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177746/20416971. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 177747/20416998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177748/20417052. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 177749/20417079. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a) a)) REDUCED to normal form. ------ 177750/20417106. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 177751/20417268. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 177752/20417286. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 177753/20417331. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.(z z)))) REDUCED to normal form. ------ 177754/20417358. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 177755/20417385. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (^y.a))) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.a))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.a))) REDUCED to normal form. ------ 177756/20417412. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177757/20417439. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 177758/20417466. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 177759/20417493. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177760/20417520. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 177761/20417574. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 177762/20417601. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.a))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 177763/20417628. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 177764/20417700. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z)) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z)) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) b)) 5. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 177765/20417718. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((((^z.z) a)(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.z)) 7. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177766/20418132. ------ 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 (^x.x))) a)(a (^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.y))) REDUCED to normal form. ------ 177767/20418159. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177768/20418177. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b c)) 3. ==[ beta ]==> ((^y.y)(b c)) 4. ==[ alpha ]==> ((^x.x)(b c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 177769/20418267. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a) c)) 5. ==[ beta ]==> ((^y.y)((a a) c)) 6. ==[ alpha ]==> ((^x.x)((a a) c)) 7. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 177770/20418294. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 177771/20418312. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((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. ------ 177772/20418375. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 177773/20418456. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 177774/20418483. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177775/20418537. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177776/20418555. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a b)) 3. ==[ beta ]==> (((a a)(^y.y))(a b)) 4. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 177777/20418564. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a) a)) REDUCED to normal form. ------ 177778/20418582. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 177779/20418600. ------ 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. ------ 177780/20429646. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177781/20429700. ------ 1. ==[ start ]==> ((^a.(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177782/20429730. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177783/20429745. ------ 1. ==[ start ]==> ((^a.b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.b)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177784/20429826. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^z.(z z)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177785/20429943. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177786/20430015. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 177787/20430186. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 177788/20430510. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177789/20430603. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((b b)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((b b)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 177790/20431068. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((b (^y.y))(^z.(^x1.x1)))((b (^y.y))(^z.(^x1.x1))))((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((b (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1))))((b (^x2.x2))(^y2.(^z2.z2)))) REDUCED to normal form. ------ 177791/20431401. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177792/20431845. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(^z.z)))(^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))) REDUCED to normal form. ------ 177793/20433606. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177794/20434086. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((y y)(y y)))) REDUCED to normal form. ------ 177795/20434443. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((((^x1.x1) b)(^y1.y1))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177796/20434752. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.x)(a (^y.(^z.z))))(^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)) REDUCED to normal form. ------ 177797/20435046. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177798/20435400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(^z1.(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177799/20435697. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177800/20436003. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 177801/20436360. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((((^y.y)(a a))(^z.a))(((^y.y)(a a))(^z.a)))((((^y.y)(a a))(^z.a))(((^y.y)(a a))(^z.a)))) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.a))(((^z.z)(a a))(^x1.a)))((((^y1.y1)(a a))(^z1.a))(((^x2.x2)(a a))(^y2.a)))) 5. ==[ beta ]==> ((((a a)(^y.a))(((^z.z)(a a))(^x1.a)))((((^y1.y1)(a a))(^z1.a))(((^x2.x2)(a a))(^y2.a)))) 6. ==[ alpha ]==> ((((a a)(^x.a))(((^y.y)(a a))(^z.a)))((((^x1.x1)(a a))(^y1.a))(((^z1.z1)(a a))(^x2.a)))) 7. ==[ beta ]==> ((((a a)(^x.a))((a a)(^z.a)))((((^x1.x1)(a a))(^y1.a))(((^z1.z1)(a a))(^x2.a)))) 8. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))((((^z.z)(a a))(^x1.a))(((^y1.y1)(a a))(^z1.a)))) 9. ==[ beta ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^x1.a))(((^y1.y1)(a a))(^z1.a)))) 10. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))(((^x1.x1)(a a))(^y1.a)))) 11. ==[ beta ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))((a a)(^y1.a)))) 12. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))((a a)(^x1.a)))) REDUCED to normal form. ------ 177802/20437830. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177803/20438601. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177804/20439045. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 177805/20439657. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177806/20439843. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z)) b)) 3. ==[ beta ]==> (((^z.(z z)) b)(((^z.(z z)) b)(^y.y))) 4. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(y y)) b)(^z.z))) 5. ==[ beta ]==> ((b b)(((^y.(y y)) b)(^z.z))) 6. ==[ alpha ]==> ((b b)(((^x.(x x)) b)(^y.y))) 7. ==[ beta ]==> ((b b)((b b)(^y.y))) 8. ==[ alpha ]==> ((b b)((b b)(^x.x))) REDUCED to normal form. ------ 177807/20440242. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 5. ==[ beta ]==> (b (^y.((^z.z) a))) 6. ==[ alpha ]==> (b (^x.((^y.y) a))) 7. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 177808/20440260. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 177809/20440431. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177810/20440557. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^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. ------ 177811/20440620. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177812/20440692. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 177813/20440701. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.b)) REDUCED to normal form. ------ 177814/20440716. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177815/20440719. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 177816/20440737. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.a)) REDUCED to normal form. ------ 177817/20440776. ------ 1. ==[ start ]==> ((a (^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 177818/20440785. ------ 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. ------ 177819/20440803. ------ 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. ------ 177820/20440821. ------ 1. ==[ start ]==> ((a b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a b)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 177821/20440830. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 177822/20440875. ------ 1. ==[ start ]==> (((a a)(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 177823/20440902. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 177824/20440938. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 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. ------ 177825/20440965. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177826/20441019. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 177827/20441091. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177828/20441100. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177829/20441127. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177830/20441181. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (a ((^y.a)(b (^z.z)))) 6. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177831/20441208. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177832/20441262. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x x)))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177833/20441280. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> (((a a) a)((^y.y) b)) 6. ==[ alpha ]==> (((a a) a)((^x.x) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177834/20441307. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 177835/20441370. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.b)(^b.(^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. ------ 177836/20441397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177837/20441478. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 177838/20441559. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177839/20441586. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 177840/20441676. ------ 1. ==[ start ]==> (((^a.(a a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(a (a (a (^y.y))))) 3. ==[ beta ]==> ((b b)(a (a (a (^y.y))))) 4. ==[ alpha ]==> ((b b)(a (a (a (^x.x))))) REDUCED to normal form. ------ 177841/20441685. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a (a a))(a a))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(a (^x.x))) REDUCED to normal form. ------ 177842/20441811. ------ 1. ==[ start ]==> (((a (a a)) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 177843/20441838. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((b a)((a a) a))) 5. ==[ beta ]==> (a ((b a)((a a) a))) REDUCED to normal form. ------ 177844/20441865. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 177845/20441892. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)(a a))) REDUCED to normal form. ------ 177846/20441919. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 177847/20441946. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 177848/20441973. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 11. ==[ beta ]==> (a (^y.(^z.z))) 12. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 177849/20442117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177850/20442144. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177851/20442180. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177852/20442234. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 177853/20442315. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 177854/20442342. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.b)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177855/20442396. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177856/20442477. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 177857/20442522. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 177858/20442549. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b (^y.y)) b)) 3. ==[ beta ]==> ((a (a (a a)))((b (^y.y)) b)) 4. ==[ alpha ]==> ((a (a (a a)))((b (^x.x)) b)) REDUCED to normal form. ------ 177859/20442747. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 177860/20442828. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.x1))) 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. ------ 177861/20442855. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 177862/20442864. ------ 1. ==[ start ]==> (((a a)(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(c ((a a)(a a)))) REDUCED to normal form. ------ 177863/20442918. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 177864/20442945. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b (^y.y))(a a))) REDUCED to normal form. ------ 177865/20442972. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177866/20442999. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 177867/20443026. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 177868/20443215. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (b ((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 177869/20443260. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.(a a)))) 3. ==[ beta ]==> ((^y.(a a))(c (^z.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(c (^y.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177870/20443422. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177871/20443503. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177872/20443638. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177873/20443710. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b (^y.y)) a)) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y)) a)) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 177874/20443737. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a)) b)) REDUCED to normal form. ------ 177875/20443764. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) b) c)) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) b) c)) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b) c)) 5. ==[ beta ]==> ((a ((a a) a))(b c)) REDUCED to normal form. ------ 177876/20444106. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a))(a a))) REDUCED to normal form. ------ 177877/20444133. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (((a a) b)(b (a (^y.y)))) 6. ==[ alpha ]==> (((a a) b)(b (a (^x.x)))) REDUCED to normal form. ------ 177878/20444160. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 177879/20444214. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 177880/20444241. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.b))((a a)((a a) a))) REDUCED to normal form. ------ 177881/20444295. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177882/20444322. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 177883/20444349. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(b a))) REDUCED to normal form. ------ 177884/20444376. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 177885/20444403. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^z.z)) b)) REDUCED to normal form. ------ 177886/20444466. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 177887/20444493. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a b))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a b))(b (^x.(^y.y)))) REDUCED to normal form. ------ 177888/20444520. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 177889/20444547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(z z)))) 7. ==[ beta ]==> ((^y.y)((b a)(^z.(z z)))) 8. ==[ alpha ]==> ((^x.x)((b a)(^y.(y y)))) 9. ==[ beta ]==> ((b a)(^y.(y y))) 10. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 177890/20444574. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177891/20444601. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((a b) a)((a a)(^y.a))) 6. ==[ alpha ]==> (((a b) a)((a a)(^x.a))) REDUCED to normal form. ------ 177892/20444628. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a b)(^y.b))) REDUCED to normal form. ------ 177893/20444655. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 177894/20444682. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 177895/20444772. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177896/20444853. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177897/20444961. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 177898/20444988. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.b))) 5. ==[ beta ]==> ((^y.b)(^z.b)) 6. ==[ alpha ]==> ((^x.b)(^y.b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177899/20445042. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 177900/20445105. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 177901/20445123. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^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. ------ 177902/20445132. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b b)) REDUCED to normal form. ------ 177903/20445159. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 177904/20445186. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (a a))) REDUCED to normal form. ------ 177905/20445519. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 177906/20445528. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177907/20445609. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177908/20445690. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (b ((^x1.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177909/20445798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177910/20445825. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 177911/20445852. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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. ------ 177912/20445987. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 177913/20446122. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177914/20446167. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y) a)) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 177915/20446194. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 177916/20446248. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z)) d)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) d)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) d)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 177917/20446401. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177918/20446446. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 177919/20446473. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(a (^z1.z1))) 3. ==[ beta ]==> ((^y.y)(a (^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177920/20446608. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 177921/20446716. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177922/20446770. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 177923/20446797. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.y2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177924/20446932. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177925/20447049. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (b a))) REDUCED to normal form. ------ 177926/20447076. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (^y.y))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 177927/20447382. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a)(^x1.x1))) REDUCED to normal form. ------ 177928/20447409. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177929/20447436. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.a))) REDUCED to normal form. ------ 177930/20447472. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a (a a)))) 5. ==[ beta ]==> ((^y.b)(a (a a))) 6. ==[ alpha ]==> ((^x.b)(a (a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177931/20447607. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177932/20447715. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177933/20447796. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177934/20447823. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.b))) 5. ==[ beta ]==> ((^y.(y y))(^z.b)) 6. ==[ alpha ]==> ((^x.(x x))(^y.b)) 7. ==[ beta ]==> ((^y.b)(^y.b)) 8. ==[ alpha ]==> ((^x.b)(^y.b)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 177935/20447877. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 177936/20447940. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 177937/20447967. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(a (^y.y)))) REDUCED to normal form. ------ 177938/20448021. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 177939/20448075. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a))((a a) a))) REDUCED to normal form. ------ 177940/20448102. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 177941/20448129. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 177942/20448192. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 177943/20448219. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177944/20448246. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)(^x.a))) REDUCED to normal form. ------ 177945/20448273. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 177946/20448300. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177947/20448327. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))((a (a a))(^x.a))) REDUCED to normal form. ------ 177948/20448354. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> (((a a)((a a) a))(a (^y.b))) 6. ==[ alpha ]==> (((a a)((a a) a))(a (^x.b))) REDUCED to normal form. ------ 177949/20448381. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177950/20448435. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z)) a)) REDUCED to normal form. ------ 177951/20448462. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((b (a (^x.x)))((a a) b)) REDUCED to normal form. ------ 177952/20448489. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b) c)) REDUCED to normal form. ------ 177953/20448606. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177954/20448831. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((b c)(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)((a a) a))) 5. ==[ beta ]==> ((b c)(a ((a a) a))) REDUCED to normal form. ------ 177955/20448858. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(a b))) REDUCED to normal form. ------ 177956/20448903. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 177957/20448930. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a a))) 5. ==[ beta ]==> ((^y.(a a))(a a)) 6. ==[ alpha ]==> ((^x.(a a))(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177958/20449065. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)((a a) a))) 3. ==[ beta ]==> (b ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177959/20449173. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177960/20449353. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a)) a)) 5. ==[ beta ]==> ((a b)((^y.(a a)) a)) 6. ==[ alpha ]==> ((a b)((^x.(a a)) a)) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 177961/20449380. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 177962/20449407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a) c)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a) c)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a) c)) 5. ==[ beta ]==> ((b a)((^y.a) c)) 6. ==[ alpha ]==> ((b a)((^x.a) c)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177963/20449569. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b)(^z.z))) REDUCED to normal form. ------ 177964/20449596. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(((a a) a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 177965/20449623. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.a)) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.a)) REDUCED to normal form. ------ 177966/20449677. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 177967/20449767. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.z))) 7. ==[ beta ]==> ((^y.b)(^z.z)) 8. ==[ alpha ]==> ((^x.b)(^y.y)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 177968/20449848. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (b ((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 177969/20450073. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((a (^x.x))(^z.z))) 8. ==[ alpha ]==> (a ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 177970/20450091. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b (^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b (^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.a))) 5. ==[ beta ]==> ((^y.y)(b (^z.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 177971/20450118. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.b))) 3. ==[ beta ]==> ((^y.y)(a (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(a (^y.b))) 5. ==[ beta ]==> (a (^y.b)) 6. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 177972/20450172. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(a (^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(a (^z.z)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 177973/20450253. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177974/20450361. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(z1 z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177975/20450397. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (a (a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (a (a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (a (a a)))) REDUCED to normal form. ------ 177976/20450424. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.y))) REDUCED to normal form. ------ 177977/20450478. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177978/20450622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177979/20450649. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 177980/20450676. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 177981/20450703. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 177982/20450730. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177983/20450784. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a)) b)) REDUCED to normal form. ------ 177984/20450811. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a) c)) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a) c)) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a) c)) 5. ==[ beta ]==> ((b (a (a a)))(a c)) REDUCED to normal form. ------ 177985/20450892. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177986/20450910. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(a a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 177987/20450919. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y)) b)) 3. ==[ beta ]==> ((a (a (a (^x.x))))(b b)) REDUCED to normal form. ------ 177988/20451315. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)((a a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y) a))) 5. ==[ beta ]==> (b ((a a)((^y.y) a))) 6. ==[ alpha ]==> (b ((a a)((^x.x) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 177989/20451333. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 177990/20451360. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(a a))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 177991/20451387. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.x2)))) 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. ------ 177992/20451441. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(^y.y))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 177993/20451477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(b (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 177994/20451504. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 177995/20451522. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 177996/20451585. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c a)) REDUCED to normal form. ------ 177997/20451630. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^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. ------ 177998/20451666. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 177999/20451693. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 178000/20451747. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b a)) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178001/20451765. ------ 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 ]==> (((a a)(^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 178002/20451774. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a b)) REDUCED to normal form. ------ 178003/20451792. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178004/20451810. ------ 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 (^x.x)))) a) REDUCED to normal form. ------ 178005/20451836. ------ 1. ==[ start ]==> (^a.((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (^x.((x (^y.y))((^z.(^x1.x1)) x))) 3. ==[ beta ]==> (^x.((x (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (^x.((x (^y.y))(^z.z))) REDUCED to normal form. ------ 178006/20451837. ------ 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. ------ 178007/20462865. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178008/20462913. ------ 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)) a) 4. ==[ alpha ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 178009/20462919. ------ 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. ------ 178010/20462946. ------ 1. ==[ start ]==> ((^a.(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a (a (^y.y))))((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 178011/20462967. ------ 1. ==[ start ]==> (((a a) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178012/20463009. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178013/20463171. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (^x.(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 178014/20463399. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 178015/20463414. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 178016/20463831. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 178017/20463840. ------ 1. ==[ start ]==> (((a (a a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 178018/20463864. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178019/20465403. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)((^x1.x1) b))(((^z.z) a)((^x1.x1) b)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)((^z.z) b))(((^x1.x1) a)((^y1.y1) b)))) 5. ==[ beta ]==> ((((^y.y) a)((^z.z) b))(((^x1.x1) a)((^y1.y1) b))) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1) b))) 7. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1) b))) 8. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z) b))) 9. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z) b))) 10. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y) b))) 11. ==[ beta ]==> ((a b)(a ((^y.y) b))) 12. ==[ alpha ]==> ((a b)(a ((^x.x) b))) 13. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 178020/20467314. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 178021/20467989. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178022/20468322. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^y.b)) REDUCED to normal form. ------ 178023/20468589. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.z))(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 178024/20468925. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178025/20468934. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178026/20469231. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 178027/20471508. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((a b)(^y.((^z.z)(y y)))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y)(x x)))) 7. ==[ beta ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 178028/20472444. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 178029/20472648. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178030/20472750. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b)(^x.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 178031/20473047. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(^x.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 178032/20473071. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(a a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a (a a))(a a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a (a a))(a a))(^x.x))) REDUCED to normal form. ------ 178033/20473497. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(z z)))) REDUCED to normal form. ------ 178034/20473659. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.a))) REDUCED to normal form. ------ 178035/20473740. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.z))) REDUCED to normal form. ------ 178036/20473848. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178037/20473902. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178038/20473929. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 178039/20473944. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178040/20473947. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 178041/20473965. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(y y))) REDUCED to normal form. ------ 178042/20473992. ------ 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))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 178043/20474004. ------ 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. ------ 178044/20474022. ------ 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. ------ 178045/20474031. ------ 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. ------ 178046/20474049. ------ 1. ==[ start ]==> (((a a) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178047/20474067. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a a))((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. ------ 178048/20474076. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 178049/20474094. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 178050/20474148. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178051/20474157. ------ 1. ==[ start ]==> (((a a) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 178052/20474175. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178053/20474184. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 178054/20474211. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 178055/20474229. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 178056/20474256. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 178057/20474292. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178058/20474337. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 178059/20474364. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.x2))) 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. ------ 178060/20474373. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 178061/20474400. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 178062/20474427. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 178063/20474454. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) 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. ------ 178064/20474481. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 178065/20474499. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 178066/20474724. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 178067/20474805. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(^a.a))(^b.b))) 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. ------ 178068/20474895. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 178069/20474913. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b b)((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((b b)((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((b b)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((b b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 178070/20474922. ------ 1. ==[ start ]==> (((a (a a))(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 178071/20474949. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 178072/20475246. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.x))((a (a a)) b)) REDUCED to normal form. ------ 178073/20475273. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 178074/20475300. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 178075/20475327. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 178076/20475417. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 178077/20475471. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a ((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 178078/20475552. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 178079/20475579. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(^z1.z1)))) 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. ------ 178080/20475588. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 178081/20475633. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 11. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178082/20475642. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 178083/20475669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178084/20475696. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 178085/20475885. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178086/20476047. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 178087/20476074. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 178088/20476101. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 178089/20476299. ------ 1. ==[ start ]==> (((a a)(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a)(a b))((b a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a b))((b a)(^x.x))) REDUCED to normal form. ------ 178090/20476326. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 178091/20476353. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a b))) REDUCED to normal form. ------ 178092/20476380. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a b)(a a))) REDUCED to normal form. ------ 178093/20476407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> (((^x.x) a)(((a a) a)((a a)(^y.y)))) 7. ==[ beta ]==> (a (((a a) a)((a a)(^y.y)))) 8. ==[ alpha ]==> (a (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 178094/20476434. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z)(b a))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b a)) REDUCED to normal form. ------ 178095/20476461. ------ 1. ==[ start ]==> (((a b)(a a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 178096/20476488. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> ((a (a a))(a ((^y.y) b))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.x) b))) 7. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 178097/20476578. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 7. ==[ beta ]==> ((b (^y.y))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 178098/20476659. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 178099/20476668. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 178100/20476722. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 178101/20476740. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 178102/20476749. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 178103/20476803. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 178104/20476830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(b a))) 7. ==[ beta ]==> (((^y.(^z.z))(b a))((^y.(^z.z))(b a))) 8. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(b a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 11. ==[ beta ]==> ((^y.(^z.z))(b a)) 12. ==[ alpha ]==> ((^x.(^y.y))(b a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178105/20476857. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 178106/20476875. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^z.z