Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 25001/1378137. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 25002/1378155. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a a)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 25003/1378164. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 25004/1378191. ------ 1. ==[ start ]==> (((^a.a) b)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.a)((a a) a))) 3. ==[ beta ]==> (b ((^y.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25005/1378218. ------ 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. ------ 25006/1378236. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25007/1378245. ------ 1. ==[ start ]==> (((a a) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(a a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(a a))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 25008/1378263. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((^y.y)(a a)) a) 6. ==[ alpha ]==> (((^x.x)(a a)) a) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 25009/1378272. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 25010/1378290. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b) b)) 3. ==[ beta ]==> ((a (^y.y))((a b) b)) 4. ==[ alpha ]==> ((a (^x.x))((a b) b)) REDUCED to normal form. ------ 25011/1378299. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 25012/1378380. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25013/1378461. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a a))) REDUCED to normal form. ------ 25014/1378506. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b) b)) 3. ==[ beta ]==> (((^y.y) a)((^z.b) b)) 4. ==[ alpha ]==> (((^x.x) a)((^y.b) b)) 5. ==[ beta ]==> (a ((^y.b) b)) 6. ==[ alpha ]==> (a ((^x.b) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 25015/1378605. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a) a)(a (^y.y))) 8. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 25016/1378632. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 25017/1378659. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(a b))) 3. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 25018/1378677. ------ 1. ==[ start ]==> (((^a.(a a)) a)(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(a (^y.(a a)))) 3. ==[ beta ]==> ((a a)(a (^y.(a a)))) 4. ==[ alpha ]==> ((a a)(a (^x.(a a)))) REDUCED to normal form. ------ 25019/1378695. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(^z.z))) 3. ==[ beta ]==> ((^y.(y y))((a b)(^z.z))) 4. ==[ alpha ]==> ((^x.(x x))((a b)(^y.y))) 5. ==[ beta ]==> (((a b)(^y.y))((a b)(^y.y))) 6. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 25020/1378722. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((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. ------ 25021/1378758. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a) 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. ------ 25022/1378776. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((a (a a))(^y.(y y))) 8. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 25023/1378785. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(x x))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 25024/1378803. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) 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. ------ 25025/1378812. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 25026/1378839. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 25027/1378866. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 25028/1378884. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a b) a)) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a b) a)) 3. ==[ beta ]==> (((a a)(a a))((a b) a)) REDUCED to normal form. ------ 25029/1378893. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 25030/1378911. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a) b)) REDUCED to normal form. ------ 25031/1379001. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 25032/1379037. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b ((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(b ((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(b ((a a) a))) REDUCED to normal form. ------ 25033/1379073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.b) a)) 3. ==[ beta ]==> ((^y.y)((^x1.b) a)) 4. ==[ alpha ]==> ((^x.x)((^y.b) a)) 5. ==[ beta ]==> ((^y.b) a) 6. ==[ alpha ]==> ((^x.b) a) 7. ==[ beta ]==> b REDUCED to normal form. ------ 25034/1379127. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1)) c)) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25035/1379190. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 25036/1379217. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b (^z.a))) REDUCED to normal form. ------ 25037/1379244. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(a (^z.b))) 3. ==[ beta ]==> ((a (^y.a))(a (^z.b))) 4. ==[ alpha ]==> ((a (^x.a))(a (^y.b))) REDUCED to normal form. ------ 25038/1379262. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 25039/1379298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^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. ------ 25040/1379676. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (^x1.(x1 x1)))) REDUCED to normal form. ------ 25041/1379703. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 25042/1379730. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(a (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.a))) REDUCED to normal form. ------ 25043/1379757. ------ 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.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. ------ 25044/1379784. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 25045/1379802. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a (^x.b))(a (^z.a))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.a))) REDUCED to normal form. ------ 25046/1379973. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25047/1379982. ------ 1. ==[ start ]==> ((a (a b))(b (a (a a)))) REDUCED to normal form. ------ 25048/1380072. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a) c)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a) c)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a) c)) IRREDUCIBLE: cycle. ------ 25049/1380135. ------ 1. ==[ start ]==> ((((a a) a) b)(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 25050/1380153. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (a a))(^z.z))) 3. ==[ beta ]==> (b ((a (a a))(^z.z))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 25051/1380162. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))(a a))) 3. ==[ beta ]==> (((a b) a)((a a)(a a))) REDUCED to normal form. ------ 25052/1380180. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 25053/1380189. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 25054/1380207. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((a (^y.y))(^z.a)) 6. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 25055/1380243. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 25056/1380261. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (a a)) a)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a)) a)) REDUCED to normal form. ------ 25057/1380270. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 25058/1380297. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25059/1380324. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.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. ------ 25060/1380351. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(z z))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 25061/1380369. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y)) a)) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 25062/1380387. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(a a))) 3. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 25063/1380414. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 25064/1380441. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 25065/1380522. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b c)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b c)) REDUCED to normal form. ------ 25066/1380540. ------ 1. ==[ start ]==> (((^a.b) b)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25067/1380585. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z)) b)) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z)) b)) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y)) b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25068/1380612. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a a) c)) 3. ==[ beta ]==> ((^y.y)((a a) c)) 4. ==[ alpha ]==> ((^x.x)((a a) c)) 5. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 25069/1380666. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) 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. ------ 25070/1380747. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 25071/1380756. ------ 1. ==[ start ]==> (((a b) b)((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a b) b)(a (^y.y))) 4. ==[ alpha ]==> (((a b) b)(a (^x.x))) REDUCED to normal form. ------ 25072/1380783. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 25073/1380801. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a) b)) 3. ==[ beta ]==> (((^y.y)(a a))((a a) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((a a) b)) 5. ==[ beta ]==> ((a a)((a a) b)) REDUCED to normal form. ------ 25074/1380810. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 25075/1380828. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25076/1380837. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.z))) REDUCED to normal form. ------ 25077/1380882. ------ 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 ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)(^y1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 9. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 10. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25078/1380891. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 25079/1380918. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(^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 ]==> ((^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. ------ 25080/1380945. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 25081/1380962. ------ 1. ==[ start ]==> (^a.((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (^x.((^y.b)(x (^z.z)))) 3. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 25082/1380963. ------ 1. ==[ start ]==> (a ((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (a ((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (a b) REDUCED to normal form. ------ 25083/1381560. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((^y.(^z.(y y)))((^y.(^z.(y y)))(^y.(^z.(y y))))) 4. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1))))) 5. ==[ beta ]==> (^y.(((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1))))((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1)))))) 6. ==[ alpha ]==> (^x.(((^y.(^z.(y y)))(^x1.(^y1.(x1 x1))))((^z1.(^x2.(z1 z1)))(^y2.(^z2.(y2 y2)))))) 7. ==[ beta ]==> (^x.((^z.((^x1.(^y1.(x1 x1)))(^x1.(^y1.(x1 x1)))))((^z1.(^x2.(z1 z1)))(^y2.(^z2.(y2 y2)))))) 8. ==[ alpha ]==> (^x.((^y.((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1)))))((^x2.(^y2.(x2 x2)))(^z2.(^x3.(z2 z2)))))) 9. ==[ beta ]==> (^x.((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1))))) 10. ==[ alpha ]==> (^x.((^y.(^z.(y y)))(^x1.(^y1.(x1 x1))))) 11. ==[ beta ]==> (^x.(^z.((^x1.(^y1.(x1 x1)))(^x1.(^y1.(x1 x1)))))) 12. ==[ alpha ]==> (^x.(^y.((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1)))))) 13. ==[ beta ]==> (^x.(^y.(^x1.((^y1.(^z1.(y1 y1)))(^y1.(^z1.(y1 y1))))))) 14. ==[ alpha ]==> (^x.(^y.(^z.((^x1.(^y1.(x1 x1)))(^z1.(^x2.(z1 z1))))))) 15. ==[ beta ]==> (^x.(^y.(^z.(^y1.((^z1.(^x2.(z1 z1)))(^z1.(^x2.(z1 z1)))))))) 16. ==[ alpha ]==> (^x.(^y.(^z.(^x1.((^y1.(^z1.(y1 y1)))(^x2.(^y2.(x2 x2)))))))) 17. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^z1.((^x2.(^y2.(x2 x2)))(^x2.(^y2.(x2 x2))))))))) 18. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.((^z1.(^x2.(z1 z1)))(^y2.(^z2.(y2 y2))))))))) 19. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^x2.((^y2.(^z2.(y2 y2)))(^y2.(^z2.(y2 y2)))))))))) 20. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.((^x2.(^y2.(x2 x2)))(^z2.(^x3.(z2 z2)))))))))) 21. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^y2.((^z2.(^x3.(z2 z2)))(^z2.(^x3.(z2 z2))))))))))) 22. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.((^y2.(^z2.(y2 y2)))(^x3.(^y3.(x3 x3))))))))))) 23. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^z2.((^x3.(^y3.(x3 x3)))(^x3.(^y3.(x3 x3)))))))))))) 24. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.((^z2.(^x3.(z2 z2)))(^y3.(^z3.(y3 y3)))))))))))) 25. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^x3.((^y3.(^z3.(y3 y3)))(^y3.(^z3.(y3 y3))))))))))))) 26. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.((^x3.(^y3.(x3 x3)))(^z3.(^x4.(z3 z3))))))))))))) 27. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^y3.((^z3.(^x4.(z3 z3)))(^z3.(^x4.(z3 z3)))))))))))))) 28. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.((^y3.(^z3.(y3 y3)))(^x4.(^y4.(x4 x4)))))))))))))) 29. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^z3.((^x4.(^y4.(x4 x4)))(^x4.(^y4.(x4 x4))))))))))))))) 30. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.((^z3.(^x4.(z3 z3)))(^y4.(^z4.(y4 y4))))))))))))))) 31. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^x4.((^y4.(^z4.(y4 y4)))(^y4.(^z4.(y4 y4)))))))))))))))) 32. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.((^x4.(^y4.(x4 x4)))(^z4.(^x5.(z4 z4)))))))))))))))) 33. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^y4.((^z4.(^x5.(z4 z4)))(^z4.(^x5.(z4 z4))))))))))))))))) 34. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.((^y4.(^z4.(y4 y4)))(^x5.(^y5.(x5 x5))))))))))))))))) 35. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^z4.((^x5.(^y5.(x5 x5)))(^x5.(^y5.(x5 x5)))))))))))))))))) UNREDUCED: maximal number of reductions reached. ------ 25084/1383243. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(z (z z)))) 3. ==[ beta ]==> (^y.((^z.(z (z z)))(^z.(z (z z))))) 4. ==[ alpha ]==> (^x.((^y.(y (y y)))(^z.(z (z z))))) 5. ==[ beta ]==> (^x.((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))) 6. ==[ alpha ]==> (^x.((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))) 7. ==[ beta ]==> (^x.(((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))) 8. ==[ alpha ]==> (^x.(((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))) 9. ==[ beta ]==> (^x.(((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))) 10. ==[ alpha ]==> (^x.(((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))) 11. ==[ beta ]==> (^x.((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))) 12. ==[ alpha ]==> (^x.((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))) 13. ==[ beta ]==> (^x.((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))) 14. ==[ alpha ]==> (^x.((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))) 15. ==[ beta ]==> (^x.(((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))) 16. ==[ alpha ]==> (^x.(((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))) 17. ==[ beta ]==> (^x.(((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))) 18. ==[ alpha ]==> (^x.(((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))) 19. ==[ beta ]==> (^x.((((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))) 20. ==[ alpha ]==> (^x.((((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))) 21. ==[ beta ]==> (^x.((((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))) 22. ==[ alpha ]==> (^x.((((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))) 23. ==[ beta ]==> (^x.(((((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))) 24. ==[ alpha ]==> (^x.(((((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))) 25. ==[ beta ]==> (^x.(((((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))) 26. ==[ alpha ]==> (^x.(((((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))) 27. ==[ beta ]==> (^x.((((((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))) 28. ==[ alpha ]==> (^x.((((((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))) 29. ==[ beta ]==> (^x.((((((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))) 30. ==[ alpha ]==> (^x.((((((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))(((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))))) 31. ==[ beta ]==> (^x.(((((((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))(((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))))) 32. ==[ alpha ]==> (^x.(((((((((^y.(y (y y)))(^z.(z (z z))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))(((^x9.(x9 (x9 x9)))(^y9.(y9 (y9 y9))))((^z9.(z9 (z9 z9)))(^x10.(x10 (x10 x10))))))) 33. ==[ beta ]==> (^x.(((((((((^z.(z (z z)))((^z.(z (z z)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8))))))(((^x9.(x9 (x9 x9)))(^y9.(y9 (y9 y9))))((^z9.(z9 (z9 z9)))(^x10.(x10 (x10 x10))))))) 34. ==[ alpha ]==> (^x.(((((((((^y.(y (y y)))((^z.(z (z z)))(^x1.(x1 (x1 x1)))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))(((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))))(((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9))))((^x10.(x10 (x10 x10)))(^y10.(y10 (y10 y10))))))) 35. ==[ beta ]==> (^x.((((((((((^z.(z (z z)))(^x1.(x1 (x1 x1))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^z.(z (z z)))(^x1.(x1 (x1 x1))))))(((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))))(((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))))(((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))))(((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))))(((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))))(((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))))(((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9))))((^x10.(x10 (x10 x10)))(^y10.(y10 (y10 y10))))))) UNREDUCED: maximal number of reductions reached. ------ 25085/1383822. ------ 1. ==[ start ]==> ((((a a) a)(^b.a)) c) 2. ==[ alpha ]==> ((((a a) a)(^x.a)) c) REDUCED to normal form. ------ 25086/1383840. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a))) a) 2. ==[ alpha ]==> (((^x.b)(a (^y.y))) a) 3. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25087/1383846. ------ 1. ==[ start ]==> ((^a.a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((^y.b)(a (^z.z))) 4. ==[ alpha ]==> ((^x.b)(a (^y.y))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 25088/1383900. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25089/1383981. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^z.(^x1.x1))(a b))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25090/1384002. ------ 1. ==[ start ]==> (((a a) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 25091/1384170. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)(^x1.a))) 3. ==[ eta ]==> ((^y.y)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25092/1384341. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 25093/1384440. ------ 1. ==[ start ]==> ((^a.(a (a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(a (^y.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^y.(a a)))(a (^y.(a a))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(a a)))(a (^z.(a a))))) REDUCED to normal form. ------ 25094/1384443. ------ 1. ==[ start ]==> ((a (a (a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(x x)))) REDUCED to normal form. ------ 25095/1384830. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(x1 b))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 b))) 4. ==[ alpha ]==> ((^x.x)(^y.(y b))) 5. ==[ beta ]==> (^y.(y b)) 6. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 25096/1385172. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 25097/1385223. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.(^y1.y1)))((^y.(^z.z))(^x1.(^y1.y1))))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2))))((^z2.(^x3.x3))(^y3.(^z3.z3)))) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2))))((^z2.(^x3.x3))(^y3.(^z3.z3)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25098/1385631. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (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)))(^x.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 25099/1385736. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.(x1 x1))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 25100/1386000. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 25101/1386108. ------ 1. ==[ start ]==> (((a b)(^a.a))(^c.d)) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.d)) REDUCED to normal form. ------ 25102/1386123. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(a (a (a a)))) 3. ==[ beta ]==> (^y.((a (a (a a)))(a (a (a a))))) 4. ==[ alpha ]==> (^x.((a (a (a a)))(a (a (a a))))) REDUCED to normal form. ------ 25103/1386126. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(y (y y)))) REDUCED to normal form. ------ 25104/1386225. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 25105/1386297. ------ 1. ==[ start ]==> (((^a.b) b)(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 25106/1386306. ------ 1. ==[ start ]==> (((a b)(a a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y) a))) 3. ==[ beta ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 25107/1386330. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.a)(^x1.x1))((^z.a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)(^z.z))((^x1.a)(^y1.y1)))) 5. ==[ beta ]==> (((^y.a)(^z.z))((^x1.a)(^y1.y1))) 6. ==[ alpha ]==> (((^x.a)(^y.y))((^z.a)(^x1.x1))) 7. ==[ beta ]==> (a ((^z.a)(^x1.x1))) 8. ==[ alpha ]==> (a ((^x.a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25108/1386513. ------ 1. ==[ start ]==> (((a b) b)(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 25109/1386567. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.b)) REDUCED to normal form. ------ 25110/1386585. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 25111/1386648. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 25112/1386702. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.a)) REDUCED to normal form. ------ 25113/1386720. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.z)) 3. ==[ beta ]==> (b (^z.z)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25114/1386732. ------ 1. ==[ start ]==> ((a a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 25115/1386750. ------ 1. ==[ start ]==> (((^a.a) a)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.a))) 3. ==[ beta ]==> (a (((a a) a)(^y.a))) 4. ==[ alpha ]==> (a (((a a) a)(^x.a))) REDUCED to normal form. ------ 25116/1386777. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)(^y.(y y))) 6. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 25117/1386786. ------ 1. ==[ start ]==> ((a b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 25118/1386804. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 25119/1386831. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 25120/1386840. ------ 1. ==[ start ]==> (((a a)(a a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.a)((a a) a))) 3. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 25121/1386858. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 25122/1386867. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25123/1386885. ------ 1. ==[ start ]==> (((a a) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a) b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 25124/1386912. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x)) a)((a a) a)) REDUCED to normal form. ------ 25125/1386939. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a b) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b) b)) REDUCED to normal form. ------ 25126/1387002. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25127/1387029. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 25128/1387056. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a a)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a a)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 25129/1387065. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(c ((a a) a))) 3. ==[ beta ]==> ((^y.a)(c ((a a) a))) 4. ==[ alpha ]==> ((^x.a)(c ((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 25130/1387092. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 25131/1387128. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a)) a)) 3. ==[ beta ]==> ((a a)((^y.(a a)) a)) 4. ==[ alpha ]==> ((a a)((^x.(a a)) a)) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25132/1387146. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(a a))) 3. ==[ beta ]==> (((^y.y) a)((a b)(a a))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(a a))) 5. ==[ beta ]==> (a ((a b)(a a))) REDUCED to normal form. ------ 25133/1387155. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b) b)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b) b)) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 25134/1387173. ------ 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)(((a a) a)(a (^x1.x1)))) 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. ------ 25135/1387227. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 25136/1387299. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(b (^y.b))) 3. ==[ beta ]==> ((a (a a))(b (^y.b))) 4. ==[ alpha ]==> ((a (a a))(b (^x.b))) REDUCED to normal form. ------ 25137/1387326. ------ 1. ==[ start ]==> ((a (a (a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(a (^x.(a a)))) REDUCED to normal form. ------ 25138/1387398. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 7. ==[ beta ]==> ((a b)(^y.a)) 8. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 25139/1387425. ------ 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. ------ 25140/1387452. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 25141/1387479. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 25142/1387506. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 25143/1387533. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a b) a)) REDUCED to normal form. ------ 25144/1387596. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 25145/1387623. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 25146/1387650. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 25147/1387686. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(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. ------ 25148/1387713. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(a (a b))) 3. ==[ beta ]==> ((^y.y)(a (a b))) 4. ==[ alpha ]==> ((^x.x)(a (a b))) 5. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 25149/1387767. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25150/1387776. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y)) c)) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 25151/1387821. ------ 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 (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 7. ==[ beta ]==> (((^y.y) a)(a (a a))) 8. ==[ alpha ]==> (((^x.x) a)(a (a a))) 9. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 25152/1387848. ------ 1. ==[ start ]==> (((^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)))) 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 (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 25153/1387911. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 25154/1387938. ------ 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)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^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. ------ 25155/1387974. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) a))) 8. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 9. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 25156/1388001. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a))) a) REDUCED to normal form. ------ 25157/1388028. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^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 a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25158/1388055. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.a)((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. ------ 25159/1388109. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 25160/1388199. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a (b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a (b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 25161/1388235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.a) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.a) a)) 5. ==[ beta ]==> (b ((^y.a) a)) 6. ==[ alpha ]==> (b ((^x.a) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25162/1388262. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y)) b)) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 25163/1388280. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 25164/1388307. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1) 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. ------ 25165/1388361. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a a)((^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. ------ 25166/1388397. ------ 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.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25167/1388424. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 25168/1388460. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.a)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 25169/1388487. ------ 1. ==[ start ]==> (((a (^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 a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 25170/1388514. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (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))) 7. ==[ beta ]==> ((a (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 25171/1388541. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 25172/1388568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 25173/1388595. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 25174/1388622. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 25175/1388631. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(b (a (a a)))) 3. ==[ beta ]==> ((^y.b)(b (a (a a)))) 4. ==[ alpha ]==> ((^x.b)(b (a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 25176/1388712. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)(a (^x1.x1)))) IRREDUCIBLE: cycle. ------ 25177/1388802. ------ 1. ==[ start ]==> (((a b) a)((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a b) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 25178/1388829. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 25179/1388883. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 25180/1388910. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (a a)) a)) REDUCED to normal form. ------ 25181/1388937. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a) b)) 5. ==[ beta ]==> ((^y.a)(((^z.z) a) b)) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25182/1388982. ------ 1. ==[ start ]==> (((^a.b)(a a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(b ((^y.y) a))) 3. ==[ beta ]==> (b (b ((^y.y) a))) 4. ==[ alpha ]==> (b (b ((^x.x) a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 25183/1389009. ------ 1. ==[ start ]==> ((a (^b.(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(a (a (a a)))) REDUCED to normal form. ------ 25184/1389081. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (^z.a))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 25185/1389108. ------ 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. ------ 25186/1389135. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(a a))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)(a a))) 7. ==[ beta ]==> (a ((^y.a)(a a))) 8. ==[ alpha ]==> (a ((^x.a)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25187/1389162. ------ 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)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25188/1389180. ------ 1. ==[ start ]==> (((^a.b) b)((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)((a a)(^y.a))) 3. ==[ beta ]==> (b ((a a)(^y.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 25189/1389189. ------ 1. ==[ start ]==> (((a b)(a a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a a))((^y.y) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.x) a)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 25190/1389216. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a (a a))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(^y.y))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 25191/1389225. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (a a))) 3. ==[ beta ]==> ((^y.(a a))(c (a a))) 4. ==[ alpha ]==> ((^x.(a a))(c (a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25192/1389252. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 25193/1389306. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(a a))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))(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. ------ 25194/1389387. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b b)) 3. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 25195/1389396. ------ 1. ==[ start ]==> (((a b) b)((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 25196/1389423. ------ 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. ------ 25197/1389441. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b (a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (a a))) 3. ==[ beta ]==> (((^y.y)(a a))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (a a))) 5. ==[ beta ]==> ((a a)(b (a a))) REDUCED to normal form. ------ 25198/1389450. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a) b)) REDUCED to normal form. ------ 25199/1389468. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(a (a (^z.z)))) 3. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 25200/1389477. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 25201/1389522. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b a)) 7. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 9. ==[ beta ]==> ((^y.y)(b a)) 10. ==[ alpha ]==> ((^x.x)(b a)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25202/1389531. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 25203/1389558. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a) a)) 5. ==[ beta ]==> ((^y.(y y))((a a) a)) 6. ==[ alpha ]==> ((^x.(x x))((a a) a)) 7. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 25204/1389585. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y) a)) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 25205/1389603. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a a)) 3. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 25206/1389611. ------ 1. ==[ start ]==> (^a.((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (^x.((x b)(^y.(^z.z)))) REDUCED to normal form. ------ 25207/1389612. ------ 1. ==[ start ]==> (a ((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (a ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25208/1391892. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(x1 x1)))(^z.(^x1.(x1 x1))))) 4. ==[ alpha ]==> (^x.((^y.(^z.(z z)))(^x1.(^y1.(y1 y1))))) 5. ==[ beta ]==> (^x.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 25209/1392489. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a))) b) 2. ==[ alpha ]==> (((^x.b)(a (^y.y))) b) 3. ==[ beta ]==> (b b) REDUCED to normal form. ------ 25210/1392498. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a))) a) 2. ==[ alpha ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 25211/1392504. ------ 1. ==[ start ]==> ((^a.a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 25212/1392513. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25213/1392531. ------ 1. ==[ start ]==> ((^a.(a a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x x))(((a a) a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(^y.a))(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 25214/1392558. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25215/1392594. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25216/1392639. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^z.z))(^x1.b))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 25217/1392678. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^y.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 25218/1392756. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.((^z.a)(^x1.a))) 4. ==[ alpha ]==> (^x.((^y.a)(^z.a))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 25219/1392903. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(x x)))) 5. ==[ beta ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 25220/1393110. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(y y)))) 5. ==[ beta ]==> ((^y.(^z.(y y)))(^y.(^z.(y y)))) 6. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(z z)))) 7. ==[ beta ]==> (^y.((^z.(^x1.(z z)))(^z.(^x1.(z z))))) 8. ==[ alpha ]==> (^x.((^y.(^z.(y y)))(^x1.(^y1.(x1 x1))))) 9. ==[ beta ]==> (^x.(^z.((^x1.(^y1.(x1 x1)))(^x1.(^y1.(x1 x1)))))) 10. ==[ alpha ]==> (^x.(^y.((^z.(^x1.(z z)))(^y1.(^z1.(y1 y1)))))) 11. ==[ beta ]==> (^x.(^y.(^x1.((^y1.(^z1.(y1 y1)))(^y1.(^z1.(y1 y1))))))) 12. ==[ alpha ]==> (^x.(^y.(^z.((^x1.(^y1.(x1 x1)))(^z1.(^x2.(z1 z1))))))) 13. ==[ beta ]==> (^x.(^y.(^z.(^y1.((^z1.(^x2.(z1 z1)))(^z1.(^x2.(z1 z1)))))))) 14. ==[ alpha ]==> (^x.(^y.(^z.(^x1.((^y1.(^z1.(y1 y1)))(^x2.(^y2.(x2 x2)))))))) 15. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^z1.((^x2.(^y2.(x2 x2)))(^x2.(^y2.(x2 x2))))))))) 16. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.((^z1.(^x2.(z1 z1)))(^y2.(^z2.(y2 y2))))))))) 17. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^x2.((^y2.(^z2.(y2 y2)))(^y2.(^z2.(y2 y2)))))))))) 18. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.((^x2.(^y2.(x2 x2)))(^z2.(^x3.(z2 z2)))))))))) 19. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^y2.((^z2.(^x3.(z2 z2)))(^z2.(^x3.(z2 z2))))))))))) 20. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.((^y2.(^z2.(y2 y2)))(^x3.(^y3.(x3 x3))))))))))) 21. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^z2.((^x3.(^y3.(x3 x3)))(^x3.(^y3.(x3 x3)))))))))))) 22. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.((^z2.(^x3.(z2 z2)))(^y3.(^z3.(y3 y3)))))))))))) 23. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^x3.((^y3.(^z3.(y3 y3)))(^y3.(^z3.(y3 y3))))))))))))) 24. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.((^x3.(^y3.(x3 x3)))(^z3.(^x4.(z3 z3))))))))))))) 25. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^y3.((^z3.(^x4.(z3 z3)))(^z3.(^x4.(z3 z3)))))))))))))) 26. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.((^y3.(^z3.(y3 y3)))(^x4.(^y4.(x4 x4)))))))))))))) 27. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^z3.((^x4.(^y4.(x4 x4)))(^x4.(^y4.(x4 x4))))))))))))))) 28. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.((^z3.(^x4.(z3 z3)))(^y4.(^z4.(y4 y4))))))))))))))) 29. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^x4.((^y4.(^z4.(y4 y4)))(^y4.(^z4.(y4 y4)))))))))))))))) 30. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.((^x4.(^y4.(x4 x4)))(^z4.(^x5.(z4 z4)))))))))))))))) 31. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^y4.((^z4.(^x5.(z4 z4)))(^z4.(^x5.(z4 z4))))))))))))))))) 32. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.((^y4.(^z4.(y4 y4)))(^x5.(^y5.(x5 x5))))))))))))))))) 33. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^z4.((^x5.(^y5.(x5 x5)))(^x5.(^y5.(x5 x5)))))))))))))))))) 34. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^y4.((^z4.(^x5.(z4 z4)))(^y5.(^z5.(y5 y5)))))))))))))))))) 35. ==[ beta ]==> (^x.(^y.(^z.(^x1.(^y1.(^z1.(^x2.(^y2.(^z2.(^x3.(^y3.(^z3.(^x4.(^y4.(^x5.((^y5.(^z5.(y5 y5)))(^y5.(^z5.(y5 y5))))))))))))))))))) UNREDUCED: maximal number of reductions reached. ------ 25221/1393299. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(a y))) 3. ==[ eta ]==> (((^x.(x x))(a a)) a) 4. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 25222/1393323. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25223/1393488. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 25224/1393659. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.((a a) a))) 3. ==[ beta ]==> ((a (^y.a))(^z.((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))(^y.((a a) a))) REDUCED to normal form. ------ 25225/1393677. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 25226/1393881. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (((((^y.y)(^z.z)) b)(((^y.y)(^z.z)) b))(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> (((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1)) b))(((^y1.y1)(^z1.z1)) b)) 5. ==[ beta ]==> ((((^y.y) b)(((^z.z)(^x1.x1)) b))(((^y1.y1)(^z1.z1)) b)) 6. ==[ alpha ]==> ((((^x.x) b)(((^y.y)(^z.z)) b))(((^x1.x1)(^y1.y1)) b)) 7. ==[ beta ]==> ((b (((^y.y)(^z.z)) b))(((^x1.x1)(^y1.y1)) b)) 8. ==[ alpha ]==> ((b (((^x.x)(^y.y)) b))(((^z.z)(^x1.x1)) b)) 9. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1)) b)) 10. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z)) b)) 11. ==[ beta ]==> ((b b)(((^y.y)(^z.z)) b)) 12. ==[ alpha ]==> ((b b)(((^x.x)(^y.y)) b)) 13. ==[ beta ]==> ((b b)((^y.y) b)) 14. ==[ alpha ]==> ((b b)((^x.x) b)) 15. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 25227/1394010. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y) b)(^z.((z z) z))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((y y) y))) 5. ==[ beta ]==> (b (^y.((y y) y))) 6. ==[ alpha ]==> (b (^x.((x x) x))) REDUCED to normal form. ------ 25228/1394145. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 25229/1394214. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25230/1394550. ------ 1. ==[ start ]==> ((((a a) a) b)(^c.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(a (a a)))) REDUCED to normal form. ------ 25231/1394568. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 25232/1394676. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(a (a a)))) REDUCED to normal form. ------ 25233/1394781. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) 5. ==[ beta ]==> (^x.((^z.(z z))((^x1.x1)(^y1.(y1 y1))))) 6. ==[ alpha ]==> (^x.((^y.(y y))((^z.z)(^x1.(x1 x1))))) 7. ==[ beta ]==> (^x.(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 8. ==[ alpha ]==> (^x.(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) IRREDUCIBLE: cycle. ------ 25234/1394784. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 25235/1394964. ------ 1. ==[ start ]==> (((a b)(a a))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.a))) REDUCED to normal form. ------ 25236/1394988. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a) a)) 3. ==[ beta ]==> ((^y.y)((((^z.z) a) a)(((^z.z) 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. ------ 25237/1395243. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 25238/1395252. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 25239/1395297. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 25240/1395333. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.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. ------ 25241/1395360. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(y y))) REDUCED to normal form. ------ 25242/1395378. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 25243/1395387. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25244/1395399. ------ 1. ==[ start ]==> ((a a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25245/1395408. ------ 1. ==[ start ]==> ((a (^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 25246/1395426. ------ 1. ==[ start ]==> ((a (a a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 25247/1395453. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(y y))) 6. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 25248/1395462. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25249/1395489. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^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. ------ 25250/1395534. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 25251/1395543. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25252/1395570. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(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. ------ 25253/1395597. ------ 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))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 25254/1395624. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 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. ------ 25255/1395651. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 25256/1395732. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.a)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 25257/1395759. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.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. ------ 25258/1395768. ------ 1. ==[ start ]==> (((a (^a.a)) b)(b (a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(b (a b))) REDUCED to normal form. ------ 25259/1395795. ------ 1. ==[ start ]==> ((((^a.a) a) a)(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a a)(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 25260/1395822. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)(a a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)(a a))) REDUCED to normal form. ------ 25261/1395849. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(a (^x1.x1)))) REDUCED to normal form. ------ 25262/1395876. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 25263/1395984. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(a b))) 3. ==[ beta ]==> ((a a)((a a)(a b))) REDUCED to normal form. ------ 25264/1396002. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.(a a)))) 3. ==[ beta ]==> ((^y.(y y))(a (^z.(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(a (^y.(a a)))) 5. ==[ beta ]==> ((a (^y.(a a)))(a (^y.(a a)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 25265/1396029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.b)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 5. ==[ beta ]==> ((^y.b)(a a)) 6. ==[ alpha ]==> ((^x.b)(a a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 25266/1396083. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25267/1396110. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> ((a (a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 25268/1396137. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^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. ------ 25269/1396191. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(a b))) 5. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 25270/1396218. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 25271/1396236. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a) a) b)) REDUCED to normal form. ------ 25272/1396353. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25273/1396380. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 5. ==[ beta ]==> ((^y.y)(^z.b)) 6. ==[ alpha ]==> ((^x.x)(^y.b)) 7. ==[ beta ]==> (^y.b) 8. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25274/1396443. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 25275/1396470. ------ 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) a))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((^z.z) 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. ------ 25276/1396497. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 25277/1396524. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 25278/1396551. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a a)((a a) a))) 3. ==[ beta ]==> ((a (^y.a))((a a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))((a a)((a a) a))) REDUCED to normal form. ------ 25279/1396569. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(a (^z.b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(a (^z.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.b))) REDUCED to normal form. ------ 25280/1396641. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 25281/1396668. ------ 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)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 25282/1396695. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 25283/1396749. ------ 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 ]==> (((^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. ------ 25284/1396776. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(^y.y)) b)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) b)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) b)) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 25285/1396812. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((^y.(y y))(^z.a)) 6. ==[ alpha ]==> ((^x.(x x))(^y.a)) 7. ==[ beta ]==> ((^y.a)(^y.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 25286/1396866. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25287/1396902. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 25288/1396929. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y))(a a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(a a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(a a))) 5. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 25289/1396983. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a ((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 25290/1397010. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 25291/1397028. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 25292/1397037. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 25293/1397109. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.b))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 25294/1397127. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> (((a a)((a a) a))(a (^y.a))) 4. ==[ alpha ]==> (((a a)((a a) a))(a (^x.a))) REDUCED to normal form. ------ 25295/1397154. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 25296/1397181. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a a)(^y.(^z.z)))) 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. ------ 25297/1397208. ------ 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)) a)(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^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. ------ 25298/1397235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (a a)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a)) b)) 5. ==[ beta ]==> ((a (^y.y))((a (a a)) b)) 6. ==[ alpha ]==> ((a (^x.x))((a (a a)) b)) REDUCED to normal form. ------ 25299/1397280. ------ 1. ==[ start ]==> (((^a.b) a)(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) a)(c ((^y.y) a))) 3. ==[ beta ]==> (b (c ((^y.y) a))) 4. ==[ alpha ]==> (b (c ((^x.x) a))) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 25300/1397298. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 25301/1397442. ------ 1. ==[ start ]==> ((((a a) a) b)((a a)(a (a a)))) REDUCED to normal form. ------ 25302/1397460. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 25303/1397487. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(a a))) 3. ==[ beta ]==> ((a b)((^y.(y y))(a a))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(a a))) 5. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 25304/1397514. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(a (^z.z))) 6. ==[ alpha ]==> ((^x.a)(a (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25305/1397568. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 25306/1397649. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^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. ------ 25307/1397658. ------ 1. ==[ start ]==> (((a b)(^a.a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(b ((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.x))(b a)) REDUCED to normal form. ------ 25308/1397676. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(z z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 25309/1397694. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x)) a)) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 25310/1397721. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a) b)) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 25311/1397802. ------ 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) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> (a (((^y.y) a)(^z.z))) 8. ==[ alpha ]==> (a (((^x.x) a)(^y.y))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 25312/1397829. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 25313/1397847. ------ 1. ==[ start ]==> (((^a.b) b)(b c)) 2. ==[ alpha ]==> (((^x.b) b)(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 25314/1397856. ------ 1. ==[ start ]==> (((a b)(a a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))((a a)(^x.a))) REDUCED to normal form. ------ 25315/1397883. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a) a)) 3. ==[ beta ]==> ((a (a a))(((^y.y) a) a)) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a) a)) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 25316/1397892. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25317/1397919. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 25318/1397973. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c (^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (^y1.y1))) 5. ==[ beta ]==> ((^y.y)(c (^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(c (^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 25319/1398054. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25320/1398063. ------ 1. ==[ start ]==> (((a b) b)(b b)) REDUCED to normal form. ------ 25321/1398108. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25322/1398117. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b (a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b (a a))) REDUCED to normal form. ------ 25323/1398135. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25324/1398144. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (a (^z.z)))) REDUCED to normal form. ------ 25325/1398189. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(a (^x1.(^y1.y1)))) 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. ------ 25326/1398198. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 25327/1398225. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(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. ------ 25328/1398252. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (a a))) REDUCED to normal form. ------ 25329/1398270. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a (^z.z))) 3. ==[ beta ]==> (b (a (^z.z))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 25330/1398279. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 25331/1400568. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^c.d)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.d)) 3. ==[ beta ]==> (^y.((^z.d)(^z.d))) 4. ==[ alpha ]==> (^x.((^y.d)(^z.d))) 5. ==[ beta ]==> (^x.d) REDUCED to normal form. ------ 25332/1401165. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a))) c) 2. ==[ alpha ]==> (((^x.b)(a (^y.y))) c) 3. ==[ beta ]==> (b c) REDUCED to normal form. ------ 25333/1401174. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a))) b) 2. ==[ alpha ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 25334/1401198. ------ 1. ==[ start ]==> ((^a.(^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25335/1401279. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25336/1401372. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(^y.(a a))) REDUCED to normal form. ------ 25337/1401441. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a) c)) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a) c)) 3. ==[ beta ]==> (^y.(((a a) a) c)) 4. ==[ alpha ]==> (^x.(((a a) a) c)) REDUCED to normal form. ------ 25338/1401588. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 25339/1401783. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a a)(a b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(a b))) 3. ==[ beta ]==> (((a a)(a b))(((a a)(a b))((a a)(a b)))) REDUCED to normal form. ------ 25340/1401993. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a y))) 3. ==[ eta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 25341/1402008. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b) a)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25342/1402371. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 25343/1402695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 25344/1402899. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25345/1403079. ------ 1. ==[ start ]==> ((^a.(a b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))(c ((^y.y) a))) 3. ==[ beta ]==> ((c ((^y.y) a)) b) 4. ==[ alpha ]==> ((c ((^x.x) a)) b) 5. ==[ beta ]==> ((c a) b) REDUCED to normal form. ------ 25346/1403262. ------ 1. ==[ start ]==> (((a b) a)(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 25347/1403370. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(a (a a)))) REDUCED to normal form. ------ 25348/1403469. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^c.d)) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.d)) REDUCED to normal form. ------ 25349/1403487. ------ 1. ==[ start ]==> (((a a)(a b))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(x (x x)))) REDUCED to normal form. ------ 25350/1403883. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(a (^z.z)))) 3. ==[ beta ]==> (((a a) a)(^y.(a (^z.z)))) 4. ==[ alpha ]==> (((a a) a)(^x.(a (^y.y)))) REDUCED to normal form. ------ 25351/1403928. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.b)) 3. ==[ beta ]==> ((^y.y)(^z.b)) 4. ==[ alpha ]==> ((^x.x)(^y.b)) 5. ==[ beta ]==> (^y.b) 6. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25352/1403937. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 25353/1403982. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25354/1403991. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 25355/1404018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(a a))) 5. ==[ beta ]==> ((^y.(y y))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(a a))) 7. ==[ beta ]==> ((^y.(a a))(^y.(a a))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25356/1404045. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 25357/1404063. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.a)) 3. ==[ beta ]==> (b (^z.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 25358/1404072. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 25359/1404102. ------ 1. ==[ start ]==> ((a (^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 25360/1404111. ------ 1. ==[ start ]==> (((^a.a) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (a ((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (a ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 25361/1404129. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((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. ------ 25362/1404156. ------ 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 x1)))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 25363/1404165. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 25364/1404183. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 25365/1404192. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (b ((^y.y)(^z.z))) 10. ==[ alpha ]==> (b ((^x.x)(^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25366/1404219. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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 REDUCED to normal form. ------ 25367/1404237. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25368/1404246. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 25369/1404264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 25370/1404273. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a a))) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 25371/1404291. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 25372/1404300. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 25373/1404318. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a b) b)) 3. ==[ beta ]==> ((^y.y)((a b) b)) 4. ==[ alpha ]==> ((^x.x)((a b) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 25374/1404327. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 25375/1404345. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a) c)) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a) c)) REDUCED to normal form. ------ 25376/1404381. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 25377/1404462. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 25378/1404489. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 25379/1404507. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a)) a)) 5. ==[ beta ]==> (a ((^y.(a a)) a)) 6. ==[ alpha ]==> (a ((^x.(a a)) a)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 25380/1404534. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.b) b)) 3. ==[ beta ]==> ((^y.y)((^x1.b) b)) 4. ==[ alpha ]==> ((^x.x)((^y.b) b)) 5. ==[ beta ]==> ((^y.b) b) 6. ==[ alpha ]==> ((^x.b) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 25381/1404606. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a a) a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 25382/1404633. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 25383/1404660. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 25384/1404678. ------ 1. ==[ start ]==> (((^a.(a a)) a)(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) a)(b (^y.b))) 3. ==[ beta ]==> ((a a)(b (^y.b))) 4. ==[ alpha ]==> ((a a)(b (^x.b))) REDUCED to normal form. ------ 25385/1404687. ------ 1. ==[ start ]==> ((a (a (a a)))((a a)(a b))) REDUCED to normal form. ------ 25386/1404723. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 25387/1404759. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((a b)((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.a)(a (^y.y)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 25388/1404777. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 25389/1404786. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 25390/1404804. ------ 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. ------ 25391/1404813. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 25392/1404831. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 25393/1404840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 25394/1404867. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25395/1404885. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a a)(^y.b))) 3. ==[ beta ]==> (((a a)(a a))((a a)(^y.b))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(^x.b))) REDUCED to normal form. ------ 25396/1404894. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a b)) REDUCED to normal form. ------ 25397/1404912. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 25398/1405002. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> ((b b)((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 25399/1405245. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(b (^z.a))) 3. ==[ beta ]==> ((a (^y.a))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.a))) REDUCED to normal form. ------ 25400/1405272. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 25401/1405506. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a)) c)) 3. ==[ beta ]==> ((^y.y)((a (a a)) c)) 4. ==[ alpha ]==> ((^x.x)((a (a a)) c)) 5. ==[ beta ]==> ((a (a a)) c) REDUCED to normal form. ------ 25402/1405596. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.a)(^c.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))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 25403/1405641. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) b)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 25404/1405731. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 25405/1405785. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 25406/1405803. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 25407/1405974. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 25408/1405983. ------ 1. ==[ start ]==> ((a (a b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))(c ((^x.x) a))) 3. ==[ beta ]==> ((a (a b))(c a)) REDUCED to normal form. ------ 25409/1406073. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z)) b)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z)) b)) IRREDUCIBLE: cycle. ------ 25410/1406136. ------ 1. ==[ start ]==> ((((a a) a) b)(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(b (^x.(x x)))) REDUCED to normal form. ------ 25411/1406163. ------ 1. ==[ start ]==> (((a b) a)(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 25412/1406181. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (a a))(^y.y))) 3. ==[ beta ]==> ((a b)((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a b)((a (a a))(^x.x))) REDUCED to normal form. ------ 25413/1406190. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a a)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 25414/1406208. ------ 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)(^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 ]==> (((^y.y) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 25415/1406244. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25416/1406262. ------ 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 y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(^y.(y y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 25417/1406271. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 25418/1406298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25419/1406325. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 25420/1406343. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(a a))((a (^y.y)) c)) 3. ==[ beta ]==> (b ((a (^y.y)) c)) 4. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 25421/1406352. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 25422/1406388. ------ 1. ==[ start ]==> (((a a)(a b))(a (a (a a)))) REDUCED to normal form. ------ 25423/1406415. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 25424/1406442. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 25425/1406469. ------ 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) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a) a)) REDUCED to normal form. ------ 25426/1406541. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25427/1406550. ------ 1. ==[ start ]==> (((a b)(a a))(b c)) REDUCED to normal form. ------ 25428/1406586. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a) a)) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a) a)) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a) a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25429/1406613. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 5. ==[ beta ]==> ((a (^y.y)) b) 6. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 25430/1406667. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a) a)) 5. ==[ beta ]==> ((^y.y)((^y1.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. ------ 25431/1406748. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 25432/1406757. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 25433/1406784. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 25434/1406802. ------ 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. ------ 25435/1406811. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 25436/1406829. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a a) b)) 3. ==[ beta ]==> ((^y.y)((a a) b)) 4. ==[ alpha ]==> ((^x.x)((a a) b)) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 25437/1406838. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 25438/1406883. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1) b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1) b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1) b)) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 9. ==[ beta ]==> ((^y.y)((^z.z) b)) 10. ==[ alpha ]==> ((^x.x)((^y.y) b)) 11. ==[ beta ]==> ((^y.y) b) 12. ==[ alpha ]==> ((^x.x) b) 13. ==[ beta ]==> b REDUCED to normal form. ------ 25439/1406892. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 25440/1406919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(a a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(a a))) 7. ==[ beta ]==> (((^y.y)(a a))((^y.y)(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. ------ 25441/1406946. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 25442/1406964. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z) a)) 3. ==[ beta ]==> (b ((^z.z) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25443/1406973. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 25444/1406990. ------ 1. ==[ start ]==> (^a.((^b.(a a))(a a))) 2. ==[ alpha ]==> (^x.((^y.(x x))(x x))) 3. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 25445/1406991. ------ 1. ==[ start ]==> (a ((^b.(a a))(a a))) 2. ==[ alpha ]==> (a ((^x.(a a))(a a))) 3. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 25446/1409478. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.((^x1.x1) a))(^z.((^x1.x1) a)))) 4. ==[ alpha ]==> ((^x.x)((^y.((^z.z) a))(^x1.((^y1.y1) a)))) 5. ==[ beta ]==> ((^y.((^z.z) a))(^x1.((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.((^y.y) a))(^z.((^x1.x1) a))) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 25447/1409877. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a))) c) 2. ==[ alpha ]==> (((a b)(^x.(^y.y))) c) REDUCED to normal form. ------ 25448/1409901. ------ 1. ==[ start ]==> ((^a.a)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.x)((^y.(a a))(a a))) 3. ==[ beta ]==> ((^y.(a a))(a a)) 4. ==[ alpha ]==> ((^x.(a a))(a a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25449/1409928. ------ 1. ==[ start ]==> ((^a.(a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((^y.b)(a (^z.z)))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (b ((^z.b)(a (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 25450/1409955. ------ 1. ==[ start ]==> ((^a.b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.b)((^y.a)((^z.z) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25451/1410036. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^z.a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((^x.a)((a a) a))(^y.y)) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25452/1410225. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25453/1410318. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((^y.y) a)(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (a (^y.((^z.z)(y y)))) 6. ==[ alpha ]==> (a (^x.((^y.y)(x x)))) 7. ==[ beta ]==> (a (^x.(x x))) REDUCED to normal form. ------ 25454/1410396. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 25455/1410495. ------ 1. ==[ start ]==> ((^a.(a (a a)))(b (^a.b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(b (^y.b))) 3. ==[ beta ]==> ((b (^y.b))((b (^y.b))(b (^y.b)))) 4. ==[ alpha ]==> ((b (^x.b))((b (^y.b))(b (^z.b)))) REDUCED to normal form. ------ 25456/1410846. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25457/1411254. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((a a) a))) 5. ==[ beta ]==> ((a a)(^y.((a a) a))) 6. ==[ alpha ]==> ((a a)(^x.((a a) a))) REDUCED to normal form. ------ 25458/1411713. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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)(^x.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 25459/1411791. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)(^b.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. ------ 25460/1411965. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^c.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(a (a a)))) 3. ==[ beta ]==> (b (^z.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 25461/1412178. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(b ((^z.z) a))) 3. ==[ beta ]==> (^y.((b ((^z.z) a))(b ((^z.z) a)))) 4. ==[ alpha ]==> (^x.((b ((^y.y) a))(b ((^z.z) a)))) 5. ==[ beta ]==> (^x.((b a)(b ((^z.z) a)))) 6. ==[ alpha ]==> (^x.((b a)(b ((^y.y) a)))) 7. ==[ beta ]==> (^x.((b a)(b a))) REDUCED to normal form. ------ 25462/1412199. ------ 1. ==[ start ]==> (((a a)(a b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(y y)))) REDUCED to normal form. ------ 25463/1412307. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z z)))) 7. ==[ beta ]==> (a (^y.(^z.(z z)))) 8. ==[ alpha ]==> (a (^x.(^y.(y y)))) REDUCED to normal form. ------ 25464/1412385. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.x1) a))((^z.z)((^x1.x1) a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.z) a))((^x1.x1)((^y1.y1) a)))) 5. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.x1) a))) 8. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z) a))) 9. ==[ beta ]==> (a ((^y.y)((^z.z) a))) 10. ==[ alpha ]==> (a ((^x.x)((^y.y) a))) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25465/1412388. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((^z.z) a))) 3. ==[ beta ]==> ((a (a a))(^y.((^z.z) a))) 4. ==[ alpha ]==> ((a (a a))(^x.((^y.y) a))) 5. ==[ beta ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 25466/1412478. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(x x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> ((^y.y)(^y1.y1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25467/1412649. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.b)) REDUCED to normal form. ------ 25468/1412703. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25469/1412757. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.a)) REDUCED to normal form. ------ 25470/1412775. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(z z))) 3. ==[ beta ]==> (b (^z.(z z))) 4. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 25471/1412784. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 25472/1412814. ------ 1. ==[ start ]==> ((a a)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a a)((^x.(a a))(a a))) 3. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25473/1412832. ------ 1. ==[ start ]==> (((^a.a) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (a ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (a ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25474/1412841. ------ 1. ==[ start ]==> ((a (a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 25475/1412859. ------ 1. ==[ start ]==> (((a a) a)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.a))) REDUCED to normal form. ------ 25476/1412868. ------ 1. ==[ start ]==> ((a b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((a b)((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 25477/1412886. ------ 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 x1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 25478/1412913. ------ 1. ==[ start ]==> (((^a.a) b)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 25479/1412922. ------ 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))(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^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. ------ 25480/1412949. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 25481/1412967. ------ 1. ==[ start ]==> (((a a) b)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 25482/1412994. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.(a a)))) REDUCED to normal form. ------ 25483/1413021. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 25484/1413048. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a b) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b) b)) REDUCED to normal form. ------ 25485/1413111. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 25486/1413138. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25487/1413228. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y) a)(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(a ((^y.y)(a a)))) 5. ==[ beta ]==> (a (a ((^y.y)(a a)))) 6. ==[ alpha ]==> (a (a ((^x.x)(a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 25488/1413237. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a)) a)) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 25489/1413255. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a b)(a a))) 3. ==[ beta ]==> ((^y.y)((a b)(a a))) 4. ==[ alpha ]==> ((^x.x)((a b)(a a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 25490/1413264. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 25491/1413309. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 25492/1413408. ------ 1. ==[ start ]==> ((a (a (a a)))(b (^a.b))) 2. ==[ alpha ]==> ((a (a (a a)))(b (^x.b))) REDUCED to normal form. ------ 25493/1413417. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(a b))) 3. ==[ beta ]==> ((^y.(y y))((a a)(a b))) 4. ==[ alpha ]==> ((^x.(x x))((a a)(a b))) 5. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 25494/1413480. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) 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. ------ 25495/1413507. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^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. ------ 25496/1413534. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 25497/1413561. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 25498/1413615. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 25499/1413651. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(^y.y))) 3. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 25500/1413705. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25501/1413732. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(^y.(y y)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(y y))(^y.(y y)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 25502/1413759. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 25503/1413768. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25504/1413795. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(b ((a a) a))) 3. ==[ beta ]==> ((^y.y)(b ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 25505/1413849. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 25506/1413858. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.a) b)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a) b)) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 25507/1413885. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) c)) 5. ==[ beta ]==> (a ((^y.(^z.z)) c)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) c)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25508/1413903. ------ 1. ==[ start ]==> (((^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))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) a))) 7. ==[ beta ]==> ((a (a a))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 25509/1413930. ------ 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 (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((^y.y) a)(a (a a))) 6. ==[ alpha ]==> (((^x.x) a)(a (a a))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 25510/1413984. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a a)((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 25511/1414020. ------ 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 ]==> ((^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. ------ 25512/1414056. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^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)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 25513/1414083. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) a)((^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. ------ 25514/1414110. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.a)(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)(a (a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 25515/1414137. ------ 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.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25516/1414164. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.a)((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. ------ 25517/1414281. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c (a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c (a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c (a (a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c (a (a a)))) 5. ==[ beta ]==> (a (c (a (a a)))) REDUCED to normal form. ------ 25518/1414362. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^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. ------ 25519/1414389. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (^y1.y1)))) 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. ------ 25520/1414398. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(c c)) REDUCED to normal form. ------ 25521/1414443. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(a (a a)))) 7. ==[ beta ]==> ((a a)((a (^y.y))(a (a a)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 25522/1414506. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 25523/1414542. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 25524/1414569. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 25525/1414596. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 25526/1414623. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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))) 7. ==[ beta ]==> (((a (a a)) a)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 25527/1414650. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 25528/1414677. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(^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. ------ 25529/1414695. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) a) c)) 3. ==[ beta ]==> (b (((^y.y) a) c)) 4. ==[ alpha ]==> (b (((^x.x) a) c)) 5. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 25530/1414704. ------ 1. ==[ start ]==> ((a (a b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(^y.a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 25531/1414713. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(c ((^z.z) a))) 3. ==[ beta ]==> ((^y.b)(c ((^z.z) a))) 4. ==[ alpha ]==> ((^x.b)(c ((^y.y) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 25532/1414794. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(a a))) IRREDUCIBLE: cycle. ------ 25533/1414875. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a a)(a (a a)))) 3. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 25534/1414911. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.y))) REDUCED to normal form. ------ 25535/1414965. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 25536/1414992. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 25537/1415019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.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. ------ 25538/1415046. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) a) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 25539/1415064. ------ 1. ==[ start ]==> (((^a.b)(a a))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(c (a (^y.y)))) 3. ==[ beta ]==> (b (c (a (^y.y)))) 4. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 25540/1415073. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y)) c)) REDUCED to normal form. ------ 25541/1415091. ------ 1. ==[ start ]==> ((a (^b.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(b ((^y.y) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(b a)) REDUCED to normal form. ------ 25542/1415109. ------ 1. ==[ start ]==> (((a a)(a b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(y y))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(x x))) REDUCED to normal form. ------ 25543/1415190. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(b (^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(b (^x.a))) REDUCED to normal form. ------ 25544/1415217. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(a (^x1.(x1 x1)))) 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. ------ 25545/1415244. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.a)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 25546/1415262. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 25547/1415271. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 25548/1415298. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((a (a a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((a (a a))((^y.y) a)) 6. ==[ alpha ]==> ((a (a a))((^x.x) a)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 25549/1415334. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c (a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c (a a))) 3. ==[ beta ]==> ((^y.y)(c (a a))) 4. ==[ alpha ]==> ((^x.x)(c (a a))) 5. ==[ beta ]==> (c (a a)) REDUCED to normal form. ------ 25550/1415388. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a ((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)(a ((^y1.y1) 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. ------ 25551/1415469. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c a)) 3. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 25552/1415478. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 25553/1415505. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 25554/1415532. ------ 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. ------ 25555/1415550. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b (a a))) 3. ==[ beta ]==> ((^y.y)(b (a a))) 4. ==[ alpha ]==> ((^x.x)(b (a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 25556/1415559. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a) b)) REDUCED to normal form. ------ 25557/1415604. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a a)(a a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a a))) 9. ==[ beta ]==> ((^y.y)((a a)(a a))) 10. ==[ alpha ]==> ((^x.x)((a a)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25558/1415613. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a) 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. ------ 25559/1415640. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(^z.z))) 5. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 7. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 25560/1415667. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a) a)) REDUCED to normal form. ------ 25561/1415685. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a (a a))) 3. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 25562/1415694. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 25563/1415720. ------ 1. ==[ start ]==> (^a.(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (^x.(((^y.y)(x x))(^z.z))) 3. ==[ beta ]==> (^x.((x x)(^z.z))) 4. ==[ alpha ]==> (^x.((x x)(^y.y))) REDUCED to normal form. ------ 25564/1415721. ------ 1. ==[ start ]==> (a (((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (a (((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> (a ((a a)(^y.y))) 4. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 25565/1416543. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> ((^x.(^y.(^z.z))) a) 4. ==[ beta ]==> (^y.(^z.z)) 5. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25566/1418634. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a)) a) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y)) a) 3. ==[ beta ]==> (((a a)(^y.y)) a) 4. ==[ alpha ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 25567/1418640. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.z)) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.y)) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25568/1418649. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25569/1418667. ------ 1. ==[ start ]==> ((^a.(a a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.(^z.z)))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 25570/1418694. ------ 1. ==[ start ]==> ((^a.b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25571/1418730. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.(^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. ------ 25572/1418841. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 25573/1418892. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 25574/1419057. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(a a)))) 5. ==[ beta ]==> (a (^y.(^z.(a a)))) 6. ==[ alpha ]==> (a (^x.(^y.(a a)))) REDUCED to normal form. ------ 25575/1419066. ------ 1. ==[ start ]==> (((a a)(^b.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a)(^x.a))(^y.(y y))) REDUCED to normal form. ------ 25576/1419273. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 5. ==[ beta ]==> (^y.(^z.(y y))) 6. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 25577/1419459. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25578/1419462. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a z))) 3. ==[ eta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 25579/1420017. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a) a) a)) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a) a) a)) 3. ==[ beta ]==> (((((a a) a) a)(((a a) a) a))(((a a) a) a)) REDUCED to normal form. ------ 25580/1420173. ------ 1. ==[ start ]==> ((((a a) a) a)(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.((x x) x))) REDUCED to normal form. ------ 25581/1420350. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^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. ------ 25582/1420530. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a) c)) 3. ==[ beta ]==> ((((^y.y) a) c) b) 4. ==[ alpha ]==> ((((^x.x) a) c) b) 5. ==[ beta ]==> ((a c) b) REDUCED to normal form. ------ 25583/1420713. ------ 1. ==[ start ]==> (((a b) a)(^c.(a (a a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(a (a a)))) REDUCED to normal form. ------ 25584/1420731. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 25585/1420917. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.a))((^z.(^x1.x1))(^y1.a)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a)))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(^x2.a)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.a)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.a))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.a))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25586/1420938. ------ 1. ==[ start ]==> (((a a)(a b))(^c.d)) 2. ==[ alpha ]==> (((a a)(a b))(^x.d)) REDUCED to normal form. ------ 25587/1421124. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)(^z.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.a))((a a)(^z.a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.a))((a a)(^z.a)))) 5. ==[ beta ]==> (((a a)(^y.a))((a a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 25588/1421136. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(a a))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(a a))(^y.((^z.z) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25589/1421217. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.a))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 25590/1421298. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^a.(^b.a))) 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. ------ 25591/1421352. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(a (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(a (^y.y)))) REDUCED to normal form. ------ 25592/1421361. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^a.c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.c)) REDUCED to normal form. ------ 25593/1421442. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 25594/1421496. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.b)) REDUCED to normal form. ------ 25595/1421514. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 25596/1421523. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 25597/1421550. ------ 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. ------ 25598/1421562. ------ 1. ==[ start ]==> ((a a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> ((a a)((a a)(^y.y))) 4. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 25599/1421571. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a a))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 25600/1421589. ------ 1. ==[ start ]==> ((a (a a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25601/1421598. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 25602/1421616. ------ 1. ==[ start ]==> ((a b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 25603/1421652. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.(^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)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25604/1421670. ------ 1. ==[ start ]==> (((a a)(a a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 25605/1421706. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25606/1421733. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25607/1421760. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(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. ------ 25608/1421787. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((^y.(a a))(^z.z)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25609/1421814. ------ 1. ==[ start ]==> ((a (^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 25610/1421895. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 25611/1421922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25612/1421931. ------ 1. ==[ start ]==> (((a (^a.a)) b)(c ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(c ((a a) a))) REDUCED to normal form. ------ 25613/1421958. ------ 1. ==[ start ]==> ((((^a.a) a) a)(b (a b))) 2. ==[ alpha ]==> ((((^x.x) a) a)(b (a b))) 3. ==[ beta ]==> ((a a)(b (a b))) REDUCED to normal form. ------ 25614/1421976. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (a ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 25615/1421985. ------ 1. ==[ start ]==> (((a a)(^b.a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a (a a))) REDUCED to normal form. ------ 25616/1422012. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(a a))) REDUCED to normal form. ------ 25617/1422039. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 25618/1422147. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a a)((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a a)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 25619/1422165. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (^z.b))) 3. ==[ beta ]==> ((^y.(y y))(b (^z.b))) 4. ==[ alpha ]==> ((^x.(x x))(b (^y.b))) 5. ==[ beta ]==> ((b (^y.b))(b (^y.b))) 6. ==[ alpha ]==> ((b (^x.b))(b (^y.b))) REDUCED to normal form. ------ 25620/1422192. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 5. ==[ beta ]==> (a (^y.(a a))) 6. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 25621/1422273. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 25622/1422300. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((^y.(y y))(a (a a))) 6. ==[ alpha ]==> ((^x.(x x))(a (a a))) 7. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 25623/1422354. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 25624/1422381. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 25625/1422399. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a b) a)) REDUCED to normal form. ------ 25626/1422426. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a) a) b)) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a) a) b)) REDUCED to normal form. ------ 25627/1422516. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 25628/1422606. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a) a)(a a))) REDUCED to normal form. ------ 25629/1422633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 25630/1422660. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 25631/1422687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (a (a a)))) REDUCED to normal form. ------ 25632/1422714. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 25633/1422732. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(b (^z.a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(b (^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.a))) REDUCED to normal form. ------ 25634/1422741. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 25635/1422804. ------ 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)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 25636/1422831. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (a a))(^y.a))) REDUCED to normal form. ------ 25637/1422858. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(a (^y.(y y)))) 8. ==[ alpha ]==> ((a a)(a (^x.(x x)))) REDUCED to normal form. ------ 25638/1422885. ------ 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)))) REDUCED to normal form. ------ 25639/1422939. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a) a) a)) REDUCED to normal form. ------ 25640/1422975. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25641/1423029. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^z.a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25642/1423065. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 25643/1423092. ------ 1. ==[ start ]==> ((((a a) a) a)(a ((a a) a))) REDUCED to normal form. ------ 25644/1423146. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(a (^x1.x1)))) REDUCED to normal form. ------ 25645/1423173. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 25646/1423200. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 25647/1423227. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25648/1423272. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 25649/1423290. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 25650/1423317. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 25651/1423344. ------ 1. ==[ start ]==> ((((^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 z)))) 3. ==[ beta ]==> ((a (a (a a)))((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 25652/1423371. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a a)(^y.(^z.z)))) 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. ------ 25653/1423398. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 25654/1423425. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (a a)) b)) REDUCED to normal form. ------ 25655/1423452. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a) c)) 3. ==[ beta ]==> ((a (a b))(a c)) REDUCED to normal form. ------ 25656/1423461. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)(^b.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. ------ 25657/1423605. ------ 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 (^x.x)) a)) REDUCED to normal form. ------ 25658/1423623. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b (^z.(z z)))) 3. ==[ beta ]==> (b (b (^z.(z z)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 25659/1423632. ------ 1. ==[ start ]==> (((a b) a)((a a)(a (a a)))) REDUCED to normal form. ------ 25660/1423650. ------ 1. ==[ start ]==> (((^a.a)(a b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(a (^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 25661/1423677. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(z z))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a a))) 5. ==[ beta ]==> ((^y.(y y))(a a)) 6. ==[ alpha ]==> ((^x.(x x))(a a)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25662/1423713. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c c)) REDUCED to normal form. ------ 25663/1423731. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 25664/1423812. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(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. ------ 25665/1423821. ------ 1. ==[ start ]==> (((a b)(^a.a))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(c (a (^y.y)))) REDUCED to normal form. ------ 25666/1423839. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 25667/1423884. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(y y)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 25668/1423911. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a) b)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a) b)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a) b)) 5. ==[ beta ]==> ((a (^y.y))((^z.a) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.a) b)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 25669/1423992. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) 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. ------ 25670/1424010. ------ 1. ==[ start ]==> (((^a.b) b)(c b)) 2. ==[ alpha ]==> (((^x.b) b)(c b)) 3. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 25671/1424019. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 25672/1424046. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)(^y.a))) 3. ==[ beta ]==> ((a (a a))((a a)(^y.a))) 4. ==[ alpha ]==> ((a (a a))((a a)(^x.a))) REDUCED to normal form. ------ 25673/1424055. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25674/1424082. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 25675/1424136. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.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. ------ 25676/1424217. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.a))) 3. ==[ beta ]==> (b (a (^x1.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 25677/1424226. ------ 1. ==[ start ]==> (((a b) b)(c a)) REDUCED to normal form. ------ 25678/1424253. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(b b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(b b)) 3. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 25679/1424271. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 25680/1424280. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(a c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(a c)) REDUCED to normal form. ------ 25681/1424298. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25682/1424307. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (a a))) REDUCED to normal form. ------ 25683/1424352. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (^y1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (^y1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.z))) 9. ==[ beta ]==> ((^y.y)(b (^z.z))) 10. ==[ alpha ]==> ((^x.x)(b (^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25684/1424361. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 25685/1424388. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b a)) 5. ==[ beta ]==> ((^y.(y y))(b a)) 6. ==[ alpha ]==> ((^x.(x x))(b a)) 7. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 25686/1424415. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a b)) REDUCED to normal form. ------ 25687/1424433. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(^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))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25688/1424442. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 25689/1424469. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a a)) 3. ==[ beta ]==> (((a a)(^y.y))(a a)) 4. ==[ alpha ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 25690/1425300. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25691/1427391. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a)) b) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y)) b) 3. ==[ beta ]==> (((a a)(^y.y)) b) 4. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 25692/1427415. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25693/1427496. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25694/1427616. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 25695/1427658. ------ 1. ==[ start ]==> ((^a.(^b.a))((a b) b)) 2. ==[ alpha ]==> ((^x.(^y.x))((a b) b)) 3. ==[ beta ]==> (^y.((a b) b)) 4. ==[ alpha ]==> (^x.((a b) b)) REDUCED to normal form. ------ 25696/1427832. ------ 1. ==[ start ]==> (((a a)(^b.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 25697/1428000. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a (^y.y))((a a) a))(((a (^y.y))((a a) a))((a (^y.y))((a a) a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a (^y.y))((a a) a))((a (^z.z))((a a) a)))) REDUCED to normal form. ------ 25698/1428225. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 25699/1428228. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 25700/1428615. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^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. ------ 25701/1428939. ------ 1. ==[ start ]==> ((((a a) a) a)(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.a))) REDUCED to normal form. ------ 25702/1429116. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25703/1429506. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 25704/1429614. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a (a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a (a a)))) 6. ==[ alpha ]==> ((^x.a)(^y.(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25705/1429683. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.z)) c)) 3. ==[ beta ]==> (^y.(((a (^z.z)) c)((a (^z.z)) c))) 4. ==[ alpha ]==> (^x.(((a (^y.y)) c)((a (^z.z)) c))) REDUCED to normal form. ------ 25706/1429731. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(y (y y)))) REDUCED to normal form. ------ 25707/1429890. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b c)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b c)) 3. ==[ beta ]==> ((^y.y)((b c)(b c))) 4. ==[ alpha ]==> ((^x.x)((b c)(b c))) 5. ==[ beta ]==> ((b c)(b c)) REDUCED to normal form. ------ 25708/1429902. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25709/1429983. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.x1)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^y1.y1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25710/1430064. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.c)) 3. ==[ beta ]==> (b (^x1.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 25711/1430073. ------ 1. ==[ start ]==> (((a b) b)(^a.(^b.a))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.x))) REDUCED to normal form. ------ 25712/1430127. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 25713/1430235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(^y1.(^z1.z1)))) 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. ------ 25714/1430262. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 25715/1430280. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.a)) 3. ==[ beta ]==> (b (^z.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 25716/1430289. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 25717/1430316. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 25718/1430346. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 25719/1430355. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(a a))) 3. ==[ beta ]==> (a ((^y.(a a))(a a))) 4. ==[ alpha ]==> (a ((^x.(a a))(a a))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 25720/1430373. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 25721/1430382. ------ 1. ==[ start ]==> (((a a) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 25722/1430400. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)(^y.a))) 3. ==[ beta ]==> ((a a)(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((a a)(((a a) a)(^x.a))) REDUCED to normal form. ------ 25723/1430427. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 25724/1430436. ------ 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)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25725/1430463. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 25726/1430490. ------ 1. ==[ start ]==> (((a a) b)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a a) b)((^x.a)((a a) a))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 25727/1430508. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 25728/1430517. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 25729/1430535. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 25730/1430544. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 25731/1430562. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((^y.y)(a a)) a) 6. ==[ alpha ]==> (((^x.x)(a a)) a) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 25732/1430571. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 25733/1430589. ------ 1. ==[ start ]==> ((a (^b.a))((a b) b)) 2. ==[ alpha ]==> ((a (^x.a))((a b) b)) REDUCED to normal form. ------ 25734/1430625. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25735/1430706. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 25736/1430733. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25737/1430760. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 25738/1430778. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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 a) REDUCED to normal form. ------ 25739/1430850. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^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)((^y.y) a)) 8. ==[ alpha ]==> (((a a) a)((^x.x) a)) 9. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 25740/1430877. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 25741/1430904. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 25742/1430931. ------ 1. ==[ start ]==> ((a (a (a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 25743/1431003. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.b)(a a))) 3. ==[ beta ]==> ((a b)((^y.b)(a a))) 4. ==[ alpha ]==> ((a b)((^x.b)(a a))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 25744/1431021. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 25745/1431048. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 25746/1431057. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 25747/1431075. ------ 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 x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 5. ==[ beta ]==> ((a (a a))(^y.(y y))) 6. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 25748/1431084. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 25749/1431111. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 25750/1431138. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 25751/1431156. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 25752/1431246. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 25753/1431372. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b) a)) 5. ==[ beta ]==> ((^y.y)((^y1.b) a)) 6. ==[ alpha ]==> ((^x.x)((^y.b) a)) 7. ==[ beta ]==> ((^y.b) a) 8. ==[ alpha ]==> ((^x.b) a) 9. ==[ beta ]==> b REDUCED to normal form. ------ 25754/1431426. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25755/1431489. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 25756/1431516. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 25757/1431543. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(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. ------ 25758/1431750. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((^y.y)(^z.z)) b) 6. ==[ alpha ]==> (((^x.x)(^y.y)) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 25759/1431840. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 25760/1431912. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25761/1431975. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(c (^y.(y y)))) REDUCED to normal form. ------ 25762/1432002. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25763/1432047. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 25764/1432218. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.(^x1.x1)))) 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. ------ 25765/1432236. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a) c)) 3. ==[ beta ]==> ((^y.b)(((^z.z) a) c)) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a) c)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 25766/1432317. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1)) a)) IRREDUCIBLE: cycle. ------ 25767/1432380. ------ 1. ==[ start ]==> ((((a a) a) b)(c (^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)(c (^x.a))) REDUCED to normal form. ------ 25768/1432407. ------ 1. ==[ start ]==> (((a b) a)(b (^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)(b (^x.(x x)))) REDUCED to normal form. ------ 25769/1432434. ------ 1. ==[ start ]==> (((a a)(^a.b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 25770/1432452. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.z))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 25771/1432488. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 25772/1432506. ------ 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 (^y.y))(^z.a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 25773/1432515. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 25774/1432542. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25775/1432569. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25776/1432587. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) a) b)) 3. ==[ beta ]==> (b (((^y.y) a) b)) 4. ==[ alpha ]==> (b (((^x.x) a) b)) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 25777/1432596. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 25778/1432614. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y)) c)) REDUCED to normal form. ------ 25779/1432632. ------ 1. ==[ start ]==> (((a a)(a b))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))(b ((^x.x) a))) 3. ==[ beta ]==> (((a a)(a b))(b a)) REDUCED to normal form. ------ 25780/1432659. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(a (a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(a (a (a a)))) REDUCED to normal form. ------ 25781/1432686. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)(a a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 25782/1432713. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 25783/1432740. ------ 1. ==[ start ]==> ((((^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))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) a)((a a)((^z.z) a))) 6. ==[ alpha ]==> (((^x.x) a)((a a)((^y.y) a))) 7. ==[ beta ]==> (a ((a a)((^y.y) a))) 8. ==[ alpha ]==> (a ((a a)((^x.x) a))) 9. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 25784/1432785. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.a)(a a))) 3. ==[ beta ]==> (b ((^y.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 25785/1432794. ------ 1. ==[ start ]==> (((a b)(a a))(c b)) REDUCED to normal form. ------ 25786/1432821. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b c)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b c)) 3. ==[ beta ]==> ((a (a a))(b c)) REDUCED to normal form. ------ 25787/1432830. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(^z.a))) 3. ==[ beta ]==> ((^y.(a a))((a a)(^z.a))) 4. ==[ alpha ]==> ((^x.(a a))((a a)(^y.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25788/1432857. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a)) 5. ==[ beta ]==> (((^y.y) a) a) 6. ==[ alpha ]==> (((^x.x) a) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25789/1432911. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((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. ------ 25790/1432992. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (b ((^x1.x1) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 25791/1433001. ------ 1. ==[ start ]==> (((a b) b)(a (^b.a))) 2. ==[ alpha ]==> (((a b) b)(a (^x.a))) REDUCED to normal form. ------ 25792/1433028. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 25793/1433046. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.(^x1.x1)))) 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. ------ 25794/1433055. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(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. ------ 25795/1433073. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.z)) a)) 3. ==[ beta ]==> ((^y.y)((a (^z.z)) a)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a)) 5. ==[ beta ]==> ((a (^y.y)) a) 6. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 25796/1433082. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 25797/1433127. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1)) a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1)) a)) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) a)) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 11. ==[ beta ]==> ((^y.(^z.z)) a) 12. ==[ alpha ]==> ((^x.(^y.y)) a) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25798/1433136. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 25799/1433163. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 25800/1433190. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 25801/1433208. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a) a)) 3. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 25802/1433217. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25803/1433244. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a (^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 25804/1434642. ------ 1. ==[ start ]==> ((^a.((a a) a))(^b.((a a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.((a a) a))) 3. ==[ beta ]==> (((^y.((a a) a))(^y.((a a) a)))(^y.((a a) a))) 4. ==[ alpha ]==> (((^x.((a a) a))(^y.((a a) a)))(^z.((a a) a))) 5. ==[ beta ]==> (((a a) a)(^z.((a a) a))) 6. ==[ alpha ]==> (((a a) a)(^x.((a a) a))) REDUCED to normal form. ------ 25805/1436226. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(a a))) 3. ==[ beta ]==> (((^y.(a a))(a a))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((^x.(a a))(a a))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a a)((^y.(a a))(a a))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25806/1436253. ------ 1. ==[ start ]==> ((^a.b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25807/1436334. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.(z z))((^x1.x1)(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 9. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 10. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 11. ==[ beta ]==> ((^y.y)(^z.z)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25808/1436523. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^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. ------ 25809/1436643. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (^y.((^z.z)(y y))) 6. ==[ alpha ]==> (^x.((^y.y)(x x))) 7. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 25810/1436694. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 25811/1436832. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(a b))) 3. ==[ beta ]==> ((^y.y)(^x1.(a b))) 4. ==[ alpha ]==> ((^x.x)(^y.(a b))) 5. ==[ beta ]==> (^y.(a b)) 6. ==[ alpha ]==> (^x.(a b)) REDUCED to normal form. ------ 25812/1437039. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^b.(a b))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(a x))) 3. ==[ eta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 25813/1437144. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(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. ------ 25814/1437237. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(x1 b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 b))) 5. ==[ beta ]==> ((^y.y)(^y1.(y1 b))) 6. ==[ alpha ]==> ((^x.x)(^y.(y b))) 7. ==[ beta ]==> (^y.(y b)) 8. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 25815/1437576. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.a)((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. ------ 25816/1437579. ------ 1. ==[ start ]==> ((a ((a a) a))(^b.((a a) a))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.((a a) a))) REDUCED to normal form. ------ 25817/1437750. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.((y y) y))) 3. ==[ beta ]==> (((a a) a)(^y.((y y) y))) 4. ==[ alpha ]==> (((a a) a)(^x.((x x) x))) REDUCED to normal form. ------ 25818/1438038. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 25819/1438089. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z))) b) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z))) b) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 25820/1438182. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) IRREDUCIBLE: cycle. ------ 25821/1438290. ------ 1. ==[ start ]==> (((^a.a)(a b))(^c.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(a (a a)))) 3. ==[ beta ]==> ((a b)(^y.(a (a a)))) 4. ==[ alpha ]==> ((a b)(^x.(a (a a)))) REDUCED to normal form. ------ 25822/1438407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(z z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25823/1438476. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c (a (^z.z)))) 3. ==[ beta ]==> (^y.((c (a (^z.z)))(c (a (^z.z))))) 4. ==[ alpha ]==> (^x.((c (a (^y.y)))(c (a (^z.z))))) REDUCED to normal form. ------ 25824/1438524. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 25825/1438632. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 25826/1438683. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(a (^y1.y1)))((^z.(^x1.x1))(a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a (^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2))))) 5. ==[ beta ]==> (((^y.(^z.z))(a (^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 6. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 9. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 10. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25827/1438857. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (b (^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 25828/1438866. ------ 1. ==[ start ]==> (((a b) b)(^b.c)) 2. ==[ alpha ]==> (((a b) b)(^x.c)) REDUCED to normal form. ------ 25829/1438920. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 25830/1438938. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.c)) 3. ==[ beta ]==> ((^y.y)(^z.c)) 4. ==[ alpha ]==> ((^x.x)(^y.c)) 5. ==[ beta ]==> (^y.c) 6. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 25831/1438992. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 11. ==[ beta ]==> (^y.(y (^z.z))) 12. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 25832/1439028. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z)) 5. ==[ beta ]==> ((^y.(y y))(^z.z)) 6. ==[ alpha ]==> ((^x.(x x))(^y.y)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25833/1439055. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 25834/1439073. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.b)) 3. ==[ beta ]==> (b (^z.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 25835/1439082. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 25836/1439109. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.a)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 25837/1439157. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (a (((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (a (((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (a ((a a)(^y.y))) 6. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 25838/1439166. ------ 1. ==[ start ]==> ((a (a a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (a a))((^x.(a a))(a a))) 3. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 25839/1439184. ------ 1. ==[ start ]==> (((a a) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25840/1439193. ------ 1. ==[ start ]==> ((a b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 25841/1439211. ------ 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. ------ 25842/1439238. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 25843/1439247. ------ 1. ==[ start ]==> (((a a)(a a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))(^y.y)) 4. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 25844/1439265. ------ 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. ------ 25845/1439274. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 10. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 25846/1439292. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.a))) 3. ==[ beta ]==> (((a a) b)(a (^y.a))) 4. ==[ alpha ]==> (((a a) b)(a (^x.a))) REDUCED to normal form. ------ 25847/1439319. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(^z.b))) REDUCED to normal form. ------ 25848/1439346. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 25849/1439373. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 25850/1439409. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 25851/1439427. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a) a) c)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a) a) c)) 3. ==[ beta ]==> ((^y.y)(((a a) a) c)) 4. ==[ alpha ]==> ((^x.x)(((a a) a) c)) 5. ==[ beta ]==> (((a a) a) c) REDUCED to normal form. ------ 25852/1439463. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25853/1439553. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(b (a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) 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. ------ 25854/1439580. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(a a)))) 5. ==[ beta ]==> (a ((^y.y)(a a))) 6. ==[ alpha ]==> (a ((^x.x)(a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 25855/1439589. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 25856/1439616. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.b) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.b) b)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 25857/1439634. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 25858/1439742. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.y))((a a) a))) 5. ==[ beta ]==> (((a (^y.y))((a a) a))((a (^y.y))((a a) a))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 25859/1439769. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)(a b))) 3. ==[ beta ]==> ((^y.y)((a a)(a b))) 4. ==[ alpha ]==> ((^x.x)((a a)(a b))) 5. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 25860/1439805. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a b)(^y.y))) 3. ==[ beta ]==> ((a b)((a b)(^y.y))) 4. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 25861/1439832. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 25862/1439859. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 25863/1439886. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 25864/1439913. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 25865/1439976. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a b))) 3. ==[ beta ]==> (((a a)(a (a a)))(a b)) REDUCED to normal form. ------ 25866/1440003. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 25867/1440048. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z)) c)) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y)) c)) 5. ==[ beta ]==> ((b b)((^y.y) c)) 6. ==[ alpha ]==> ((b b)((^x.x) c)) 7. ==[ beta ]==> ((b b) c) REDUCED to normal form. ------ 25868/1440057. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(^a.a))(^b.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. ------ 25869/1440084. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 25870/1440174. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (a b))) 5. ==[ beta ]==> ((^y.y)(a (a b))) 6. ==[ alpha ]==> ((^x.x)(a (a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 25871/1440183. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.b) a)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.b) a)) 3. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 25872/1440228. ------ 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)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25873/1440237. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25874/1440255. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((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)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 25875/1440309. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 25876/1440408. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.(^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)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 25877/1440435. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((a a)(a ((^x.x) a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25878/1440462. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x))) a) REDUCED to normal form. ------ 25879/1440489. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 25880/1440516. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)((a a) a))) 3. ==[ beta ]==> ((a ((a a) a))((a a) a)) REDUCED to normal form. ------ 25881/1440687. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(a ((a a) a))) 3. ==[ beta ]==> (((a a) a)(a ((a a) a))) REDUCED to normal form. ------ 25882/1440714. ------ 1. ==[ start ]==> (((^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))(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(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. ------ 25883/1440723. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 25884/1440768. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((a a)(a ((^x.x) a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 25885/1440867. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(^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)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 25886/1440894. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^x1.x1))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 25887/1440921. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (a a)))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 25888/1440948. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 25889/1440975. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 25890/1441002. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 25891/1441020. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a)) b)) 2. ==[ alpha ]==> (((^x.b) a)((a (a a)) b)) 3. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 25892/1441029. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 25893/1441119. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a ((^z.z)(^x1.x1)))) IRREDUCIBLE: cycle. ------ 25894/1441182. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a) c)) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a) c)) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 25895/1441200. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 25896/1441227. ------ 1. ==[ start ]==> (((^a.a)(a b))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a a)(a (a a)))) 3. ==[ beta ]==> ((a b)((a a)(a (a a)))) REDUCED to normal form. ------ 25897/1441290. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 25898/1441317. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 25899/1441344. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.(y y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25900/1441371. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 25901/1441398. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a) b)) 3. ==[ beta ]==> (((a b)(^x.x))(a b)) REDUCED to normal form. ------ 25902/1441416. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c (a (^y.y)))) REDUCED to normal form. ------ 25903/1441434. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 25904/1441461. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(z z))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 25905/1441542. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (^z.a))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.a))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.a))) 7. ==[ beta ]==> (a (b (^y.a))) 8. ==[ alpha ]==> (a (b (^x.a))) REDUCED to normal form. ------ 25906/1441569. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 25907/1441587. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 25908/1441596. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(a a))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 25909/1441623. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 25910/1441632. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b c)) 3. ==[ beta ]==> ((^y.(a a))(b c)) 4. ==[ alpha ]==> ((^x.(a a))(b c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25911/1441713. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(b (a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 25912/1441794. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 25913/1441803. ------ 1. ==[ start ]==> (((a b) b)((^a.a) c)) 2. ==[ alpha ]==> (((a b) b)((^x.x) c)) 3. ==[ beta ]==> (((a b) b) c) REDUCED to normal form. ------ 25914/1441830. ------ 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. ------ 25915/1441848. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b b)) 3. ==[ beta ]==> (((^y.y)(a a))(b b)) 4. ==[ alpha ]==> (((^x.x)(a a))(b b)) 5. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 25916/1441857. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 25917/1441875. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(a c)) 3. ==[ beta ]==> ((^y.y)(a c)) 4. ==[ alpha ]==> ((^x.x)(a c)) 5. ==[ beta ]==> (a c) REDUCED to normal form. ------ 25918/1441884. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z)) a)) REDUCED to normal form. ------ 25919/1441929. ------ 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 ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a (a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a (a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (a (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (^z.z)))) 9. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 10. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 11. ==[ beta ]==> (a (a (^y.y))) 12. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 25920/1441938. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1)) 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. ------ 25921/1441965. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1) b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1) 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. ------ 25922/1441992. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 25923/1442010. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a b)) 3. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 25924/1442019. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 25925/1442046. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 25926/1443786. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.z))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25927/1445046. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((((^y.y)(a a))(^z.z))(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 25928/1445073. ------ 1. ==[ start ]==> ((^a.b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 25929/1445154. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^z.(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25930/1445247. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^y.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 25931/1445271. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (^y.((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (^x.((^y.(a a))(^z.z))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 25932/1445463. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 5. ==[ beta ]==> (^y.(^z.(a a))) 6. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 25933/1445472. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 x1))) REDUCED to normal form. ------ 25934/1445838. ------ 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. ------ 25935/1446057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.y1))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 25936/1446066. ------ 1. ==[ start ]==> (((a (a a)) b)(^a.(a b))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(x b))) REDUCED to normal form. ------ 25937/1446570. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(^z.a))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.a))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.a))) REDUCED to normal form. ------ 25938/1446729. ------ 1. ==[ start ]==> ((^a.(^a.b))(a (^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(a (^z.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25939/1446732. ------ 1. ==[ start ]==> ((a (^a.b))(^a.(^c.a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.y))) REDUCED to normal form. ------ 25940/1446909. ------ 1. ==[ start ]==> ((^a.(a b))((a (a a)) b)) 2. ==[ alpha ]==> ((^x.(x b))((a (a a)) b)) 3. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 25941/1447002. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 25942/1447119. ------ 1. ==[ start ]==> (((a a)(^a.b))(^c.(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(a (a a)))) REDUCED to normal form. ------ 25943/1447137. ------ 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)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 25944/1447296. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.(^y1.y1)))((^z.a)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.(a ((^y1.a)(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.(^x1.x1))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 25945/1447503. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))(^x1.(^y1.y1)))((a (^z.z))(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 25946/1447542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 5. ==[ beta ]==> (^y.((^z.z) a)) 6. ==[ alpha ]==> (^x.((^y.y) a)) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 25947/1447686. ------ 1. ==[ start ]==> (((a b) b)(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(a (^y.y)))) REDUCED to normal form. ------ 25948/1447758. ------ 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)(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 5. ==[ beta ]==> (^y.(a (^z.z))) 6. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 25949/1447767. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.c)) REDUCED to normal form. ------ 25950/1447812. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.(^z.(^x1.x1))) 12. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 25951/1447821. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 25952/1447893. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(a a))) 3. ==[ beta ]==> (b (^z.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 25953/1447902. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 25954/1447929. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(z z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 25955/1447995. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(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. ------ 25956/1448004. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^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. ------ 25957/1448022. ------ 1. ==[ start ]==> ((a b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 25958/1448031. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.b)(a (^y.y)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 25959/1448076. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^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. ------ 25960/1448103. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 25961/1448112. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25962/1448139. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 25963/1448166. ------ 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)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 25964/1448193. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^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 ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 25965/1448220. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 25966/1448238. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a b) b)) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a b) b)) REDUCED to normal form. ------ 25967/1448301. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 25968/1448328. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25969/1448382. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 25970/1448391. ------ 1. ==[ start ]==> (((a a)(^b.a))(b (a b))) 2. ==[ alpha ]==> (((a a)(^x.a))(b (a b))) REDUCED to normal form. ------ 25971/1448409. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a a))) 6. ==[ alpha ]==> ((^x.x)(^y.(a a))) 7. ==[ beta ]==> (^y.(a a)) 8. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 25972/1448418. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (a a))) REDUCED to normal form. ------ 25973/1448445. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(a a))) 3. ==[ beta ]==> ((a (^y.y))((a b)(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(a a))) REDUCED to normal form. ------ 25974/1448553. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^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)))) 5. ==[ beta ]==> ((a a)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 25975/1448598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(b (^x1.b))) 3. ==[ beta ]==> ((^y.y)(b (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(b (^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 25976/1448652. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(a a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 7. ==[ beta ]==> ((^y.b)(a a)) 8. ==[ alpha ]==> ((^x.b)(a a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 25977/1448706. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) 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. ------ 25978/1448760. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 25979/1448787. ------ 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)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 25980/1448805. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.b))) REDUCED to normal form. ------ 25981/1448832. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a b) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a b) a)) 3. ==[ beta ]==> (((a (^x.x)) a)((a b) a)) REDUCED to normal form. ------ 25982/1448859. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a) a) b)) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a) a) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a) b)) REDUCED to normal form. ------ 25983/1448922. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 25984/1448949. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25985/1449003. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 25986/1449012. ------ 1. ==[ start ]==> (((a (a a)) b)(a (a b))) REDUCED to normal form. ------ 25987/1449039. ------ 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 ]==> (((^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. ------ 25988/1449066. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 25989/1449093. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (a a)) a)) REDUCED to normal form. ------ 25990/1449120. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.a))(a (a (a a)))) REDUCED to normal form. ------ 25991/1449147. ------ 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.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 25992/1449174. ------ 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 ]==> ((^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. ------ 25993/1449210. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^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. ------ 25994/1449237. ------ 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)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 25995/1449264. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(^y.a))) 5. ==[ beta ]==> ((a a)((a (a a))(^y.a))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.a))) REDUCED to normal form. ------ 25996/1449291. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 25997/1449318. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 25998/1449381. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 25999/1449435. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (a ((^z.(z z))(^x1.a))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.a))) 7. ==[ beta ]==> (a ((^y.a)(^y.a))) 8. ==[ alpha ]==> (a ((^x.a)(^y.a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26000/1449471. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c (a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(c (a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(c (a (a a)))) 5. ==[ beta ]==> (b (c (a (a a)))) REDUCED to normal form. ------ 26001/1449498. ------ 1. ==[ start ]==> ((((a a) a) a)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)(b ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) a)(b (^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)(b (^x.x))) REDUCED to normal form. ------ 26002/1449552. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 26003/1449579. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 26004/1449606. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(a ((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 26005/1449633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26006/1449660. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.y)(^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. ------ 26007/1449678. ------ 1. ==[ start ]==> ((a (^a.b))(a (^c.a))) 2. ==[ alpha ]==> ((a (^x.b))(a (^y.a))) REDUCED to normal form. ------ 26008/1449696. ------ 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))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 26009/1449723. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 26010/1449750. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((a (a (a a)))(a (^y.a))) 6. ==[ alpha ]==> ((a (a (a a)))(a (^x.a))) REDUCED to normal form. ------ 26011/1449777. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) a)((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 26012/1449804. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 26013/1449831. ------ 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))((^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. ------ 26014/1449858. ------ 1. ==[ start ]==> ((a (a b))((a (a a)) b)) REDUCED to normal form. ------ 26015/1449867. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26016/1449948. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 26017/1450011. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a) b)(a (a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a) b)(a (a (^x.x)))) REDUCED to normal form. ------ 26018/1450029. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c (^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 26019/1450038. ------ 1. ==[ start ]==> (((a b) a)((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b) a)((a (^x.x))((^y.y) a))) 3. ==[ beta ]==> (((a b) a)((a (^x.x)) a)) REDUCED to normal form. ------ 26020/1450056. ------ 1. ==[ start ]==> (((^a.a)(a b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(b (^y.(y y)))) 3. ==[ beta ]==> ((a b)(b (^y.(y y)))) 4. ==[ alpha ]==> ((a b)(b (^x.(x x)))) REDUCED to normal form. ------ 26021/1450065. ------ 1. ==[ start ]==> (((a a)(^a.b))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a a)(a (a a)))) REDUCED to normal form. ------ 26022/1450083. ------ 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 (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 26023/1450137. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 26024/1450218. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26025/1450245. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 26026/1450263. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.x)) c)) REDUCED to normal form. ------ 26027/1450317. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z)) a)) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) a)) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 26028/1450344. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.a) b)) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a) b)) 3. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 26029/1450425. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.y))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.x))) REDUCED to normal form. ------ 26030/1450452. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 26031/1450461. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26032/1450488. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.a)((^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. ------ 26033/1450542. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26034/1450623. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 26035/1450632. ------ 1. ==[ start ]==> (((a b) b)((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((a a)(a (^x.x)))) REDUCED to normal form. ------ 26036/1450677. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26037/1450686. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b b)) REDUCED to normal form. ------ 26038/1450704. ------ 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)((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 26039/1450713. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a c)) REDUCED to normal form. ------ 26040/1450758. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 11. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 12. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26041/1450767. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 26042/1450794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 26043/1450821. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b a)) REDUCED to normal form. ------ 26044/1450839. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (b ((^z.z)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 26045/1450848. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 26046/1450875. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a (a a))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 26047/1450910. ------ 1. ==[ start ]==> (^a.((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (^x.((x x)((^y.y)(x x)))) 3. ==[ beta ]==> (^x.((x x)(x x))) REDUCED to normal form. ------ 26048/1450911. ------ 1. ==[ start ]==> (a ((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 3. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 26049/1453860. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a))) a) 2. ==[ alpha ]==> (((a a)((^x.x)(a a))) a) 3. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 26050/1453866. ------ 1. ==[ start ]==> ((^a.a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(a a))) 4. ==[ alpha ]==> ((a a)((^x.x)(a a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 26051/1453956. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26052/1454103. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 26053/1454118. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (^y.(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (^x.(((^y.y)(a a)) a)) 5. ==[ beta ]==> (^x.((a a) a)) REDUCED to normal form. ------ 26054/1454319. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 26055/1454361. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.b) b)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26056/1454460. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^z.z)(^x1.x1)))((((^y.y) a)((^z.z)(^x1.x1)))(((^y.y) a)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((((^x1.x1) a)((^y1.y1)(^z1.z1)))(((^x2.x2) a)((^y2.y2)(^z2.z2))))) 5. ==[ beta ]==> ((a ((^y.y)(^z.z)))((((^x1.x1) a)((^y1.y1)(^z1.z1)))(((^x2.x2) a)((^y2.y2)(^z2.z2))))) 6. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((((^z.z) a)((^x1.x1)(^y1.y1)))(((^z1.z1) a)((^x2.x2)(^y2.y2))))) 7. ==[ beta ]==> ((a (^y.y))((((^z.z) a)((^x1.x1)(^y1.y1)))(((^z1.z1) a)((^x2.x2)(^y2.y2))))) 8. ==[ alpha ]==> ((a (^x.x))((((^y.y) a)((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2))))) 9. ==[ beta ]==> ((a (^x.x))((a ((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2))))) 10. ==[ alpha ]==> ((a (^x.x))((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1))))) 11. ==[ beta ]==> ((a (^x.x))((a (^z.z))(((^x1.x1) a)((^y1.y1)(^z1.z1))))) 12. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1))))) 13. ==[ beta ]==> ((a (^x.x))((a (^y.y))(a ((^x1.x1)(^y1.y1))))) 14. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a ((^z.z)(^x1.x1))))) 15. ==[ beta ]==> ((a (^x.x))((a (^y.y))(a (^x1.x1)))) 16. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 26057/1454535. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.(y y)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(x x)))) REDUCED to normal form. ------ 26058/1454685. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26059/1454913. ------ 1. ==[ start ]==> (((a (a a)) b)(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.x))) REDUCED to normal form. ------ 26060/1456101. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(a (a a)))) REDUCED to normal form. ------ 26061/1456143. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a) b)) 3. ==[ beta ]==> (^y.((((^z.z) a) b)(((^z.z) a) b))) 4. ==[ alpha ]==> (^x.((((^y.y) a) b)(((^z.z) a) b))) 5. ==[ beta ]==> (^x.((a b)(((^z.z) a) b))) 6. ==[ alpha ]==> (^x.((a b)(((^y.y) a) b))) 7. ==[ beta ]==> (^x.((a b)(a b))) REDUCED to normal form. ------ 26062/1456218. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(z (z z)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(z (z z)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 26063/1456317. ------ 1. ==[ start ]==> (((^a.b) b)(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 26064/1456389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(^y1.a))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 26065/1456560. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(^z.y))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.y))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.x))) REDUCED to normal form. ------ 26066/1456605. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 26067/1456614. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 26068/1456668. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 26069/1456722. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 26070/1456740. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 26071/1456749. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 26072/1456776. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 26073/1456812. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.y)) 3. ==[ beta ]==> (((a a)(a a))(^y.y)) 4. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 26074/1456824. ------ 1. ==[ start ]==> ((a a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 26075/1456860. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.x1))) 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. ------ 26076/1456869. ------ 1. ==[ start ]==> (((a a) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a) a)((^x.(a a))(a a))) 3. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 26077/1456887. ------ 1. ==[ start ]==> (((^a.a)(a a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 26078/1456896. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 26079/1456914. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 26080/1456923. ------ 1. ==[ start ]==> (((^a.a) b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.a)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26081/1456950. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(^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. ------ 26082/1456968. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((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. ------ 26083/1456977. ------ 1. ==[ start ]==> (((a a) b)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) b)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) b)((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a) b)((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a) b)(^y.y)) 10. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 26084/1457004. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 26085/1457022. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((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. ------ 26086/1457031. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 26087/1457049. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 26088/1457058. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 26089/1457076. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((a (^x.a))((a a) a)) REDUCED to normal form. ------ 26090/1457112. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 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. ------ 26091/1457193. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 26092/1457220. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.a)(^z.a))) 3. ==[ beta ]==> ((a a)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a a)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 26093/1457247. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 26094/1457274. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(a a))) REDUCED to normal form. ------ 26095/1457319. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.b) b)) 3. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 26096/1457337. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^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. ------ 26097/1457364. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 26098/1457391. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26099/1457418. ------ 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)))) 3. ==[ beta ]==> ((a (a (a a)))(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (a (a a)))(a (^y.y))) 6. ==[ alpha ]==> ((a (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 26100/1457490. ------ 1. ==[ start ]==> ((((^a.a) a) b)(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(a (^y.(a a)))) 3. ==[ beta ]==> ((a b)(a (^y.(a a)))) 4. ==[ alpha ]==> ((a b)(a (^x.(a a)))) REDUCED to normal form. ------ 26101/1457508. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)(^z.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 26102/1457517. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.b)(a a))) 3. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 26103/1457535. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a) a)(^y.(^z.z)))) 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. ------ 26104/1457562. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^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. ------ 26105/1457571. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 26106/1457598. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26107/1457616. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^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. ------ 26108/1457625. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 26109/1457643. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 26110/1457733. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) 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. ------ 26111/1457868. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.b))) 3. ==[ beta ]==> (((a (a a)) b)(^y.b)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.b)) REDUCED to normal form. ------ 26112/1457940. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 5. ==[ beta ]==> ((^y.(^z.z)) c) 6. ==[ alpha ]==> ((^x.(^y.y)) c) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26113/1458030. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.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. ------ 26114/1458237. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a) a)) 3. ==[ beta ]==> ((^y.y)(((a a) a) a)) 4. ==[ alpha ]==> ((^x.x)(((a a) a) a)) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 26115/1458291. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (a a)) c)) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (a a)) c)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (a a)) c)) 5. ==[ beta ]==> (a ((a (a a)) c)) REDUCED to normal form. ------ 26116/1458327. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26117/1458354. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 26118/1458516. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 26119/1458705. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 26120/1458723. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a)) b)) 3. ==[ beta ]==> ((^y.b)((a (a a)) b)) 4. ==[ alpha ]==> ((^x.b)((a (a a)) b)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26121/1458885. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26122/1458894. ------ 1. ==[ start ]==> (((a b) a)(c (^b.a))) 2. ==[ alpha ]==> (((a b) a)(c (^x.a))) REDUCED to normal form. ------ 26123/1458921. ------ 1. ==[ start ]==> (((a a)(^a.b))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(b (^y.(y y)))) REDUCED to normal form. ------ 26124/1458975. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 26125/1458993. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 26126/1459002. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 26127/1459029. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26128/1459056. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 26129/1459074. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a a))((a (a a)) a)) 3. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 26130/1459083. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 26131/1459101. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a) b)) 3. ==[ beta ]==> ((a (^x.(a a)))(a b)) REDUCED to normal form. ------ 26132/1459119. ------ 1. ==[ start ]==> (((a a)(a b))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(c (a (^x.x)))) REDUCED to normal form. ------ 26133/1459146. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(b ((^y.y) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(b a)) REDUCED to normal form. ------ 26134/1459173. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(a (a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(a (a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a (a (a a)))) 5. ==[ beta ]==> ((a (^y.y))(a (a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (a a)))) REDUCED to normal form. ------ 26135/1459200. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)(a a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 26136/1459227. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a ((a (^y.y))(a (^z.z)))) 8. ==[ alpha ]==> (a ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 26137/1459254. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a a) a)) REDUCED to normal form. ------ 26138/1459272. ------ 1. ==[ start ]==> (((^a.b) b)(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(a (^y.(y y)))) 3. ==[ beta ]==> (b (a (^y.(y y)))) 4. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 26139/1459317. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26140/1459344. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 5. ==[ beta ]==> ((a a)(^y.a)) 6. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 26141/1459398. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1)) b)) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1)) 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. ------ 26142/1459479. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (b ((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26143/1459488. ------ 1. ==[ start ]==> (((a b) b)(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 26144/1459515. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(a (^y.a))) 3. ==[ beta ]==> (((a a) a)(a (^y.a))) 4. ==[ alpha ]==> (((a a) a)(a (^x.a))) REDUCED to normal form. ------ 26145/1459533. ------ 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. ------ 26146/1459542. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 26147/1459560. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 26148/1459569. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)(a (^a.a)))) 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. ------ 26149/1459614. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a a) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a a) b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a) b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a) b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a) b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a) b)) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a) b)) 9. ==[ beta ]==> ((^y.y)((a a) b)) 10. ==[ alpha ]==> ((^x.x)((a a) b)) 11. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 26150/1459623. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 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. ------ 26151/1459650. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (^z.z))) 5. ==[ beta ]==> ((^y.(y y))(b (^z.z))) 6. ==[ alpha ]==> ((^x.(x x))(b (^y.y))) 7. ==[ beta ]==> ((b (^y.y))(b (^y.y))) 8. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 26152/1459677. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 26153/1459695. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a)(^z.z))) 3. ==[ beta ]==> (b ((a a)(^z.z))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 26154/1459704. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 26155/1459731. ------ 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)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 26156/1459767. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a a)) 3. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 26157/1459775. ------ 1. ==[ start ]==> (^a.(b (^b.(a a)))) 2. ==[ alpha ]==> (^x.(b (^y.(x x)))) REDUCED to normal form. ------ 26158/1459776. ------ 1. ==[ start ]==> (a (b (^b.(a a)))) 2. ==[ alpha ]==> (a (b (^x.(a a)))) REDUCED to normal form. ------ 26159/1461489. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26160/1462725. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a))) b) 2. ==[ alpha ]==> (((a a)((^x.x)(a a))) b) 3. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 26161/1462740. ------ 1. ==[ start ]==> ((^a.a)(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 3. ==[ beta ]==> (b (^y.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 26162/1462749. ------ 1. ==[ start ]==> ((^a.(^a.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26163/1462794. ------ 1. ==[ start ]==> ((^a.b)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26164/1462875. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26165/1463235. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a b)(a a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26166/1463607. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(a z))) 3. ==[ eta ]==> (((a (^x.x))((^y.y) a)) a) 4. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 26167/1463685. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.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. ------ 26168/1463985. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 26169/1464117. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z))((^x1.x1)(^y1.y1)))((^y.(^z.z))((^x1.x1)(^y1.y1))))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2))))((^z2.(^x3.x3))((^y3.y3)(^z3.z3)))) 5. ==[ beta ]==> (((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2))))((^z2.(^x3.x3))((^y3.y3)(^z3.z3)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 11. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26170/1464318. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.((y1 y1) y1))) 3. ==[ beta ]==> ((^y.y)(^y1.((y1 y1) y1))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y) y))) 5. ==[ beta ]==> (^y.((y y) y)) 6. ==[ alpha ]==> (^x.((x x) x)) REDUCED to normal form. ------ 26171/1464450. ------ 1. ==[ start ]==> ((^a.(^a.b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26172/1464453. ------ 1. ==[ start ]==> ((a (^a.b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 26173/1464606. ------ 1. ==[ start ]==> ((((a a) a)(a a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 26174/1464630. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.x1)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 26175/1465092. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 26176/1465200. ------ 1. ==[ start ]==> (((a b)(a a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 26177/1465224. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.a)(a a))((^z.a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)(a a))((^z.a)(a a)))) 5. ==[ beta ]==> (((^y.a)(a a))((^z.a)(a a))) 6. ==[ alpha ]==> (((^x.a)(a a))((^y.a)(a a))) 7. ==[ beta ]==> (a ((^y.a)(a a))) 8. ==[ alpha ]==> (a ((^x.a)(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26178/1465434. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.c)) 3. ==[ beta ]==> (((a a) a)(^y.c)) 4. ==[ alpha ]==> (((a a) a)(^x.c)) REDUCED to normal form. ------ 26179/1465488. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 26180/1465542. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 26181/1465596. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 26182/1465623. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 26183/1465686. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 26184/1465707. ------ 1. ==[ start ]==> ((a a)(b (^b.(a a)))) 2. ==[ alpha ]==> ((a a)(b (^x.(a a)))) REDUCED to normal form. ------ 26185/1465716. ------ 1. ==[ start ]==> ((a (^a.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 26186/1465752. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(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. ------ 26187/1465761. ------ 1. ==[ start ]==> ((a b)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(a a))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 26188/1465779. ------ 1. ==[ start ]==> (((a a)(^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 26189/1465806. ------ 1. ==[ start ]==> (((^a.a) b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x) b)(((a a) a)(^y.a))) 3. ==[ beta ]==> (b (((a a) a)(^y.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 26190/1465833. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 26191/1465842. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 26192/1465860. ------ 1. ==[ start ]==> (((a a) b)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 26193/1465914. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 26194/1465941. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(a a)))) REDUCED to normal form. ------ 26195/1465977. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 26196/1465995. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a b) b)) 3. ==[ beta ]==> ((^y.y)((a b) b)) 4. ==[ alpha ]==> ((^x.x)((a b) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 26197/1466004. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 26198/1466148. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(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. ------ 26199/1466184. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a)) a)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 26200/1466202. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a b)(a a))) REDUCED to normal form. ------ 26201/1466310. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((^y.y) a)((^z.z)(^x1.x1)))(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> ((a (^x.x))(a ((^z.z)(^x1.x1)))) 12. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.z)))) 13. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 14. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 26202/1466337. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((a (^y.y))((a a) a)) 6. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 26203/1466400. ------ 1. ==[ start ]==> (((a (a a)) a)((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a)) a)((a b)(^x.x))) REDUCED to normal form. ------ 26204/1466427. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 26205/1466454. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.a)) REDUCED to normal form. ------ 26206/1466481. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 26207/1466508. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 26208/1466544. ------ 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)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 26209/1466571. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(a b))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a b))) 5. ==[ beta ]==> (((a (^x.x)) a)(a b)) REDUCED to normal form. ------ 26210/1466598. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 26211/1466616. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a) a) b)) 3. ==[ beta ]==> ((b b)(((a a) a) b)) REDUCED to normal form. ------ 26212/1466652. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26213/1466742. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b ((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(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. ------ 26214/1466778. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.b) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.b) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.b) a)) 5. ==[ beta ]==> (a ((^y.b) a)) 6. ==[ alpha ]==> (a ((^x.b) a)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 26215/1466796. ------ 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 ]==> ((^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. ------ 26216/1466805. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 26217/1466823. ------ 1. ==[ start ]==> (((^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.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^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. ------ 26218/1466832. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 26219/1466877. ------ 1. ==[ start ]==> (((^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)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 26220/1466949. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.b))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.b))) REDUCED to normal form. ------ 26221/1467003. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(^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)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26222/1467030. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a (a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 26223/1467057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.a)(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)(a (a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 26224/1467084. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 26225/1467255. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a 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)))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 26226/1467282. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(a ((a a) a))) 3. ==[ beta ]==> ((^y.y)(a ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(a ((a a) a))) 5. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 26227/1467291. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 26228/1467318. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 26229/1467336. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^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)))) 7. ==[ beta ]==> ((a a)((a (a a))(a (^y.y)))) 8. ==[ alpha ]==> ((a a)((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 26230/1467345. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y y)) c)) 3. ==[ beta ]==> (((a (a a))(^x.a))(c c)) REDUCED to normal form. ------ 26231/1467417. ------ 1. ==[ start ]==> ((a (^a.b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 26232/1467462. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(^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)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 26233/1467489. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((a (a (a a)))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 26234/1467516. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 26235/1467543. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26236/1467570. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 26237/1467588. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (b (((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26238/1467597. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 26239/1467687. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b (a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b (a (a a)))) IRREDUCIBLE: cycle. ------ 26240/1467750. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x)) b)) 3. ==[ beta ]==> ((((a a) a) b)(b b)) REDUCED to normal form. ------ 26241/1467768. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 26242/1467777. ------ 1. ==[ start ]==> (((a b) a)((^b.a) c)) 2. ==[ alpha ]==> (((a b) a)((^x.a) c)) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 26243/1467795. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a b)((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a b)((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a b)((a (^x.x)) a)) REDUCED to normal form. ------ 26244/1467822. ------ 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)))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 26245/1467858. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 26246/1467885. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 26247/1467912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.a)((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.a)((a (^y.y))(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26248/1467939. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 26249/1467966. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 26250/1468002. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 26251/1468029. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 26252/1468056. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^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 (^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. ------ 26253/1468137. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 26254/1468164. ------ 1. ==[ start ]==> (((a b)(a a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(a (^x.(x x)))) REDUCED to normal form. ------ 26255/1468191. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(a a))) 3. ==[ beta ]==> ((a (a a))((^y.a)(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(a a))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 26256/1468200. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c b)) 3. ==[ beta ]==> ((^y.(a a))(c b)) 4. ==[ alpha ]==> ((^x.(a a))(c b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26257/1468227. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(b c)) 3. ==[ beta ]==> ((^y.y)(b c)) 4. ==[ alpha ]==> ((^x.x)(b c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 26258/1468281. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c (a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c (a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (a a))) 5. ==[ beta ]==> ((^y.y)(c (a a))) 6. ==[ alpha ]==> ((^x.x)(c (a a))) 7. ==[ beta ]==> (c (a a)) REDUCED to normal form. ------ 26259/1468362. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (b ((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 26260/1468371. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 26261/1468425. ------ 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. ------ 26262/1468443. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b b)) 3. ==[ beta ]==> ((^y.y)(b b)) 4. ==[ alpha ]==> ((^x.x)(b b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 26263/1468452. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 26264/1468497. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b (a a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b (a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b (a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b (a a))) 9. ==[ beta ]==> ((^y.y)(b (a a))) 10. ==[ alpha ]==> ((^x.x)(b (a a))) 11. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 26265/1468506. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 26266/1468533. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z)) a)) 7. ==[ beta ]==> (((^y.(^z.z)) a)((^y.(^z.z)) a)) 8. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) a)) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 11. ==[ beta ]==> ((^y.(^z.z)) a) 12. ==[ alpha ]==> ((^x.(^y.y)) a) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26267/1468560. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y) b)) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 26268/1468578. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b a)) 3. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 26269/1468587. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 26270/1468614. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a a) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 26271/1468650. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (^y.y))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 26272/1468923. ------ 1. ==[ start ]==> ((^a.(^b.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (^x.(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 26273/1471650. ------ 1. ==[ start ]==> ((^a.(^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26274/1471695. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26275/1471731. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26276/1471776. ------ 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 y1)))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))(^y1.(y1 y1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.z)) 7. ==[ beta ]==> ((^y.(y y))(^z.z)) 8. ==[ alpha ]==> ((^x.(x x))(^y.y)) 9. ==[ beta ]==> ((^y.y)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26277/1471893. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (^x.((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (^x.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 26278/1471896. ------ 1. ==[ start ]==> ((a (^b.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(^y.(a a))) REDUCED to normal form. ------ 26279/1472121. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 26280/1472310. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(a b))) 3. ==[ beta ]==> ((a b)(^y.(a b))) 4. ==[ alpha ]==> ((a b)(^x.(a b))) REDUCED to normal form. ------ 26281/1472328. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 7. ==[ beta ]==> (^y.(^z.(y y))) 8. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 26282/1472460. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26283/1472715. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.(z b))) 3. ==[ beta ]==> (((^y.y) a)(^z.(z b))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(y b))) 5. ==[ beta ]==> (a (^y.(y b))) 6. ==[ alpha ]==> (a (^x.(x b))) REDUCED to normal form. ------ 26284/1473018. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a (^y.y))(^z.(^x1.x1)))((a (^y.y))(^z.(^x1.x1))))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1))))((a (^x2.x2))(^y2.(^z2.z2)))) REDUCED to normal form. ------ 26285/1473057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((a a) a))) 3. ==[ beta ]==> ((^y.y)(^y1.((a a) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((a a) a))) 5. ==[ beta ]==> (^y.((a a) a)) 6. ==[ alpha ]==> (^x.((a a) a)) REDUCED to normal form. ------ 26286/1473219. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 26287/1473228. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((x1 x1) x1))) REDUCED to normal form. ------ 26288/1473351. ------ 1. ==[ start ]==> ((^a.(^a.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26289/1473531. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z)) a) b) 4. ==[ alpha ]==> ((((^x.x)(^y.y)) a) b) 5. ==[ beta ]==> (((^y.y) a) b) 6. ==[ alpha ]==> (((^x.x) a) b) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 26290/1473894. ------ 1. ==[ start ]==> (((^a.b)(a a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(a (a a)))) 3. ==[ beta ]==> (b (^y.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 26291/1473918. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (^y.(((^z.(z z))(^x1.x1))((^z.(z z))(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((^y.(y y))(^z.z))((^x1.(x1 x1))(^y1.y1)))) 5. ==[ beta ]==> (^x.(((^z.z)(^z.z))((^x1.(x1 x1))(^y1.y1)))) 6. ==[ alpha ]==> (^x.(((^y.y)(^z.z))((^x1.(x1 x1))(^y1.y1)))) 7. ==[ beta ]==> (^x.((^z.z)((^x1.(x1 x1))(^y1.y1)))) 8. ==[ alpha ]==> (^x.((^y.y)((^z.(z z))(^x1.x1)))) 9. ==[ beta ]==> (^x.((^z.(z z))(^x1.x1))) 10. ==[ alpha ]==> (^x.((^y.(y y))(^z.z))) 11. ==[ beta ]==> (^x.((^z.z)(^z.z))) 12. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 13. ==[ beta ]==> (^x.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26292/1474092. ------ 1. ==[ start ]==> (((^a.b) b)(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) b)(^y.((^z.z) a))) 3. ==[ beta ]==> (b (^y.((^z.z) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 26293/1474125. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)(^x1.x1))(((^z.z) a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)(^z.z))(((^x1.x1) a)(^y1.y1)))) 5. ==[ beta ]==> ((((^y.y) a)(^z.z))(((^x1.x1) a)(^y1.y1))) 6. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1))) 7. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 26294/1474353. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.y))) 5. ==[ beta ]==> ((a a)(^y.(^z.y))) 6. ==[ alpha ]==> ((a a)(^x.(^y.x))) REDUCED to normal form. ------ 26295/1474470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.(a (^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. ------ 26296/1474497. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 26297/1474515. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(^a.(^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. ------ 26298/1474551. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.b)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 26299/1474587. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.a)) 3. ==[ beta ]==> (((a a)(a a))(^y.a)) 4. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 26300/1474626. ------ 1. ==[ start ]==> ((a (^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 26301/1474635. ------ 1. ==[ start ]==> (((^a.a) a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) a)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (a ((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 26302/1474671. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> ((a b)((a a)(^y.y))) 4. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 26303/1474680. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(a a))) 3. ==[ beta ]==> ((a a)((^y.(a a))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(a a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 26304/1474707. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 26305/1474725. ------ 1. ==[ start ]==> (((a a)(a a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 26306/1474752. ------ 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 x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 26307/1474761. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^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. ------ 26308/1474788. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 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. ------ 26309/1474815. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^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. ------ 26310/1474842. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a 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. ------ 26311/1474869. ------ 1. ==[ start ]==> ((a (^b.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 26312/1474887. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^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. ------ 26313/1474914. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a b) b)) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a b) b)) REDUCED to normal form. ------ 26314/1474950. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.a)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 26315/1474977. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(x2 x2)))) 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. ------ 26316/1475031. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.a))) 5. ==[ beta ]==> (a ((^y.a)(^z.a))) 6. ==[ alpha ]==> (a ((^x.a)(^y.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26317/1475040. ------ 1. ==[ start ]==> (((a a)(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))(c ((a a) a))) REDUCED to normal form. ------ 26318/1475058. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.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. ------ 26319/1475067. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (a b))) REDUCED to normal form. ------ 26320/1475094. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 26321/1475130. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.b) b)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b) b)) 3. ==[ beta ]==> (((a a) a)((^y.b) b)) 4. ==[ alpha ]==> (((a a) a)((^x.b) b)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 26322/1475202. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 26323/1475247. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(c (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(c (^x1.a))) 3. ==[ beta ]==> ((^y.y)(c (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(c (^y.a))) 5. ==[ beta ]==> (c (^y.a)) 6. ==[ alpha ]==> (c (^x.a)) REDUCED to normal form. ------ 26324/1475283. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a a)(a b))) 3. ==[ beta ]==> ((a b)((a a)(a b))) REDUCED to normal form. ------ 26325/1475301. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.(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. ------ 26326/1475328. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)(a a))) 3. ==[ beta ]==> ((a (a a))((^y.b)(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(a a))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 26327/1475409. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26328/1475436. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 26329/1475481. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a a)(^z.b))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.b))) REDUCED to normal form. ------ 26330/1475508. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a b) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((a b) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a b) a)) REDUCED to normal form. ------ 26331/1475535. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a) a) b)) REDUCED to normal form. ------ 26332/1475571. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26333/1475598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 7. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 26334/1475661. ------ 1. ==[ start ]==> (((a (a a)) b)(b ((a a) a))) REDUCED to normal form. ------ 26335/1475688. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(a (a b))) 3. ==[ beta ]==> (((^y.y) a)(a (a b))) 4. ==[ alpha ]==> (((^x.x) a)(a (a b))) 5. ==[ beta ]==> (a (a (a b))) REDUCED to normal form. ------ 26336/1475715. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 26337/1475742. ------ 1. ==[ start ]==> (((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.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (^z.z))) REDUCED to normal form. ------ 26338/1475769. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.a))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.a))((a (a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.a))((a (a a)) a)) REDUCED to normal form. ------ 26339/1475796. ------ 1. ==[ start ]==> (((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)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 26340/1475823. ------ 1. ==[ start ]==> ((((^a.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)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26341/1475886. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 26342/1475913. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 26343/1475940. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 26344/1475967. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(a (^y.(y y)))) 8. ==[ alpha ]==> ((a a)(a (^x.(x x)))) REDUCED to normal form. ------ 26345/1475994. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 26346/1476030. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.a)((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. ------ 26347/1476084. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 26348/1476165. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 26349/1476201. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((a a) a))) REDUCED to normal form. ------ 26350/1476228. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 26351/1476255. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 26352/1476282. ------ 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) a)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26353/1476309. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 26354/1476327. ------ 1. ==[ start ]==> ((a (^a.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 26355/1476372. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 26356/1476399. ------ 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.(^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. ------ 26357/1476426. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a (a a)) a)(a (^y.a))) 6. ==[ alpha ]==> (((a (a a)) a)(a (^x.a))) REDUCED to normal form. ------ 26358/1476453. ------ 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 (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 26359/1476480. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 26360/1476507. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y)) a)) 3. ==[ beta ]==> ((a (a b))((^y.y) a)) 4. ==[ alpha ]==> ((a (a b))((^x.x) a)) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 26361/1476516. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26362/1476597. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(y1 y1)))) IRREDUCIBLE: cycle. ------ 26363/1476660. ------ 1. ==[ start ]==> ((((a a) a) b)((a (a a))(a a))) REDUCED to normal form. ------ 26364/1476687. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) a)(a (^y.y)))) 3. ==[ beta ]==> (((a b) a)(a (a (^y.y)))) 4. ==[ alpha ]==> (((a b) a)(a (a (^x.x)))) REDUCED to normal form. ------ 26365/1476705. ------ 1. ==[ start ]==> (((^a.a)(a b))(c (^b.a))) 2. ==[ alpha ]==> (((^x.x)(a b))(c (^y.a))) 3. ==[ beta ]==> ((a b)(c (^y.a))) 4. ==[ alpha ]==> ((a b)(c (^x.a))) REDUCED to normal form. ------ 26366/1476714. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.b))((a (^y.y)) a)) REDUCED to normal form. ------ 26367/1476732. ------ 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)(b (^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 26368/1476786. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y))(a a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(a a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 26369/1476822. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c c)) 3. ==[ beta ]==> (((^y.y)(^z.a))(c c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c c)) 5. ==[ beta ]==> ((^y.a)(c c)) 6. ==[ alpha ]==> ((^x.a)(c c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26370/1476867. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (b ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 26371/1476894. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 26372/1476912. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a) b)) 3. ==[ beta ]==> (((a a)(a b))(a b)) REDUCED to normal form. ------ 26373/1476993. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x)) a)) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 26374/1477020. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a) b)) 5. ==[ beta ]==> (((^y.y) a)((^z.a) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.a) b)) 7. ==[ beta ]==> (a ((^y.a) b)) 8. ==[ alpha ]==> (a ((^x.a) b)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26375/1477065. ------ 1. ==[ start ]==> (((^a.b) b)((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) b)((a a)((^y.y) a))) 3. ==[ beta ]==> (b ((a a)((^y.y) a))) 4. ==[ alpha ]==> (b ((a a)((^x.x) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 26376/1477101. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 26377/1477110. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(a a))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(a a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26378/1477137. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 26379/1477191. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.z1))) 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. ------ 26380/1477272. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> (b (c (^x1.x1))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 26381/1477281. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))(a a))) REDUCED to normal form. ------ 26382/1477308. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a a)(a (^a.a)))) 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. ------ 26383/1477326. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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. ------ 26384/1477335. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c a)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c a)) REDUCED to normal form. ------ 26385/1477353. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26386/1477362. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b b)) REDUCED to normal form. ------ 26387/1477407. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26388/1477416. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 26389/1477443. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (a (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))(a (a (^y.y)))) 7. ==[ beta ]==> ((a (a (^y.y)))(a (a (^y.y)))) 8. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 26390/1477470. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 26391/1477488. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 26392/1477497. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 26393/1477524. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a b)) 3. ==[ beta ]==> (((a a)(^y.y))(a b)) 4. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 26394/1477560. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.a) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y) a)) 3. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 4. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 26395/1477586. ------ 1. ==[ start ]==> (^a.((a (^a.a))(a b))) 2. ==[ alpha ]==> (^x.((x (^y.y))(x b))) REDUCED to normal form. ------ 26396/1477587. ------ 1. ==[ start ]==> (a ((a (^a.a))(a b))) 2. ==[ alpha ]==> (a ((a (^x.x))(a b))) REDUCED to normal form. ------ 26397/1477842. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(a a)))) REDUCED to normal form. ------ 26398/1480563. ------ 1. ==[ start ]==> (((a (^a.a))(a b)) a) 2. ==[ alpha ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 26399/1480569. ------ 1. ==[ start ]==> ((^a.a)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.x)((a (^y.y))(a b))) 3. ==[ beta ]==> ((a (^y.y))(a b)) 4. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 26400/1480596. ------ 1. ==[ start ]==> ((^a.(a a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x x))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 26401/1480659. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26402/1480821. ------ 1. ==[ start ]==> ((^a.(^b.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a a)(^z.(a a)))) 3. ==[ beta ]==> (^y.((a a)(^z.(a a)))) 4. ==[ alpha ]==> (^x.((a a)(^y.(a a)))) REDUCED to normal form. ------ 26403/1480824. ------ 1. ==[ start ]==> ((a (^b.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 26404/1481049. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 26405/1481064. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(a a)) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26406/1481163. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a (a a))(a (a a)))((a (a a))(a (a a))))) REDUCED to normal form. ------ 26407/1481265. ------ 1. ==[ start ]==> (((a (a a)) a)(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 26408/1481388. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26409/1481643. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.y))) 5. ==[ beta ]==> (a (^y.(^z.y))) 6. ==[ alpha ]==> (a (^x.(^y.x))) REDUCED to normal form. ------ 26410/1481985. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 26411/1482156. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.a))) REDUCED to normal form. ------ 26412/1482453. ------ 1. ==[ start ]==> (((^a.b) a)(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) 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 (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 26413/1482723. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 26414/1482822. ------ 1. ==[ start ]==> (((^a.b)(a a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 26415/1482831. ------ 1. ==[ start ]==> (((a b)(^a.a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(a (a a)))) REDUCED to normal form. ------ 26416/1482846. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a)) a)) 3. ==[ beta ]==> (^y.(((a (a a)) a)((a (a a)) a))) 4. ==[ alpha ]==> (^x.(((a (a a)) a)((a (a a)) a))) REDUCED to normal form. ------ 26417/1482948. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(x (x x)))) REDUCED to normal form. ------ 26418/1483029. ------ 1. ==[ start ]==> (((a b)(a a))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y) a))) 3. ==[ beta ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 26419/1483281. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.c)) 3. ==[ beta ]==> (((^y.y)(a a))(^z.c)) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.c)) 5. ==[ beta ]==> ((a a)(^y.c)) 6. ==[ alpha ]==> ((a a)(^x.c)) REDUCED to normal form. ------ 26420/1483290. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.y))) REDUCED to normal form. ------ 26421/1483398. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(^y1.(^z1.z1)))) 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. ------ 26422/1483443. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.z)) 3. ==[ beta ]==> (b (^z.z)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26423/1483452. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 26424/1483479. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^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. ------ 26425/1483515. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(y y))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 26426/1483542. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 26427/1483554. ------ 1. ==[ start ]==> ((a a)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a a)((a (^x.x))(a b))) REDUCED to normal form. ------ 26428/1483572. ------ 1. ==[ start ]==> (((^a.a) a)(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x) a)(b (^y.(a a)))) 3. ==[ beta ]==> (a (b (^y.(a a)))) 4. ==[ alpha ]==> (a (b (^x.(a a)))) REDUCED to normal form. ------ 26429/1483581. ------ 1. ==[ start ]==> ((a (a a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a a))((a a)((^x.x)(a a)))) 3. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 26430/1483617. ------ 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. ------ 26431/1483626. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 26432/1483644. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 26433/1483653. ------ 1. ==[ start ]==> (((^a.a) b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 26434/1483698. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26435/1483707. ------ 1. ==[ start ]==> (((a a) b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 26436/1483725. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((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. ------ 26437/1483734. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 9. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 10. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 26438/1483761. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 26439/1483779. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 26440/1483788. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 26441/1483806. ------ 1. ==[ start ]==> ((a (^b.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 26442/1483842. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((^y.(a a))(^z.z)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26443/1483887. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a) c)) 3. ==[ beta ]==> ((^y.a)(((a a) a) c)) 4. ==[ alpha ]==> ((^x.a)(((a a) a) c)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 26444/1483923. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 26445/1483950. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26446/1483977. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 26447/1484004. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 26448/1484031. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 26449/1484049. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a)) a)) 3. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 26450/1484067. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a b)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a b)(a a))) 3. ==[ beta ]==> (((a a) a)((a b)(a a))) REDUCED to normal form. ------ 26451/1484094. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 26452/1484121. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^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))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 26453/1484148. ------ 1. ==[ start ]==> ((a (a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26454/1484220. ------ 1. ==[ start ]==> ((((^a.a) a) b)(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a) b)(b (^y.b))) 3. ==[ beta ]==> ((a b)(b (^y.b))) 4. ==[ alpha ]==> ((a b)(b (^x.b))) REDUCED to normal form. ------ 26455/1484247. ------ 1. ==[ start ]==> (((a (a a)) a)(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)(a (^x.(a a)))) REDUCED to normal form. ------ 26456/1484265. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a b)(^y.y))) 3. ==[ beta ]==> ((a (a a))((a b)(^y.y))) 4. ==[ alpha ]==> ((a (a a))((a b)(^x.x))) REDUCED to normal form. ------ 26457/1484274. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 26458/1484292. ------ 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.(^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. ------ 26459/1484301. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 26460/1484328. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 26461/1484346. ------ 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 y)))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 26462/1484355. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26463/1484373. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 26464/1484463. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.b)(^z.z))) 3. ==[ beta ]==> ((b b)((^y.b)(^z.z))) 4. ==[ alpha ]==> ((b b)((^x.b)(^y.y))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 26465/1484508. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26466/1484598. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 26467/1484625. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z)(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.b))) 5. ==[ beta ]==> (a ((^y.y)(^z.b))) 6. ==[ alpha ]==> (a ((^x.x)(^y.b))) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 26468/1484643. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) a)) 5. ==[ beta ]==> ((^y.y)((^z.b) a)) 6. ==[ alpha ]==> ((^x.x)((^y.b) a)) 7. ==[ beta ]==> ((^y.b) a) 8. ==[ alpha ]==> ((^x.b) a) 9. ==[ beta ]==> b REDUCED to normal form. ------ 26469/1484796. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 26470/1484967. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 5. ==[ beta ]==> ((a a)(^y.a)) 6. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 26471/1485021. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> (a (((^z.z)(^x1.x1)) b)) 6. ==[ alpha ]==> (a (((^x.x)(^y.y)) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 26472/1485057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.a))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.a))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 7. ==[ beta ]==> (b ((^y.a)(^y.a))) 8. ==[ alpha ]==> (b ((^x.a)(^y.a))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26473/1485084. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 26474/1485138. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.a)) REDUCED to normal form. ------ 26475/1485183. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z)) b)) 7. ==[ beta ]==> ((a a)((^y.(^z.z)) b)) 8. ==[ alpha ]==> ((a a)((^x.(^y.y)) b)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26476/1485282. ------ 1. ==[ start ]==> (((a a)((a a) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a a)((^x.x)(^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. ------ 26477/1485435. ------ 1. ==[ start ]==> (((^a.b) a)((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^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. ------ 26478/1485453. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26479/1485615. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(z z)) b)) 3. ==[ beta ]==> (b ((^z.(z z)) b)) 4. ==[ alpha ]==> (b ((^x.(x x)) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 26480/1485642. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a) c)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a) c)) 3. ==[ beta ]==> ((a b)((^y.a) c)) 4. ==[ alpha ]==> ((a b)((^x.a) c)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 26481/1485651. ------ 1. ==[ start ]==> (((a a)(^a.b))(c (^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))(c (^y.a))) REDUCED to normal form. ------ 26482/1485705. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a (^b.(^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)))) REDUCED to normal form. ------ 26483/1485723. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 26484/1485732. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 26485/1485759. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26486/1485786. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) 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. ------ 26487/1485804. ------ 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 ((a a)(^y.(y y)))) 4. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 26488/1485813. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(a (a a))) REDUCED to normal form. ------ 26489/1485831. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a)) a)) REDUCED to normal form. ------ 26490/1485903. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))(b ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 26491/1485930. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(a (a (a a)))) REDUCED to normal form. ------ 26492/1485957. ------ 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) 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))) 9. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 26493/1485984. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 26494/1486002. ------ 1. ==[ start ]==> (((^a.b) b)(b (^b.a))) 2. ==[ alpha ]==> (((^x.b) b)(b (^y.a))) 3. ==[ beta ]==> (b (b (^y.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 26495/1486011. ------ 1. ==[ start ]==> (((a b)(a a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))((a a)((^x.x) a))) 3. ==[ beta ]==> (((a b)(a a))((a a) a)) REDUCED to normal form. ------ 26496/1486047. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26497/1486074. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((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. ------ 26498/1486128. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a) a)) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) 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. ------ 26499/1486209. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> (b ((^x1.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26500/1486218. ------ 1. ==[ start ]==> (((a b) b)(c (^a.a))) 2. ==[ alpha ]==> (((a b) b)(c (^x.x))) REDUCED to normal form. ------ 26501/1486245. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(b (^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 26502/1486272. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(a (^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.a))) REDUCED to normal form. ------ 26503/1486290. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26504/1486299. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 26505/1486344. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1)) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1)) a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1)) a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1)) a)) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1)) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) a)) 9. ==[ beta ]==> ((^y.y)((a (^z.z)) a)) 10. ==[ alpha ]==> ((^x.x)((a (^y.y)) a)) 11. ==[ beta ]==> ((a (^y.y)) a) 12. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 26506/1486353. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a))(^a.a))) 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. ------ 26507/1486380. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26508/1486407. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 26509/1486425. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a) b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z) b)) 3. ==[ beta ]==> (b ((^z.z) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 26510/1486434. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 26511/1486461. ------ 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. ------ 26512/1486497. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (a a))) 3. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 26513/1486524. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 26514/1486590. ------ 1. ==[ start ]==> ((^a.b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26515/1487031. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26516/1488426. ------ 1. ==[ start ]==> ((^a.(a b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.((^z.z)(^x1.x1))) b) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.z))) b) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26517/1489020. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(x1 x1)))(^z.(^x1.(x1 x1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(z z)))(^x1.(^y1.(y1 y1))))) 5. ==[ beta ]==> ((^y.(^z.(z z)))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26518/1489509. ------ 1. ==[ start ]==> (((a (^a.a))(a b)) b) 2. ==[ alpha ]==> (((a (^x.x))(a b)) b) REDUCED to normal form. ------ 26519/1489533. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26520/1489551. ------ 1. ==[ start ]==> ((^a.(a a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x x))(b (^y.(a a)))) 3. ==[ beta ]==> ((b (^y.(a a)))(b (^y.(a a)))) 4. ==[ alpha ]==> ((b (^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 26521/1489578. ------ 1. ==[ start ]==> ((^a.b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(a (^y.(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26522/1489581. ------ 1. ==[ start ]==> ((a b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 26523/1489797. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 26524/1489848. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.b)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 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. ------ 26525/1490019. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26526/1490022. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 26527/1490418. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) a)(a (^y.y))) a) 4. ==[ beta ]==> ((a (a (^y.y))) a) 5. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 26528/1490616. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z b))) 5. ==[ beta ]==> ((^y.y)(^z.(z b))) 6. ==[ alpha ]==> ((^x.x)(^y.(y b))) 7. ==[ beta ]==> (^y.(y b)) 8. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 26529/1490796. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.b))) REDUCED to normal form. ------ 26530/1490901. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((^y.a)(a (a a)))((^y.a)(a (a a))))((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((((^x.a)(a (a a)))((^y.a)(a (a a))))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((a ((^y.a)(a (a a))))((^z.a)(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.a)(a (a a))))((^y.a)(a (a a)))) 7. ==[ beta ]==> ((a a)((^y.a)(a (a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)(a (a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 26531/1491234. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26532/1491408. ------ 1. ==[ start ]==> (((^a.b) a)(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 26533/1491414. ------ 1. ==[ start ]==> ((^a.(a b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z))) b) 5. ==[ beta ]==> (((^y.y)(^z.z)) b) 6. ==[ alpha ]==> (((^x.x)(^y.y)) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 26534/1491417. ------ 1. ==[ start ]==> ((a (a b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a b))(^x.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 26535/1491786. ------ 1. ==[ start ]==> (((a b)(^a.a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 26536/1491903. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 26537/1492008. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(a (^z.(z z)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(z z)))(a (^z.(z z))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(y y)))(a (^z.(z z))))) 5. ==[ beta ]==> ((a (^y.(y y)))(a (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(y y)))) REDUCED to normal form. ------ 26538/1492011. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 26539/1492182. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (b (^x1.x1)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26540/1492245. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.c)) REDUCED to normal form. ------ 26541/1492398. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(a a))) 3. ==[ beta ]==> (b (^z.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 26542/1492407. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 26543/1492470. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 26544/1492497. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 26545/1492527. ------ 1. ==[ start ]==> ((a (^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 26546/1492545. ------ 1. ==[ start ]==> ((a (a a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (a a))(b (^x.(a a)))) REDUCED to normal form. ------ 26547/1492554. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 26548/1492572. ------ 1. ==[ start ]==> ((a b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 26549/1492590. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(a a))(^a.a))) 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. ------ 26550/1492617. ------ 1. ==[ start ]==> (((^a.a) b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 26551/1492626. ------ 1. ==[ start ]==> (((a a)(a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 26552/1492644. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(^z.a))) 3. ==[ beta ]==> ((^y.y)(((a a) 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. ------ 26553/1492671. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a a) b)(^y.(y y))) 6. ==[ alpha ]==> (((a a) b)(^x.(x x))) REDUCED to normal form. ------ 26554/1492698. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 26555/1492752. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 26556/1492788. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 26557/1492806. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((^y.y)(a a)) a) 6. ==[ alpha ]==> (((^x.x)(a a)) a) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 26558/1492815. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 26559/1492842. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 26560/1493013. ------ 1. ==[ start ]==> ((a (^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (a a))) REDUCED to normal form. ------ 26561/1493121. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(y y))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(x x))((a (a a))(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26562/1493148. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 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))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 26563/1493202. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((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. ------ 26564/1493238. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(^y.y))) REDUCED to normal form. ------ 26565/1493265. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 26566/1493292. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 26567/1493319. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 26568/1493355. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 26569/1493382. ------ 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)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 26570/1493409. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(a b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a b))) 5. ==[ beta ]==> ((a (a (^x.x)))(a b)) REDUCED to normal form. ------ 26571/1493427. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a b) a)) 2. ==[ alpha ]==> (((^x.(x x)) b)((a b) a)) 3. ==[ beta ]==> ((b b)((a b) a)) REDUCED to normal form. ------ 26572/1493436. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.b)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 26573/1493607. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a b))) 5. ==[ beta ]==> ((^y.y)(a (a b))) 6. ==[ alpha ]==> ((^x.x)(a (a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 26574/1493616. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 26575/1493634. ------ 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))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 26576/1493670. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 26577/1493688. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 26578/1493760. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 26579/1493787. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.b))) REDUCED to normal form. ------ 26580/1493841. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.(^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)) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 26581/1493868. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((a a)(a ((^x.x) a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 26582/1493895. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.a)(a (a a)))) 3. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 26583/1494021. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a (a a)) c)) 3. ==[ beta ]==> (((^y.y) b)((a (a a)) c)) 4. ==[ alpha ]==> (((^x.x) b)((a (a a)) c)) 5. ==[ beta ]==> (b ((a (a a)) c)) REDUCED to normal form. ------ 26584/1494093. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(b ((^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. ------ 26585/1494147. ------ 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.x1))(a a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(a a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(a a))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^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. ------ 26586/1494156. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 26587/1494228. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 26588/1494246. ------ 1. ==[ start ]==> (((a a)((a a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 26589/1494300. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((a (a (a a)))((^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. ------ 26590/1494327. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (((a (a a)) a)((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 26591/1494354. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 26592/1494381. ------ 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)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 26593/1494399. ------ 1. ==[ start ]==> (((^a.b) a)((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.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. ------ 26594/1494408. ------ 1. ==[ start ]==> ((a (a b))((^a.a)((^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. ------ 26595/1494561. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y)) a)) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 26596/1494579. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (a a))(a a))) 3. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 26597/1494588. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a)) b)) 2. ==[ alpha ]==> (((a b) a)((^x.(x x)) b)) 3. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 26598/1494606. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a b)(a (a (^x.x)))) REDUCED to normal form. ------ 26599/1494615. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a) c)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a) c)) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 26600/1494633. ------ 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 (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 26601/1494696. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 26602/1494723. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26603/1494750. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 26604/1494777. ------ 1. ==[ start ]==> (((a b)(^a.a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 26605/1494813. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))(^a.a))) 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. ------ 26606/1494840. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 26607/1494867. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26608/1494894. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^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. ------ 26609/1494966. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z)) c)) 3. ==[ beta ]==> (b ((^y.(^z.z)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26610/1494975. ------ 1. ==[ start ]==> (((a b)(a a))(b (^b.a))) 2. ==[ alpha ]==> (((a b)(a a))(b (^x.a))) REDUCED to normal form. ------ 26611/1495002. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(a (^y.(y y)))) 3. ==[ beta ]==> ((a (a a))(a (^y.(y y)))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(x x)))) REDUCED to normal form. ------ 26612/1495038. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c b)) 3. ==[ beta ]==> ((^y.y)(c b)) 4. ==[ alpha ]==> ((^x.x)(c b)) 5. ==[ beta ]==> (c b) REDUCED to normal form. ------ 26613/1495173. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> (b (a ((^x1.x1) a))) 4. ==[ alpha ]==> (b (a ((^x.x) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 26614/1495182. ------ 1. ==[ start ]==> (((a b) b)((^b.a) a)) 2. ==[ alpha ]==> (((a b) b)((^x.a) a)) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 26615/1495209. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) b)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 26616/1495227. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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. ------ 26617/1495236. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) c)) 3. ==[ beta ]==> (((a a)(^x.(a a))) c) REDUCED to normal form. ------ 26618/1495254. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c a)) 3. ==[ beta ]==> ((^y.y)(c a)) 4. ==[ alpha ]==> ((^x.x)(c a)) 5. ==[ beta ]==> (c a) REDUCED to normal form. ------ 26619/1495263. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 26620/1495317. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 26621/1495344. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a) b)) 5. ==[ beta ]==> ((^y.(y y))((a a) b)) 6. ==[ alpha ]==> ((^x.(x x))((a a) b)) 7. ==[ beta ]==> (((a a) b)((a a) b)) REDUCED to normal form. ------ 26622/1495371. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 26623/1495389. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a)(a a))) 3. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 26624/1495398. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 26625/1495425. ------ 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))) REDUCED to normal form. ------ 26626/1495461. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 26627/1495488. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 26628/1496004. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26629/1497399. ------ 1. ==[ start ]==> ((^a.(a b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26630/1497786. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(a (a a)))) 3. ==[ beta ]==> (^y.((^z.(a (a a)))(^z.(a (a a))))) 4. ==[ alpha ]==> (^x.((^y.(a (a a)))(^z.(a (a a))))) 5. ==[ beta ]==> (^x.(a (a a))) REDUCED to normal form. ------ 26631/1498482. ------ 1. ==[ start ]==> (((a (^a.a))(a b)) c) 2. ==[ alpha ]==> (((a (^x.x))(a b)) c) REDUCED to normal form. ------ 26632/1498596. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26633/1498641. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^z.a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 26634/1498758. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(a b))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26635/1498830. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a b) b)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a b) b)) 3. ==[ eta ]==> ((^y.y)((a b) b)) 4. ==[ alpha ]==> ((^x.x)((a b) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 26636/1499001. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26637/1499004. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 26638/1499220. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 26639/1499325. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26640/1499451. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a) a) b)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26641/1499598. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^b.(^a.b))) 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. ------ 26642/1499607. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 26643/1499883. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((((^y.y) a)(^z.(z z)))(((^y.y) a)(^z.(z z))))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (((((^x.x) a)(^y.(y y)))(((^z.z) a)(^x1.(x1 x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a (^y.(y y)))(((^z.z) a)(^x1.(x1 x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((a (^x.(x x)))(((^y.y) a)(^z.(z z))))(((^x1.x1) a)(^y1.(y1 y1)))) 7. ==[ beta ]==> (((a (^x.(x x)))(a (^z.(z z))))(((^x1.x1) a)(^y1.(y1 y1)))) 8. ==[ alpha ]==> (((a (^x.(x x)))(a (^y.(y y))))(((^z.z) a)(^x1.(x1 x1)))) 9. ==[ beta ]==> (((a (^x.(x x)))(a (^y.(y y))))(a (^x1.(x1 x1)))) 10. ==[ alpha ]==> (((a (^x.(x x)))(a (^y.(y y))))(a (^z.(z z)))) REDUCED to normal form. ------ 26644/1500120. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.((z z) z))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.((z z) z))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.((y y) y))) REDUCED to normal form. ------ 26645/1500216. ------ 1. ==[ start ]==> ((^a.(^a.b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(c (^z.(z z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26646/1500396. ------ 1. ==[ start ]==> ((^a.(a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z))) b) 4. ==[ alpha ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 26647/1500399. ------ 1. ==[ start ]==> ((a (a b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 26648/1500408. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26649/1500552. ------ 1. ==[ start ]==> ((((a a) a) b)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a) b)(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 26650/1500660. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a a)))) REDUCED to normal form. ------ 26651/1500678. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 26652/1500783. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (^y.(((^z.z)(a (a a)))((^z.z)(a (a a))))) 4. ==[ alpha ]==> (^x.(((^y.y)(a (a a)))((^z.z)(a (a a))))) 5. ==[ beta ]==> (^x.((a (a a))((^z.z)(a (a a))))) 6. ==[ alpha ]==> (^x.((a (a a))((^y.y)(a (a a))))) 7. ==[ beta ]==> (^x.((a (a a))(a (a a)))) REDUCED to normal form. ------ 26653/1500786. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(a (a a)))) REDUCED to normal form. ------ 26654/1501002. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.(z z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26655/1501083. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 5. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1) 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. ------ 26656/1501164. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (b (^x1.(^y1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 26657/1501173. ------ 1. ==[ start ]==> (((a b) b)(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)(^x.((^y.y) x))) 3. ==[ eta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 26658/1501227. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 26659/1501245. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.z))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 26660/1501299. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(a (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(a (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(^z.(a (^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 11. ==[ beta ]==> (^y.(a (^z.z))) 12. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 26661/1501308. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 26662/1501362. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 26663/1501389. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 26664/1501479. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 26665/1501527. ------ 1. ==[ start ]==> (((^a.a) a)((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a b))) 3. ==[ beta ]==> (a ((a (^y.y))(a b))) 4. ==[ alpha ]==> (a ((a (^x.x))(a b))) REDUCED to normal form. ------ 26666/1501545. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 26667/1501554. ------ 1. ==[ start ]==> (((a a) a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) a)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 26668/1501599. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 26669/1501617. ------ 1. ==[ start ]==> (((a a)(a a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 26670/1501644. ------ 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. ------ 26671/1501680. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^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. ------ 26672/1501707. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^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. ------ 26673/1501734. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(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 REDUCED to normal form. ------ 26674/1501761. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 26675/1501779. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 26676/1501806. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a) a)) REDUCED to normal form. ------ 26677/1501833. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a b) b)) 2. ==[ alpha ]==> ((a ((^x.x) a))((a b) b)) 3. ==[ beta ]==> ((a a)((a b) b)) REDUCED to normal form. ------ 26678/1501842. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 26679/1501923. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (a ((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 26680/1501950. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26681/1501986. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (a b))) 3. ==[ beta ]==> ((a (^y.y))(b (a b))) 4. ==[ alpha ]==> ((a (^x.x))(b (a b))) REDUCED to normal form. ------ 26682/1502004. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 26683/1502022. ------ 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) a)((^y.(a a)) a)) 4. ==[ alpha ]==> (((a a) a)((^x.(a a)) a)) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 26684/1502049. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b) b)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 26685/1502094. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x)) 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)((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 26686/1502175. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a b)((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a b)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 26687/1502193. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.b))) 5. ==[ beta ]==> ((^y.y)(b (^z.b))) 6. ==[ alpha ]==> ((^x.x)(b (^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 26688/1502202. ------ 1. ==[ start ]==> (((a (a a)) a)((a a)(a b))) REDUCED to normal form. ------ 26689/1502220. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(a (^y.(a a)))) 3. ==[ beta ]==> ((a (a a))(a (^y.(a a)))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(a a)))) REDUCED to normal form. ------ 26690/1502247. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.b)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 5. ==[ beta ]==> ((^y.b)(a a)) 6. ==[ alpha ]==> ((^x.b)(a a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 26691/1502301. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 26692/1502328. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26693/1502346. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) a)(^y.(^z.z)))) 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. ------ 26694/1502400. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a a)(^z.b))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 26695/1502427. ------ 1. ==[ start ]==> (((a (a a))(a a))((a b) a)) REDUCED to normal form. ------ 26696/1502454. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((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. ------ 26697/1502463. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^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. ------ 26698/1502490. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.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. ------ 26699/1502544. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(^x2.x2)))) 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. ------ 26700/1502553. ------ 1. ==[ start ]==> (((a (a a)) b)(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(c ((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a (a a)) b)(c (^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(c (^x.x))) REDUCED to normal form. ------ 26701/1502580. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(b ((a a) a))) 3. ==[ beta ]==> (((^y.y) a)(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)(b ((a a) a))) 5. ==[ beta ]==> (a (b ((a a) a))) REDUCED to normal form. ------ 26702/1502598. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26703/1502607. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 26704/1502634. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a) a)(a a))) REDUCED to normal form. ------ 26705/1502661. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.a))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.a))(a (^y.y))) REDUCED to normal form. ------ 26706/1502688. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 26707/1502715. ------ 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 (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 7. ==[ beta ]==> (((^y.y) a)(a (a a))) 8. ==[ alpha ]==> (((^x.x) a)(a (a a))) 9. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 26708/1502805. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)(^z.z))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((a ((^x.x) 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. ------ 26709/1502832. ------ 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)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 26710/1502859. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^y.a))) 5. ==[ beta ]==> ((a a)((a (a a))(^y.a))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.a))) REDUCED to normal form. ------ 26711/1502886. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) 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. ------ 26712/1502922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 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. ------ 26713/1502976. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (a ((^z.a)(^x1.x1))) 6. ==[ alpha ]==> (a ((^x.a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26714/1503057. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 26715/1503084. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26716/1503093. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 26717/1503120. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(a ((a a) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(a ((a a) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a ((a a) a))) REDUCED to normal form. ------ 26718/1503147. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 26719/1503174. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26720/1503201. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 26721/1503219. ------ 1. ==[ start ]==> ((a (^a.b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(c (^y.(y y)))) REDUCED to normal form. ------ 26722/1503291. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (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))) 7. ==[ beta ]==> ((a (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 26723/1503318. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 26724/1503345. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.a))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 26725/1503372. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 26726/1503399. ------ 1. ==[ start ]==> ((a (a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 26727/1503408. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26728/1503489. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.a))) IRREDUCIBLE: cycle. ------ 26729/1503552. ------ 1. ==[ start ]==> ((((a a) a) b)(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(a ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) b)(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)(a (^x.x))) REDUCED to normal form. ------ 26730/1503579. ------ 1. ==[ start ]==> (((a b) a)((a (a a))(a a))) REDUCED to normal form. ------ 26731/1503606. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (a (^y.y)))) REDUCED to normal form. ------ 26732/1503660. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 26733/1503678. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 26734/1503759. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26735/1503786. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (a a))) REDUCED to normal form. ------ 26736/1503804. ------ 1. ==[ start ]==> (((a a)(a b))((a (a a)) a)) REDUCED to normal form. ------ 26737/1503831. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) a) b)) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a b)) REDUCED to normal form. ------ 26738/1503912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z)) a)) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z)) a)) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y)) a)) 7. ==[ beta ]==> (a ((^y.(y y)) a)) 8. ==[ alpha ]==> (a ((^x.(x x)) a)) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 26739/1503939. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.a) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 26740/1503957. ------ 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 ((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 26741/1503966. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y)) c)) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 26742/1504002. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> ((^y.(a a))(a (^z.(z z)))) 4. ==[ alpha ]==> ((^x.(a a))(a (^y.(y y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26743/1504029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 26744/1504083. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.a)((^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. ------ 26745/1504164. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 26746/1504173. ------ 1. ==[ start ]==> (((a b) b)(a ((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)(a ((^x.x) a))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 26747/1504200. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (^y.y))(a a))) 3. ==[ beta ]==> (((a a) a)((a (^y.y))(a a))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))(a a))) REDUCED to normal form. ------ 26748/1504218. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 26749/1504227. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 26750/1504245. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(a (^z.a))) 3. ==[ beta ]==> ((^y.y)(a (^z.a))) 4. ==[ alpha ]==> ((^x.x)(a (^y.a))) 5. ==[ beta ]==> (a (^y.a)) 6. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 26751/1504254. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c a)) REDUCED to normal form. ------ 26752/1504299. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a)(a (^a.a)))) 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. ------ 26753/1504308. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a c)) REDUCED to normal form. ------ 26754/1504335. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b (a a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (a a))) 5. ==[ beta ]==> ((^y.(y y))(b (a a))) 6. ==[ alpha ]==> ((^x.(x x))(b (a a))) 7. ==[ beta ]==> ((b (a a))(b (a a))) REDUCED to normal form. ------ 26755/1504362. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 26756/1504380. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b (^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b (^z.z))) 3. ==[ beta ]==> (b (b (^z.z))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 26757/1504389. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 26758/1504416. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b a)) 3. ==[ beta ]==> (((a a)(^y.y))(b a)) 4. ==[ alpha ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 26759/1504452. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a a) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a) a)) 3. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 26760/1504479. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a) a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y) a)) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 26761/1504505. ------ 1. ==[ start ]==> (^a.(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (^x.(((^y.y) x)((x x) x))) 3. ==[ beta ]==> (^x.(x ((x x) x))) REDUCED to normal form. ------ 26762/1504506. ------ 1. ==[ start ]==> (a (((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (a (((^x.x) a)((a a) a))) 3. ==[ beta ]==> (a (a ((a a) a))) REDUCED to normal form. ------ 26763/1504563. ------ 1. ==[ start ]==> ((^a.b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.b)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26764/1506786. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(x1 x1)))(^z.(^x1.(x1 x1))))) 4. ==[ alpha ]==> (^x.((^y.(^z.(z z)))(^x1.(^y1.(y1 y1))))) 5. ==[ beta ]==> (^x.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 26765/1507509. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a)) a) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a)) a) 3. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 26766/1507515. ------ 1. ==[ start ]==> ((^a.a)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a a) a)) 4. ==[ alpha ]==> (((^x.x) a)((a a) a)) 5. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 26767/1507542. ------ 1. ==[ start ]==> ((^a.(a a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(a b))) 3. ==[ beta ]==> (((a (^y.y))(a b))((a (^y.y))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))(a b))) REDUCED to normal form. ------ 26768/1507569. ------ 1. ==[ start ]==> ((^a.b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.b)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26769/1507572. ------ 1. ==[ start ]==> ((a b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 26770/1507605. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26771/1507767. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (^y.((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (^x.((a (^y.y))(^z.b))) REDUCED to normal form. ------ 26772/1507806. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^y.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 26773/1508031. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a) a)(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (((a a) a)(^x.((^y.y)(x x)))) 5. ==[ beta ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 26774/1508109. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1) a))((((^y.y)(^z.z))((^x1.x1) a))(((^y.y)(^z.z))((^x1.x1) a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((((^x1.x1)(^y1.y1))((^z1.z1) a))(((^x2.x2)(^y2.y2))((^z2.z2) a)))) 5. ==[ beta ]==> (((^y.y)((^z.z) a))((((^x1.x1)(^y1.y1))((^z1.z1) a))(((^x2.x2)(^y2.y2))((^z2.z2) a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y) a))((((^z.z)(^x1.x1))((^y1.y1) a))(((^z1.z1)(^x2.x2))((^y2.y2) a)))) 7. ==[ beta ]==> (((^y.y) a)((((^z.z)(^x1.x1))((^y1.y1) a))(((^z1.z1)(^x2.x2))((^y2.y2) a)))) 8. ==[ alpha ]==> (((^x.x) a)((((^y.y)(^z.z))((^x1.x1) a))(((^y1.y1)(^z1.z1))((^x2.x2) a)))) 9. ==[ beta ]==> (a ((((^y.y)(^z.z))((^x1.x1) a))(((^y1.y1)(^z1.z1))((^x2.x2) a)))) 10. ==[ alpha ]==> (a ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a)))) 11. ==[ beta ]==> (a (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a)))) 12. ==[ alpha ]==> (a (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) a)))) 13. ==[ beta ]==> (a (((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) a)))) 14. ==[ alpha ]==> (a (((^x.x) a)(((^y.y)(^z.z))((^x1.x1) a)))) 15. ==[ beta ]==> (a (a (((^y.y)(^z.z))((^x1.x1) a)))) 16. ==[ alpha ]==> (a (a (((^x.x)(^y.y))((^z.z) a)))) 17. ==[ beta ]==> (a (a ((^y.y)((^z.z) a)))) 18. ==[ alpha ]==> (a (a ((^x.x)((^y.y) a)))) 19. ==[ beta ]==> (a (a ((^y.y) a))) 20. ==[ alpha ]==> (a (a ((^x.x) a))) 21. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 26775/1508238. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 26776/1508334. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 26777/1508427. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(a y))) 3. ==[ eta ]==> (((^x.(x x)) b) a) 4. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 26778/1508616. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 26779/1509129. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 26780/1509417. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26781/1509561. ------ 1. ==[ start ]==> ((((a a) a) b)(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 26782/1509696. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 26783/1509792. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a a)(^z.(z z)))) 3. ==[ beta ]==> (^y.(((a a)(^z.(z z)))((a a)(^z.(z z))))) 4. ==[ alpha ]==> (^x.(((a a)(^y.(y y)))((a a)(^z.(z z))))) REDUCED to normal form. ------ 26784/1509795. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 26785/1509921. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(z (z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(z (z z)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(y (y y)))) 7. ==[ beta ]==> (a (^y.(y (y y)))) 8. ==[ alpha ]==> (a (^x.(x (x x)))) REDUCED to normal form. ------ 26786/1509999. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((^y.y)(((a a)((^z.z) a))((a a)((^z.z) a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)((^y.y) a))((a a)((^z.z) a)))) 5. ==[ beta ]==> (((a a)((^y.y) a))((a a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)((^x.x) a))((a a)((^y.y) a))) 7. ==[ beta ]==> (((a a) a)((a a)((^y.y) a))) 8. ==[ alpha ]==> (((a a) a)((a a)((^x.x) a))) 9. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 26787/1510092. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.a))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 26788/1510173. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.x1)) 3. ==[ beta ]==> (b (^x1.x1)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26789/1510182. ------ 1. ==[ start ]==> (((a b) b)(^b.(^b.a))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.a))) REDUCED to normal form. ------ 26790/1510254. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.c)) 3. ==[ beta ]==> ((^y.y)(^z.c)) 4. ==[ alpha ]==> ((^x.x)(^y.c)) 5. ==[ beta ]==> (^y.c) 6. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 26791/1510263. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.z))) REDUCED to normal form. ------ 26792/1510317. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 26793/1510371. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 26794/1510425. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 26795/1510461. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.b)) 3. ==[ beta ]==> (((a a)(a a))(^y.b)) 4. ==[ alpha ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 26796/1510488. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(y y))) REDUCED to normal form. ------ 26797/1510515. ------ 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. ------ 26798/1510527. ------ 1. ==[ start ]==> ((a a)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a a)(((^x.x) a)((a a) a))) 3. ==[ beta ]==> ((a a)(a ((a a) a))) REDUCED to normal form. ------ 26799/1510554. ------ 1. ==[ start ]==> ((a (a a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (a a))((a (^x.x))(a b))) REDUCED to normal form. ------ 26800/1510572. ------ 1. ==[ start ]==> (((a a) a)(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a) a)(b (^x.(a a)))) REDUCED to normal form. ------ 26801/1510581. ------ 1. ==[ start ]==> ((a b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 26802/1510617. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 26803/1510626. ------ 1. ==[ start ]==> (((^a.a) b)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(a a))) 3. ==[ beta ]==> (b ((^y.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 26804/1510653. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 26805/1510671. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26806/1510680. ------ 1. ==[ start ]==> (((a a) b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a) b)((^x.a)((^y.y) a))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 26807/1510698. ------ 1. ==[ start ]==> (((^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 z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 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. ------ 26808/1510707. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 26809/1510725. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((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. ------ 26810/1510734. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 26811/1510761. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 26812/1510779. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 26813/1510815. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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 ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26814/1510860. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a b) b)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a b) b)) 3. ==[ beta ]==> ((^y.a)((a b) b)) 4. ==[ alpha ]==> ((^x.a)((a b) b)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 26815/1510896. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 26816/1510923. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26817/1510950. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 26818/1510977. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 26819/1511004. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 26820/1511040. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) a)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a) a)(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a) a)(a (a a))) REDUCED to normal form. ------ 26821/1511067. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(a a))) REDUCED to normal form. ------ 26822/1511094. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a 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. ------ 26823/1511121. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)((^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. ------ 26824/1511193. ------ 1. ==[ start ]==> ((((^a.a) a) b)(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)(c (^y.a))) 3. ==[ beta ]==> ((a b)(c (^y.a))) 4. ==[ alpha ]==> ((a b)(c (^x.a))) REDUCED to normal form. ------ 26825/1511220. ------ 1. ==[ start ]==> (((a (a a)) a)(b (^a.b))) 2. ==[ alpha ]==> (((a (a a)) a)(b (^x.b))) REDUCED to normal form. ------ 26826/1511247. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(a a)))) REDUCED to normal form. ------ 26827/1511265. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) 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. ------ 26828/1511274. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.b)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 26829/1511319. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.a)) 8. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 26830/1511328. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 26831/1511346. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 26832/1511436. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(a b))) 3. ==[ beta ]==> ((b b)((^y.y)(a b))) 4. ==[ alpha ]==> ((b b)((^x.x)(a b))) 5. ==[ beta ]==> ((b b)(a b)) REDUCED to normal form. ------ 26833/1511481. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a) b)) 3. ==[ beta ]==> ((^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. ------ 26834/1511571. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 26835/1511625. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 26836/1511643. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.b) a)) 3. ==[ beta ]==> ((^y.y)((^z.b) a)) 4. ==[ alpha ]==> ((^x.x)((^y.b) a)) 5. ==[ beta ]==> ((^y.b) a) 6. ==[ alpha ]==> ((^x.b) a) 7. ==[ beta ]==> b REDUCED to normal form. ------ 26837/1511697. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 26838/1511769. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 26839/1511796. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)((a a) a))) REDUCED to normal form. ------ 26840/1511940. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(^x2.x2)))) 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. ------ 26841/1511994. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a) a) a)) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a) a) a)) 5. ==[ beta ]==> (a (((a a) a) a)) REDUCED to normal form. ------ 26842/1512030. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26843/1512057. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(x x))(^y.a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.a)(^y.a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.a)(^y.a))) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 26844/1512111. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^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. ------ 26845/1512255. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 26846/1512282. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 26847/1512408. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(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. ------ 26848/1512426. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((a a)(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 26849/1512570. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^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. ------ 26850/1512588. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26851/1512615. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y)) b)) 3. ==[ beta ]==> ((a b)((^y.(y y)) b)) 4. ==[ alpha ]==> ((a b)((^x.(x x)) b)) 5. ==[ beta ]==> ((a b)(b b)) REDUCED to normal form. ------ 26852/1512642. ------ 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)((^z.a) c)) 4. ==[ alpha ]==> ((^x.x)((^y.a) c)) 5. ==[ beta ]==> ((^y.a) c) 6. ==[ alpha ]==> ((^x.a) c) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26853/1512678. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 26854/1512705. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 26855/1512732. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(a a))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(a a))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 26856/1512759. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 26857/1512777. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (^y.y))(^z.a))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 26858/1512786. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 26859/1512804. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 26860/1512903. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 26861/1512930. ------ 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 ]==> (((^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. ------ 26862/1512957. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) 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. ------ 26863/1512975. ------ 1. ==[ start ]==> (((^a.b) b)(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 26864/1512984. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 26865/1513011. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)((^y.y) 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. ------ 26866/1513047. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((^y.y) a)(^z.z)) 6. ==[ alpha ]==> (((^x.x) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 26867/1513101. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.a))) 5. ==[ beta ]==> ((^y.y)((a a)(^y1.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. ------ 26868/1513182. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a) c)) 3. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 26869/1513191. ------ 1. ==[ start ]==> (((a b) b)((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b) b)(^y.a)) 4. ==[ alpha ]==> (((a b) b)(^x.a)) REDUCED to normal form. ------ 26870/1513236. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) b)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) b)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26871/1513245. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 26872/1513263. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z) c)) 3. ==[ beta ]==> ((^y.y)((^z.z) c)) 4. ==[ alpha ]==> ((^x.x)((^y.y) c)) 5. ==[ beta ]==> ((^y.y) c) 6. ==[ alpha ]==> ((^x.x) c) 7. ==[ beta ]==> c REDUCED to normal form. ------ 26873/1513272. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (^z.a))) REDUCED to normal form. ------ 26874/1513317. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)((a a)(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 11. ==[ beta ]==> ((a a)(^y.(^z.z))) 12. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 26875/1513326. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a)(a (^a.a)))) 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. ------ 26876/1513353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26877/1513380. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 26878/1513398. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26879/1513407. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 26880/1513434. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 26881/1513470. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a b)) 3. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 26882/1513497. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a (a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a (a a))) REDUCED to normal form. ------ 26883/1513524. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a a)) 3. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 26884/1516536. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a)) b) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a)) b) 3. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 26885/1516560. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26886/1516605. ------ 1. ==[ start ]==> ((^a.b)(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.b)(b (^y.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 26887/1516686. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((^z.b)(a (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.z)) 5. ==[ beta ]==> (b (^z.z)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 26888/1516842. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 5. ==[ beta ]==> (^y.(^z.(a a))) 6. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 26889/1516851. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^y.(a a))) REDUCED to normal form. ------ 26890/1516875. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(a a))(^x1.x1))) 3. ==[ eta ]==> ((^y.y)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((^y.(a a))(^z.z)) 6. ==[ alpha ]==> ((^x.(a a))(^y.y)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26891/1517046. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(b (a b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(b (a b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 26892/1517067. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 26893/1517463. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(^z.b))) 3. ==[ beta ]==> ((b b)(^y.(^z.b))) 4. ==[ alpha ]==> ((b b)(^x.(^y.b))) REDUCED to normal form. ------ 26894/1517472. ------ 1. ==[ start ]==> (((a (a a))(a a))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(a x))) 3. ==[ eta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 26895/1517496. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.b)(^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. ------ 26896/1517670. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.(z b))) 3. ==[ beta ]==> ((^y.y)(^z.(z b))) 4. ==[ alpha ]==> ((^x.x)(^y.(y b))) 5. ==[ beta ]==> (^y.(y b)) 6. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 26897/1517850. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.b))) 5. ==[ beta ]==> ((a a)(^y.(^z.b))) 6. ==[ alpha ]==> ((a a)(^x.(^y.b))) REDUCED to normal form. ------ 26898/1517928. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((^y.(y y))((^z.z) a))((^y.(y y))((^z.z) a)))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((((^x.(x x))((^y.y) a))((^z.(z z))((^x1.x1) a)))((^y1.(y1 y1))((^z1.z1) a))) 5. ==[ beta ]==> (((((^y.y) a)((^y.y) a))((^z.(z z))((^x1.x1) a)))((^y1.(y1 y1))((^z1.z1) a))) 6. ==[ alpha ]==> (((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) a)))((^y1.(y1 y1))((^z1.z1) a))) 7. ==[ beta ]==> (((a ((^y.y) a))((^z.(z z))((^x1.x1) a)))((^y1.(y1 y1))((^z1.z1) a))) 8. ==[ alpha ]==> (((a ((^x.x) a))((^y.(y y))((^z.z) a)))((^x1.(x1 x1))((^y1.y1) a))) 9. ==[ beta ]==> (((a a)((^y.(y y))((^z.z) a)))((^x1.(x1 x1))((^y1.y1) a))) 10. ==[ alpha ]==> (((a a)((^x.(x x))((^y.y) a)))((^z.(z z))((^x1.x1) a))) 11. ==[ beta ]==> (((a a)(((^y.y) a)((^y.y) a)))((^z.(z z))((^x1.x1) a))) 12. ==[ alpha ]==> (((a a)(((^x.x) a)((^y.y) a)))((^z.(z z))((^x1.x1) a))) 13. ==[ beta ]==> (((a a)(a ((^y.y) a)))((^z.(z z))((^x1.x1) a))) 14. ==[ alpha ]==> (((a a)(a ((^x.x) a)))((^y.(y y))((^z.z) a))) 15. ==[ beta ]==> (((a a)(a a))((^y.(y y))((^z.z) a))) 16. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((^y.y) a))) 17. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^y.y) a))) 18. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) a))) 19. ==[ beta ]==> (((a a)(a a))(a ((^y.y) a))) 20. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) a))) 21. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 26899/1518183. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.((z z) z))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.((z z) z))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((z z) z))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.((z z) z))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.((y y) y))) 7. ==[ beta ]==> ((a a)(^y.((y y) y))) 8. ==[ alpha ]==> ((a a)(^x.((x x) x))) REDUCED to normal form. ------ 26900/1518261. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 26901/1518441. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(a (a a))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(a (a a))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 26902/1518615. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 26903/1518849. ------ 1. ==[ start ]==> (((a a)(a b))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(a (a a)))) REDUCED to normal form. ------ 26904/1518957. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z z)))) 7. ==[ beta ]==> (a (^y.(^z.(z z)))) 8. ==[ alpha ]==> (a (^x.(^y.(y y)))) REDUCED to normal form. ------ 26905/1519035. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b (^z.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.a))(b (^z.a)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.a))(b (^z.a)))) 5. ==[ beta ]==> ((b (^y.a))(b (^z.a))) 6. ==[ alpha ]==> ((b (^x.a))(b (^y.a))) REDUCED to normal form. ------ 26906/1519047. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(a a))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(a a))(^y.((^z.z) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26907/1519218. ------ 1. ==[ start ]==> (((a b) b)(^c.c)) 2. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 26908/1519290. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 5. ==[ beta ]==> (^y.(a (^z.z))) 6. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 26909/1519299. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.c)) REDUCED to normal form. ------ 26910/1519353. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 26911/1519407. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.b)) REDUCED to normal form. ------ 26912/1519425. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.(a (^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. ------ 26913/1519461. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.b)) 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. ------ 26914/1519497. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(a a))) 3. ==[ beta ]==> (((a a)(a a))(^y.(a a))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(a a))) REDUCED to normal form. ------ 26915/1519524. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 26916/1519551. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 26917/1519581. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((a (^x.x))(a ((a a) a))) REDUCED to normal form. ------ 26918/1519608. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a b))) 5. ==[ beta ]==> ((a (^y.y))(a b)) 6. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 26919/1519626. ------ 1. ==[ start ]==> ((a b)(b (^b.(a a)))) 2. ==[ alpha ]==> ((a b)(b (^x.(a a)))) REDUCED to normal form. ------ 26920/1519635. ------ 1. ==[ start ]==> (((^a.a)(a a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 26921/1519671. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 26922/1519680. ------ 1. ==[ start ]==> (((a a)(a a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a a))) 3. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 26923/1519698. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((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. ------ 26924/1519707. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 26925/1519725. ------ 1. ==[ start ]==> (((a a) b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 26926/1519752. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(z z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y y))) REDUCED to normal form. ------ 26927/1519779. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 26928/1519842. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 26929/1519860. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 26930/1519869. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 26931/1519896. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a a)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(^y.y))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 26932/1519941. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a) a) c)) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a) c)) REDUCED to normal form. ------ 26933/1520067. ------ 1. ==[ start ]==> ((a (^a.(a a)))(b (a b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(b (a b))) REDUCED to normal form. ------ 26934/1520085. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(a a))) 6. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 26935/1520175. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1) a))(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 7. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 8. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) a))) 9. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 10. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))((^x1.x1) a))) 11. ==[ beta ]==> (a (((^y.y)(^z.z))((^x1.x1) a))) 12. ==[ alpha ]==> (a (((^x.x)(^y.y))((^z.z) a))) 13. ==[ beta ]==> (a ((^y.y)((^z.z) a))) 14. ==[ alpha ]==> (a ((^x.x)((^y.y) a))) 15. ==[ beta ]==> (a ((^y.y) a)) 16. ==[ alpha ]==> (a ((^x.x) a)) 17. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26936/1520202. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.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. ------ 26937/1520256. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))((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. ------ 26938/1520283. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)(a b))) 3. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 26939/1520319. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a b)(^z.z))) REDUCED to normal form. ------ 26940/1520346. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 26941/1520373. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.a)) REDUCED to normal form. ------ 26942/1520409. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 26943/1520436. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 26944/1520463. ------ 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)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 26945/1520481. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a a)(^y.b))) 3. ==[ beta ]==> ((b b)((a a)(^y.b))) 4. ==[ alpha ]==> ((b b)((a a)(^x.b))) REDUCED to normal form. ------ 26946/1520490. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a b))) 3. ==[ beta ]==> (((a (a a))(a a))(a b)) REDUCED to normal form. ------ 26947/1520517. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^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. ------ 26948/1520661. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(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. ------ 26949/1520688. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(a (a b))) 3. ==[ beta ]==> ((^y.y)(a (a b))) 4. ==[ alpha ]==> ((^x.x)(a (a b))) 5. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 26950/1520697. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.b) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 26951/1520724. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a) b)) 3. ==[ beta ]==> ((a (^y.a))((^z.a) b)) 4. ==[ alpha ]==> ((a (^x.a))((^y.a) b)) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 26952/1520742. ------ 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)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a (^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 26953/1520751. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 26954/1520841. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(b (^y.a))) REDUCED to normal form. ------ 26955/1520868. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (^z.b))) 3. ==[ beta ]==> ((a ((^y.y) a))(a (^z.b))) 4. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.b))) 5. ==[ beta ]==> ((a a)(a (^y.b))) 6. ==[ alpha ]==> ((a a)(a (^x.b))) REDUCED to normal form. ------ 26956/1520922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.(^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)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 26957/1520949. ------ 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))(((^y.y) a)((^y.y) a))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a) a))(a ((^y.y) a))) 6. ==[ alpha ]==> ((a ((a a) a))(a ((^x.x) a))) 7. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 26958/1521075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (b (((^y.y)(^z.z)) b)) 6. ==[ alpha ]==> (b (((^x.x)(^y.y)) b)) 7. ==[ beta ]==> (b ((^y.y) b)) 8. ==[ alpha ]==> (b ((^x.x) b)) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 26959/1521201. ------ 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 ]==> ((((^y.y) a)((^y.y) a))(a ((a a) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a ((a a) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(a ((a a) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(a ((a a) a))) 7. ==[ beta ]==> ((a a)(a ((a a) a))) REDUCED to normal form. ------ 26960/1521210. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a) a)) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 26961/1521237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 26962/1521282. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.b))(a ((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.b))(a ((^y.y) a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 26963/1521327. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 26964/1521381. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a (a a)) a)((^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. ------ 26965/1521408. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))((a (^z.z))(a (^z.z)))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 26966/1521435. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 26967/1521453. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 26968/1521462. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 26969/1521633. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 26970/1521642. ------ 1. ==[ start ]==> (((a b) a)((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 26971/1521660. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (a a))(a a))) 3. ==[ beta ]==> ((a b)((a (a a))(a a))) REDUCED to normal form. ------ 26972/1521669. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y)) b)) 3. ==[ beta ]==> (((a a)(^x.b))(b b)) REDUCED to normal form. ------ 26973/1521687. ------ 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)(((^z.z) a)(a (^x1.x1)))) 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. ------ 26974/1521741. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(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. ------ 26975/1521777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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 REDUCED to normal form. ------ 26976/1521804. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 26977/1521822. ------ 1. ==[ start ]==> (((^a.b)(a a))(c c)) 2. ==[ alpha ]==> (((^x.b)(a a))(c c)) 3. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 26978/1521831. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 26979/1521867. ------ 1. ==[ start ]==> (((a a)(a b))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 26980/1521894. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(^z.z))) 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. ------ 26981/1521921. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 26982/1521948. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^z.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. ------ 26983/1521975. ------ 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 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(y y)))) 9. ==[ beta ]==> (a (^y.(y y))) 10. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 26984/1522020. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a) b)) 2. ==[ alpha ]==> (((^x.b) b)((^y.a) b)) 3. ==[ beta ]==> (b ((^y.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 26985/1522029. ------ 1. ==[ start ]==> (((a b)(a a))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 26986/1522056. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (^y.a))) 3. ==[ beta ]==> ((a (a a))(b (^y.a))) 4. ==[ alpha ]==> ((a (a a))(b (^x.a))) REDUCED to normal form. ------ 26987/1522065. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((^y.(a a))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((^x.(a a))((a a)((^y.y) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 26988/1522146. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(b c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b c)) 5. ==[ beta ]==> ((^y.y)(b c)) 6. ==[ alpha ]==> ((^x.x)(b c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 26989/1522227. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (a (^x1.x1)))) 3. ==[ beta ]==> (b (b (a (^x1.x1)))) 4. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 26990/1522236. ------ 1. ==[ start ]==> (((a b) b)((a a) c)) REDUCED to normal form. ------ 26991/1522263. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a) a)) 3. ==[ beta ]==> (((a a) a)((^y.a) a)) 4. ==[ alpha ]==> (((a a) a)((^x.a) a)) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 26992/1522281. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(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))) REDUCED to normal form. ------ 26993/1522290. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 26994/1522308. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a a)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y)))) 5. ==[ beta ]==> ((a a)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 26995/1522317. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) c) REDUCED to normal form. ------ 26996/1522362. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b b)) 7. ==[ beta ]==> (((^y.y)(^z.z))(b b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b b)) 9. ==[ beta ]==> ((^y.y)(b b)) 10. ==[ alpha ]==> ((^x.x)(b b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 26997/1522371. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 26998/1522398. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z)) a)) 5. ==[ beta ]==> ((^y.(y y))((a (^z.z)) a)) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.y)) a)) 7. ==[ beta ]==> (((a (^y.y)) a)((a (^y.y)) a)) 8. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y)) a)) REDUCED to normal form. ------ 26999/1522425. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a) b)) REDUCED to normal form. ------ 27000/1522443. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a (a (^z.z)))) 3. ==[ beta ]==> (b (a (a (^z.z)))) 4. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 27001/1522452. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27002/1522479. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 27003/1522515. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(a a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 27004/1522542. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 27005/1522569. ------ 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. ------ 27006/1525749. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^z.(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27007/1525866. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)((a a) a))) 3. ==[ beta ]==> (^y.((^z.a)((a a) a))) 4. ==[ alpha ]==> (^x.((^y.a)((a a) a))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 27008/1525938. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(a a)) a)) 3. ==[ eta ]==> ((^y.y)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((^y.y)(a a)) a) 6. ==[ alpha ]==> (((^x.x)(a a)) a) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 27009/1526109. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 27010/1526355. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 5. ==[ beta ]==> (^y.(^z.(y y))) 6. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 27011/1526433. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27012/1526559. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a b) 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. ------ 27013/1526733. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.(^x1.z))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 27014/1526742. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(z b))) REDUCED to normal form. ------ 27015/1526991. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (a a))(^y.a))) 3. ==[ beta ]==> ((((a (a a))(^y.a))((a (a a))(^y.a)))((a (a a))(^y.a))) 4. ==[ alpha ]==> ((((a (a a))(^x.a))((a (a a))(^y.a)))((a (a a))(^z.a))) REDUCED to normal form. ------ 27016/1527084. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.((a a) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.((a a) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.((a a) a))) 5. ==[ beta ]==> (a (^z.((a a) a))) 6. ==[ alpha ]==> (a (^x.((a a) a))) REDUCED to normal form. ------ 27017/1527246. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(^x1.a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.a))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.a))) 7. ==[ beta ]==> ((a a)(^y.(^z.a))) 8. ==[ alpha ]==> ((a a)(^x.(^y.a))) REDUCED to normal form. ------ 27018/1527255. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((y y) y))) REDUCED to normal form. ------ 27019/1527504. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (^y.y))(^z.(z z))) b) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 27020/1527678. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27021/1527687. ------ 1. ==[ start ]==> (((a b) a)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) a)(^x.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 27022/1527891. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))((^y1.y1) a))((^z.(^x1.x1))((^y1.y1) a)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))((^x1.x1) a))((^y1.(^z1.z1))((^x2.x2) a)))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))((^x2.x2) a)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))((^y1.y1) a)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))((^y1.y1) a))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1) a))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27023/1527912. ------ 1. ==[ start ]==> (((a a)(a b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(y y)))) REDUCED to normal form. ------ 27024/1528137. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 27025/1528308. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.((^z.z) y))) 3. ==[ eta ]==> ((((^x.x)(a a)) a)(^z.z)) 4. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.y)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 27026/1528362. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 27027/1528488. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(^a.(^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. ------ 27028/1528497. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 27029/1528587. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 27030/1528614. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.a)) 3. ==[ beta ]==> ((a ((a a) a))(^y.a)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.a)) REDUCED to normal form. ------ 27031/1528662. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (a (((^y.y) a)((a a) a))) 4. ==[ alpha ]==> (a (((^x.x) a)((a a) a))) 5. ==[ beta ]==> (a (a ((a a) a))) REDUCED to normal form. ------ 27032/1528689. ------ 1. ==[ start ]==> (((a a) a)((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a a) a)((a (^x.x))(a b))) REDUCED to normal form. ------ 27033/1528707. ------ 1. ==[ start ]==> (((^a.a)(a a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(a a)))) 3. ==[ beta ]==> ((a a)(b (^y.(a a)))) 4. ==[ alpha ]==> ((a a)(b (^x.(a a)))) REDUCED to normal form. ------ 27034/1528716. ------ 1. ==[ start ]==> (((a a)(^a.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 27035/1528752. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x)(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. ------ 27036/1528779. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 27037/1528788. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27038/1528842. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^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. ------ 27039/1528869. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 27040/1528896. ------ 1. ==[ start ]==> ((a (^b.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 27041/1528914. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 27042/1528941. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 27043/1528968. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((a a)(((^y.y)(a a)) a)) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a)) a)) 5. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 27044/1528977. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27045/1529004. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 27046/1529058. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27047/1529085. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27048/1529139. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 27049/1529184. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 27050/1529211. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.b) b)) 3. ==[ beta ]==> ((a (a a))((^y.b) b)) 4. ==[ alpha ]==> ((a (a a))((^x.b) b)) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 27051/1529229. ------ 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 (^y.y)))) 4. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 27052/1529310. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)(a (^y.y))) 8. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 27053/1529337. ------ 1. ==[ start ]==> (((a (a a)) a)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 27054/1529355. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(b (^y.b))) 3. ==[ beta ]==> ((a (a a))(b (^y.b))) 4. ==[ alpha ]==> ((a (a a))(b (^x.b))) REDUCED to normal form. ------ 27055/1529364. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(a b))) REDUCED to normal form. ------ 27056/1529382. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 5. ==[ beta ]==> (a (^y.(a a))) 6. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 27057/1529463. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27058/1529481. ------ 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. ------ 27059/1529508. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.z)))) REDUCED to normal form. ------ 27060/1529562. ------ 1. ==[ start ]==> (((a (a a))(a a))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.b))) REDUCED to normal form. ------ 27061/1529589. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a b) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b) a)) 3. ==[ beta ]==> ((a (^y.y))((a b) a)) 4. ==[ alpha ]==> ((a (^x.x))((a b) a)) REDUCED to normal form. ------ 27062/1529598. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> ((^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. ------ 27063/1529679. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.(z1 z1)))) 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. ------ 27064/1529742. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 27065/1529760. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 5. ==[ beta ]==> ((^y.y)(^z.b)) 6. ==[ alpha ]==> ((^x.x)(^y.b)) 7. ==[ beta ]==> (^y.b) 8. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27066/1529769. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (a b))) REDUCED to normal form. ------ 27067/1529796. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)(a a))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)(a a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 27068/1529823. ------ 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)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 27069/1529850. ------ 1. ==[ start ]==> ((((^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))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) a))) 7. ==[ beta ]==> ((a (a a))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 27070/1529967. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 27071/1529994. ------ 1. ==[ start ]==> ((((^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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 27072/1530021. ------ 1. ==[ start ]==> ((a ((a a) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a) a))((a (a a))(^x.a))) REDUCED to normal form. ------ 27073/1530057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.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. ------ 27074/1530111. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)((a a) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)((a a) a))) 5. ==[ beta ]==> (a ((^z.z)((a a) a))) 6. ==[ alpha ]==> (a ((^x.x)((a a) a))) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 27075/1530192. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.a))) 5. ==[ beta ]==> (((a a) a)((^y.a)(^y.a))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(^y.a))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 27076/1530219. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.a)(^z.(z z))) 6. ==[ alpha ]==> ((^x.a)(^y.(y y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27077/1530228. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (a (a a)))) REDUCED to normal form. ------ 27078/1530255. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 27079/1530282. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(a ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(a ((a a) a))) REDUCED to normal form. ------ 27080/1530309. ------ 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.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27081/1530336. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 27082/1530453. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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))) 7. ==[ beta ]==> (((a (a a)) a)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 27083/1530480. ------ 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 a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 27084/1530507. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a a))(a (^y.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.a))) REDUCED to normal form. ------ 27085/1530525. ------ 1. ==[ start ]==> (((^a.b) a)(c d)) 2. ==[ alpha ]==> (((^x.b) a)(c d)) 3. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 27086/1530534. ------ 1. ==[ start ]==> ((a (a b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 27087/1530543. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27088/1530624. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 27089/1530687. ------ 1. ==[ start ]==> ((((a a) a) b)(b (a (a a)))) REDUCED to normal form. ------ 27090/1530705. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 27091/1530714. ------ 1. ==[ start ]==> (((a b) a)(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(a ((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b) a)(a (^y.y))) 4. ==[ alpha ]==> (((a b) a)(a (^x.x))) REDUCED to normal form. ------ 27092/1530741. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(a a))) REDUCED to normal form. ------ 27093/1530795. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 27094/1530813. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(b (^y.(y y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b (^y.(y y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 27095/1530822. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(a (a a)))) REDUCED to normal form. ------ 27096/1530894. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 27097/1530903. ------ 1. ==[ start ]==> (((a b)(^a.a))(c c)) 2. ==[ alpha ]==> (((a b)(^x.x))(c c)) REDUCED to normal form. ------ 27098/1530921. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 27099/1530939. ------ 1. ==[ start ]==> (((a a)(a b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a a)(^x.(x x)))) REDUCED to normal form. ------ 27100/1530966. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (a a)) a)) REDUCED to normal form. ------ 27101/1530993. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) a) b)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a) b)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a) b)) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a) b)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a) b)) 7. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 27102/1531074. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 27103/1531092. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)(a a))) 3. ==[ beta ]==> (b (((^y.y) a)(a a))) 4. ==[ alpha ]==> (b (((^x.x) a)(a a))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 27104/1531101. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a) b)) 2. ==[ alpha ]==> (((a b)(a a))((^x.a) b)) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 27105/1531137. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (^z.a))) 3. ==[ beta ]==> ((^y.(a a))(b (^z.a))) 4. ==[ alpha ]==> ((^x.(a a))(b (^y.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27106/1531164. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 5. ==[ beta ]==> (a (^y.(y y))) 6. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 27107/1531218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.x2)))) 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. ------ 27108/1531299. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 27109/1531308. ------ 1. ==[ start ]==> (((a b) b)(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(b (a (^x.x)))) REDUCED to normal form. ------ 27110/1531335. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(a ((^y.y) a))) 3. ==[ beta ]==> (((a a) a)(a ((^y.y) a))) 4. ==[ alpha ]==> (((a a) a)(a ((^x.x) a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 27111/1531362. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(a a))) REDUCED to normal form. ------ 27112/1531380. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 27113/1531389. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(a (^z.z)))) REDUCED to normal form. ------ 27114/1531434. ------ 1. ==[ start ]==> (((^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))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 11. ==[ beta ]==> ((^y.(^z.z))(a a)) 12. ==[ alpha ]==> ((^x.(^y.y))(a a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27115/1531443. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 27116/1531497. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b (a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b (a a))) REDUCED to normal form. ------ 27117/1531515. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 27118/1531524. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 27119/1531551. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 27120/1531587. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(^y.y))) 3. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 27121/1531614. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a) a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a) a)) REDUCED to normal form. ------ 27122/1531641. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y) a)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) a)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) a)) 5. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 27123/1531667. ------ 1. ==[ start ]==> (^a.((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (^x.((x (x x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (^x.((x (x x))(^z.z))) 4. ==[ alpha ]==> (^x.((x (x x))(^y.y))) REDUCED to normal form. ------ 27124/1531668. ------ 1. ==[ start ]==> (a ((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (a ((a (a a))((^x.x)(^y.y)))) 3. ==[ beta ]==> (a ((a (a a))(^y.y))) 4. ==[ alpha ]==> (a ((a (a a))(^x.x))) REDUCED to normal form. ------ 27125/1534698. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a))) a) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y))) a) 3. ==[ beta ]==> (((a (a a))(^y.y)) a) 4. ==[ alpha ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 27126/1534704. ------ 1. ==[ start ]==> ((^a.a)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 27127/1534731. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((((^y.y) a)((a a) a))(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((a ((a a) a))(((^y.y) a)((a a) a))) 6. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)((a a) a))) 7. ==[ beta ]==> ((a ((a a) a))(a ((a a) a))) REDUCED to normal form. ------ 27128/1534758. ------ 1. ==[ start ]==> ((^a.b)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.b)((a (^y.y))(a b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 27129/1534806. ------ 1. ==[ start ]==> (((^a.a) b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27130/1534956. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (^x.(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (^x.(a (^z.a))) 6. ==[ alpha ]==> (^x.(a (^y.a))) REDUCED to normal form. ------ 27131/1535247. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^z.(z z))) REDUCED to normal form. ------ 27132/1535298. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a) a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a (^y.y)))((((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)))(((a a) a)(a (^z.z))))) REDUCED to normal form. ------ 27133/1535454. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 27134/1535523. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27135/1535832. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.z))) REDUCED to normal form. ------ 27136/1536174. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(^x1.a))) 5. ==[ beta ]==> (a (^z.(^x1.a))) 6. ==[ alpha ]==> (a (^x.(^y.a))) REDUCED to normal form. ------ 27137/1536345. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 27138/1536414. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z)) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27139/1536594. ------ 1. ==[ start ]==> ((^a.(a b))(c d)) 2. ==[ alpha ]==> ((^x.(x b))(c d)) 3. ==[ beta ]==> ((c d) b) REDUCED to normal form. ------ 27140/1536777. ------ 1. ==[ start ]==> (((a b) a)(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27141/1536912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(^y1.(^z1.z1)))) 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. ------ 27142/1536981. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.(((a (^z.z))(^x1.a))((a (^z.z))(^x1.a)))) 4. ==[ alpha ]==> (^x.(((a (^y.y))(^z.a))((a (^x1.x1))(^y1.a)))) REDUCED to normal form. ------ 27143/1537137. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(y (y y)))) REDUCED to normal form. ------ 27144/1537188. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))(a (^x1.x1)))((a (^z.z))(a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))(a (^z.z)))((a (^x1.x1))(a (^y1.y1))))) 5. ==[ beta ]==> (((a (^y.y))(a (^z.z)))((a (^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 27145/1537398. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(^z.a))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.a))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.a))) REDUCED to normal form. ------ 27146/1537533. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a (^z.z)))(^y.(a (^z.z)))) 8. ==[ alpha ]==> ((^x.(a (^y.y)))(^z.(a (^x1.x1)))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27147/1537578. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.b)) 3. ==[ beta ]==> (b (^z.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 27148/1537587. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 27149/1537677. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.b)) REDUCED to normal form. ------ 27150/1537704. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(y y))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(y y))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(x x))) REDUCED to normal form. ------ 27151/1537731. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.z)) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 27152/1537743. ------ 1. ==[ start ]==> ((a a)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a a)((a (a a))((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a a)((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a a)((a (a a))(^x.x))) REDUCED to normal form. ------ 27153/1537770. ------ 1. ==[ start ]==> ((a (a a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a (a a))(((^x.x) a)((a a) a))) 3. ==[ beta ]==> ((a (a a))(a ((a a) a))) REDUCED to normal form. ------ 27154/1537797. ------ 1. ==[ start ]==> ((a b)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a b)((a (^x.x))(a b))) REDUCED to normal form. ------ 27155/1537815. ------ 1. ==[ start ]==> (((a a)(^a.a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 27156/1537842. ------ 1. ==[ start ]==> (((^a.a) b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 27157/1537869. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 27158/1537887. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27159/1537896. ------ 1. ==[ start ]==> (((a a) b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 27160/1537914. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 27161/1537941. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^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. ------ 27162/1537950. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27163/1537968. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 27164/1537977. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 10. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 27165/1537995. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a (^x.a))(a (^z.a))) 4. ==[ alpha ]==> ((a (^x.a))(a (^y.a))) REDUCED to normal form. ------ 27166/1538031. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 27167/1538076. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a)) a)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27168/1538103. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b) b)) 3. ==[ beta ]==> ((^y.y)((a b) b)) 4. ==[ alpha ]==> ((^x.x)((a b) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 27169/1538112. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 27170/1538166. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 27171/1538193. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 27172/1538220. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 27173/1538256. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(b (a b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(b (a b))) 3. ==[ beta ]==> (((a a) a)(b (a b))) REDUCED to normal form. ------ 27174/1538283. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a a))) REDUCED to normal form. ------ 27175/1538310. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a b)(a a))) 3. ==[ beta ]==> ((a (a a))((a b)(a a))) REDUCED to normal form. ------ 27176/1538337. ------ 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. ------ 27177/1538463. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.b))) REDUCED to normal form. ------ 27178/1538490. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.(a a)))) REDUCED to normal form. ------ 27179/1538517. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 27180/1538535. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 27181/1538562. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 27182/1538652. ------ 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)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 27183/1538697. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b) a)) 3. ==[ beta ]==> ((^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. ------ 27184/1538724. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a) a) b)) 3. ==[ beta ]==> ((^y.y)(((a a) a) b)) 4. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 27185/1538787. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(^y.(y y)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 27186/1538814. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27187/1538841. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27188/1538868. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.b)) REDUCED to normal form. ------ 27189/1538985. ------ 1. ==[ start ]==> (((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)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a (a a)))) REDUCED to normal form. ------ 27190/1539012. ------ 1. ==[ start ]==> (((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)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 27191/1539039. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((a a)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a a)((a a) a))) 5. ==[ beta ]==> ((a a)((a a)((a a) a))) REDUCED to normal form. ------ 27192/1539156. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(z1 z1)))) 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. ------ 27193/1539210. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a a)(^z.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a a)(^z.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a a)(^z.a))) 5. ==[ beta ]==> (a ((a a)(^z.a))) 6. ==[ alpha ]==> (a ((a a)(^x.a))) REDUCED to normal form. ------ 27194/1539246. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 27195/1539273. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 27196/1539327. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 27197/1539354. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 27198/1539381. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.a)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 27199/1539453. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y)) c)) 3. ==[ beta ]==> ((a (^x.b))(c c)) REDUCED to normal form. ------ 27200/1539471. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a) a))(a ((^y.y) a))) 4. ==[ alpha ]==> (((a a)((a a) a))(a ((^x.x) a))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 27201/1539498. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 27202/1539525. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((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. ------ 27203/1539624. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 27204/1539633. ------ 1. ==[ start ]==> ((a (a b))(c d)) REDUCED to normal form. ------ 27205/1539642. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.b)((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27206/1539723. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a)) b)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a)) b)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a)) b)) IRREDUCIBLE: cycle. ------ 27207/1539786. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 27208/1539813. ------ 1. ==[ start ]==> (((a b) a)((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 27209/1539831. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((a b)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((a b)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 27210/1539858. ------ 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)((^z.(z z)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y y)) b)) 5. ==[ beta ]==> ((^y.(y y)) b) 6. ==[ alpha ]==> ((^x.(x x)) b) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 27211/1539894. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c (^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c (^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 27212/1539921. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 27213/1539948. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^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. ------ 27214/1539975. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 27215/1539993. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 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. ------ 27216/1540002. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 27217/1540020. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 27218/1540146. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(b ((^z.z) a))) 5. ==[ beta ]==> (((^y.y) a)(b ((^z.z) a))) 6. ==[ alpha ]==> (((^x.x) a)(b ((^y.y) a))) 7. ==[ beta ]==> (a (b ((^y.y) a))) 8. ==[ alpha ]==> (a (b ((^x.x) a))) 9. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 27219/1540173. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a (a (a a)))) REDUCED to normal form. ------ 27220/1540200. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)(a a))) 3. ==[ beta ]==> (((a b)(a a))(a (a a))) REDUCED to normal form. ------ 27221/1540227. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 27222/1540236. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z)) c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27223/1540317. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(^x2.x2)))) 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. ------ 27224/1540398. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1)) b)) 3. ==[ beta ]==> (b ((a (^x1.x1)) b)) 4. ==[ alpha ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 27225/1540407. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 27226/1540434. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 27227/1540452. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a) a)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a) a)) 5. ==[ beta ]==> ((a a)((^y.a) a)) 6. ==[ alpha ]==> ((a a)((^x.a) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 27228/1540461. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c (^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 27229/1540479. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27230/1540488. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 27231/1540533. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 11. ==[ beta ]==> ((a (^y.y))(^z.z)) 12. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27232/1540542. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(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. ------ 27233/1540569. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(a (^a.a)))) 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. ------ 27234/1540596. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 27235/1540614. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a) b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a) b)) 3. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 27236/1540623. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 27237/1540650. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b (^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 27238/1540686. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(b a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b a)) 3. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 27239/1540713. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a b)) REDUCED to normal form. ------ 27240/1540740. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a (a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a (a a))) 3. ==[ beta ]==> ((a ((a a) a))(a (a a))) REDUCED to normal form. ------ 27241/1540767. ------ 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))(^y.y))(a a)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 27242/1541103. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^y.y)(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^y.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 27243/1541724. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> ((^x.((^y.y)(^z.z))) a) 4. ==[ beta ]==> ((^y.y)(^z.z)) 5. ==[ alpha ]==> ((^x.x)(^y.y)) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27244/1543806. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a))) b) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y))) b) 3. ==[ beta ]==> (((a (a a))(^y.y)) b) 4. ==[ alpha ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 27245/1543830. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27246/1543875. ------ 1. ==[ start ]==> ((^a.b)(c (^a.b))) 2. ==[ alpha ]==> ((^x.b)(c (^y.b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 27247/1543911. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27248/1543956. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> (((^z.(a a))(a a))(^y.y)) 4. ==[ alpha ]==> (((^x.(a a))(a a))(^y.y)) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 27249/1544145. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^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 ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27250/1544148. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 27251/1544364. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 27252/1544766. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27253/1544769. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(a z))) 3. ==[ eta ]==> ((a ((^x.x)(^y.y))) a) 4. ==[ beta ]==> ((a (^y.y)) a) 5. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 27254/1545147. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 27255/1545198. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.(^z.z))(a (^x1.x1)))((^y.(^z.z))(a (^x1.x1))))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1))))((^x2.(^y2.y2))(a (^z2.z2)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(a (^z1.z1))))((^x2.(^y2.y2))(a (^z2.z2)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(a (^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 7. ==[ beta ]==> (((^y.(^z.z))(a (^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 8. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 12. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27256/1545531. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27257/1545711. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((^y.a)((^z.z) a)) b) 4. ==[ alpha ]==> (((^x.a)((^y.y) a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 27258/1545912. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)(^x.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 27259/1546098. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c c)) 3. ==[ beta ]==> (^y.((c c)(c c))) 4. ==[ alpha ]==> (^x.((c c)(c c))) REDUCED to normal form. ------ 27260/1546146. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(a (a a)))) REDUCED to normal form. ------ 27261/1546254. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 27262/1546344. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 5. ==[ beta ]==> (^y.((^z.z) a)) 6. ==[ alpha ]==> (^x.((^y.y) a)) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 27263/1546533. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.x)((^y.y)(a a)))(^x1.x1)) 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. ------ 27264/1546704. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 27265/1546767. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27266/1546794. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(a a))) REDUCED to normal form. ------ 27267/1546821. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 27268/1546848. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 27269/1546878. ------ 1. ==[ start ]==> ((a (^a.a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 27270/1546905. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a) a))) 5. ==[ beta ]==> (((^y.y) a)((a a) a)) 6. ==[ alpha ]==> (((^x.x) a)((a a) a)) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 27271/1546923. ------ 1. ==[ start ]==> ((a b)(c (^a.b))) 2. ==[ alpha ]==> ((a b)(c (^x.b))) REDUCED to normal form. ------ 27272/1546932. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(a b))) 3. ==[ beta ]==> ((a a)((a (^y.y))(a b))) 4. ==[ alpha ]==> ((a a)((a (^x.x))(a b))) REDUCED to normal form. ------ 27273/1546959. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 27274/1546995. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.x1))) 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. ------ 27275/1547004. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 27276/1547022. ------ 1. ==[ start ]==> (((a a) b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 27277/1547049. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a) a)(^y.a))) REDUCED to normal form. ------ 27278/1547076. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 27279/1547103. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 27280/1547139. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^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. ------ 27281/1547157. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 27282/1547166. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 27283/1547193. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27284/1547238. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a b) b)) 2. ==[ alpha ]==> (((a (^x.x)) b)((a b) b)) REDUCED to normal form. ------ 27285/1547382. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 27286/1547409. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(a a))) REDUCED to normal form. ------ 27287/1547454. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.b) b)) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.b) b)) 3. ==[ beta ]==> ((a a)((^y.b) b)) 4. ==[ alpha ]==> ((a a)((^x.b) b)) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 27288/1547472. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((^y.(y y))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((^x.(x x))(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a (^y.y)))(((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 27289/1547499. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) 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. ------ 27290/1547553. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z))) 9. ==[ beta ]==> (a ((^y.y)(^z.z))) 10. ==[ alpha ]==> (a ((^x.x)(^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27291/1547580. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 27292/1547607. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a a)(a b))) 3. ==[ beta ]==> ((^y.y)((a a)(a b))) 4. ==[ alpha ]==> ((^x.x)((a a)(a b))) 5. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 27293/1547643. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 27294/1547670. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 27295/1547706. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 27296/1547733. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y))(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 27297/1547760. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 27298/1547778. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (^y.y))(^z.a))) 3. ==[ beta ]==> ((b b)((a (^y.y))(^z.a))) 4. ==[ alpha ]==> ((b b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 27299/1547787. ------ 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)) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 27300/1547814. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^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. ------ 27301/1547985. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(b ((a a) a))) 3. ==[ beta ]==> ((^y.y)(b ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 27302/1548021. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.b) a)) 3. ==[ beta ]==> ((a (^y.a))((^z.b) a)) 4. ==[ alpha ]==> ((a (^x.a))((^y.b) a)) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 27303/1548039. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(a a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 27304/1548075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27305/1548165. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b (^z.a))) 3. ==[ beta ]==> ((a ((^y.y) a))(b (^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.a))) 5. ==[ beta ]==> ((a a)(b (^y.a))) 6. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 27306/1548192. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 27307/1548246. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 27308/1548372. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 27309/1548399. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y)) b)) 3. ==[ beta ]==> ((((a a) a) a)((^y.y) b)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x) b)) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 27310/1548498. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a a)(b (^y.y))) 10. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 27311/1548561. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 27312/1548579. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 27313/1548651. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(b (^b.(^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. ------ 27314/1548705. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27315/1548732. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 27316/1548750. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 27317/1548759. ------ 1. ==[ start ]==> ((a (a b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 27318/1548768. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(c d)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(c d)) 3. ==[ beta ]==> ((^y.b)(c d)) 4. ==[ alpha ]==> ((^x.b)(c d)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27319/1548930. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b (a (a a)))) 3. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 27320/1548957. ------ 1. ==[ start ]==> (((^a.a)(a b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)(a ((^y.y)(^z.z)))) 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. ------ 27321/1548966. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 27322/1548984. ------ 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))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a a))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 27323/1549020. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) c)) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 27324/1549038. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(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. ------ 27325/1549101. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 27326/1549128. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 27327/1549146. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c c)) 2. ==[ alpha ]==> ((a (^x.(a a)))(c c)) REDUCED to normal form. ------ 27328/1549164. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 27329/1549191. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 27330/1549218. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27331/1549245. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 27332/1549272. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> (a ((^y.(^z.z))(^x1.a))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(^z.a))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27333/1549299. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.(z z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 27334/1549317. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.b) b)((^y.(y y)) a)) 3. ==[ beta ]==> (b ((^y.(y y)) a)) 4. ==[ alpha ]==> (b ((^x.(x x)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 27335/1549362. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))(a (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27336/1549389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 5. ==[ beta ]==> ((a a)((^y.y) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 27337/1549443. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c b)) 5. ==[ beta ]==> ((^y.y)(c b)) 6. ==[ alpha ]==> ((^x.x)(c b)) 7. ==[ beta ]==> (c b) REDUCED to normal form. ------ 27338/1549524. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c (a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (a a))) 3. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 27339/1549533. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b) b)((a (^x.x)) b)) REDUCED to normal form. ------ 27340/1549578. ------ 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))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27341/1549587. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a) a)) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 27342/1549605. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.z))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a))) 5. ==[ beta ]==> ((a (^y.y))(a a)) 6. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 27343/1549614. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 27344/1549668. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 27345/1549695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 27346/1549722. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y)) a)) REDUCED to normal form. ------ 27347/1549740. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b (a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b (a a))) 3. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 27348/1549749. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 27349/1549776. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^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))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 27350/1549812. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 27351/1549839. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(a a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 27352/1549866. ------ 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))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 27353/1549893. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a (^z.z))) 3. ==[ beta ]==> (((a (a a))(^y.y))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 27354/1553055. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27355/1553067. ------ 1. ==[ start ]==> (((^a.a) b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (b (^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 27356/1553100. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((((^z.z)(a a))(^x1.x1))(^y.y)) 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. ------ 27357/1553217. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^x.(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (^x.(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^x.((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (^x.((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (^x.((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 11. ==[ beta ]==> (^x.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27358/1553289. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(^z.(a a)))) 3. ==[ eta ]==> ((^y.y)((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 27359/1553301. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.a)(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.a)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27360/1553460. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 27361/1553559. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.b) b)) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.b) b)) 3. ==[ beta ]==> (((^y.b) b)(((^y.b) b)((^y.b) b))) 4. ==[ alpha ]==> (((^x.b) b)(((^y.b) b)((^z.b) b))) 5. ==[ beta ]==> (b (((^y.b) b)((^z.b) b))) 6. ==[ alpha ]==> (b (((^x.b) b)((^y.b) b))) 7. ==[ beta ]==> (b (b ((^y.b) b))) 8. ==[ alpha ]==> (b (b ((^x.b) b))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 27362/1553715. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^c.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(a b))) REDUCED to normal form. ------ 27363/1553784. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27364/1553910. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27365/1553922. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.x)(^y.(^z.z))) a) 4. ==[ beta ]==> ((^y.(^z.z)) a) 5. ==[ alpha ]==> ((^x.(^y.y)) a) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27366/1554120. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(z b))) 3. ==[ beta ]==> ((a (^y.a))(^z.(z b))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(y b))) REDUCED to normal form. ------ 27367/1554342. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((((^y.y)(^z.z))(^x1.(^y1.y1)))(((^y.y)(^z.z))(^x1.(^y1.y1))))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2))))(((^z2.z2)(^x3.x3))(^y3.(^z3.z3)))) 5. ==[ beta ]==> ((((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2))))(((^z2.z2)(^x3.x3))(^y3.(^z3.z3)))) 6. ==[ alpha ]==> ((((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))(((^y2.y2)(^z2.z2))(^x3.(^y3.y3)))) 7. ==[ beta ]==> (((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2))))(((^y2.y2)(^z2.z2))(^x3.(^y3.y3)))) 8. ==[ alpha ]==> (((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))) 9. ==[ beta ]==> ((^y.y)(((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 11. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 13. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 14. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 15. ==[ beta ]==> (^y.(^z.z)) 16. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27368/1554633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((y1 y1) y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((y1 y1) y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((x1 x1) x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1) x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z) z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27369/1554855. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((^y.y) a)(^z.a)) b) 4. ==[ alpha ]==> ((((^x.x) a)(^y.a)) b) 5. ==[ beta ]==> ((a (^y.a)) b) 6. ==[ alpha ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 27370/1555056. ------ 1. ==[ start ]==> (((^a.a)(a b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27371/1555065. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 27372/1555173. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a (a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a (a a)))) 6. ==[ alpha ]==> ((^x.a)(^y.(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27373/1555242. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.a)(a (^x1.x1)))((^z.a)(a (^x1.x1))))) 4. ==[ alpha ]==> (^x.(((^y.a)(a (^z.z)))((^x1.a)(a (^y1.y1))))) 5. ==[ beta ]==> (^x.(a ((^x1.a)(a (^y1.y1))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(a (^z.z))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 27374/1555416. ------ 1. ==[ start ]==> (((^a.b) b)(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(y (y y)))) 3. ==[ beta ]==> (b (^y.(y (y y)))) 4. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 27375/1555449. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a) b)) 3. ==[ beta ]==> ((^y.y)(((^z.a) b)((^z.a) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.a) b)((^z.a) b))) 5. ==[ beta ]==> (((^y.a) b)((^z.a) b)) 6. ==[ alpha ]==> (((^x.a) b)((^y.a) b)) 7. ==[ beta ]==> (a ((^y.a) b)) 8. ==[ alpha ]==> (a ((^x.a) b)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27376/1555677. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.a))) 5. ==[ beta ]==> ((a a)(^y.(^z.a))) 6. ==[ alpha ]==> ((a a)(^x.(^y.a))) REDUCED to normal form. ------ 27377/1555686. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 27378/1555758. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 11. ==[ beta ]==> (^y.(^z.y)) 12. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 27379/1555821. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.c)) REDUCED to normal form. ------ 27380/1555875. ------ 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)))) REDUCED to normal form. ------ 27381/1555911. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.y)) 3. ==[ beta ]==> (((a a)(a a))(^y.y)) 4. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 27382/1555938. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 27383/1555992. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.a)) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.a)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.a)) REDUCED to normal form. ------ 27384/1556040. ------ 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)))) 5. ==[ beta ]==> (a ((a (a a))(^y.y))) 6. ==[ alpha ]==> (a ((a (a a))(^x.x))) REDUCED to normal form. ------ 27385/1556067. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) a)((a a) a))) 3. ==[ beta ]==> (((a a) a)(a ((a a) a))) REDUCED to normal form. ------ 27386/1556094. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 27387/1556112. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 27388/1556121. ------ 1. ==[ start ]==> (((^a.a) b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 27389/1556157. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(a a))(^a.a))) 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. ------ 27390/1556166. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27391/1556193. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a (^y1.y1)))) 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. ------ 27392/1556247. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 27393/1556274. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.a))(^z.z)) 10. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 27394/1556319. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 27395/1556346. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(^y.(a a)))) 3. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 27396/1556355. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27397/1556382. ------ 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)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27398/1556463. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(z1 z1)))) 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. ------ 27399/1556517. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 27400/1556589. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(a a)) a)) 3. ==[ beta ]==> ((a (a a))((^y.(a a)) a)) 4. ==[ alpha ]==> ((a (a a))((^x.(a a)) a)) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 27401/1556607. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a b)(a a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a b)(a a))) 3. ==[ beta ]==> ((a a)((a b)(a a))) REDUCED to normal form. ------ 27402/1556616. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.b) b)) 2. ==[ alpha ]==> ((a (a (a a)))((^x.b) b)) 3. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 27403/1556688. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 27404/1556715. ------ 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)))) 3. ==[ beta ]==> (((a (a a)) a)(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a)) a)(a (^y.y))) 6. ==[ alpha ]==> (((a (a a)) a)(a (^x.x))) REDUCED to normal form. ------ 27405/1556742. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 27406/1556760. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(b (^x1.b))) 3. ==[ beta ]==> ((^y.y)(b (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(b (^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 27407/1556769. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(a b))) REDUCED to normal form. ------ 27408/1556814. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(a a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(a a))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 27409/1556841. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 27410/1556859. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.a)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.a)) REDUCED to normal form. ------ 27411/1556886. ------ 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 z)))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 27412/1556913. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 27413/1556967. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((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. ------ 27414/1556976. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> ((^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. ------ 27415/1557003. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^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)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 27416/1557057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.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. ------ 27417/1557111. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(^z1.z1)))) 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. ------ 27418/1557120. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(c (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 27419/1557147. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b ((a a) a))) REDUCED to normal form. ------ 27420/1557174. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(a (a b))) 3. ==[ beta ]==> ((a (^y.a))(a (a b))) 4. ==[ alpha ]==> ((a (^x.a))(a (a b))) REDUCED to normal form. ------ 27421/1557201. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 27422/1557228. ------ 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)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27423/1557372. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 27424/1557399. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^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. ------ 27425/1557435. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((^z1.z1) 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. ------ 27426/1557489. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27427/1557570. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 27428/1557597. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((^y.(y y))(^z.a)) 6. ==[ alpha ]==> ((^x.(x x))(^y.a)) 7. ==[ beta ]==> ((^y.a)(^y.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 27429/1557651. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 27430/1557660. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(b ((^y.y)(^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. ------ 27431/1557687. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27432/1557714. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 27433/1557858. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27434/1557885. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 27435/1557912. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> ((a (a b))(a (^y.a))) 4. ==[ alpha ]==> ((a (a b))(a (^x.a))) REDUCED to normal form. ------ 27436/1557921. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.b)((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((^z.z) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27437/1558002. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) IRREDUCIBLE: cycle. ------ 27438/1558065. ------ 1. ==[ start ]==> ((((a a) a) b)(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a) b)(c ((^x.x) a))) 3. ==[ beta ]==> ((((a a) a) b)(c a)) REDUCED to normal form. ------ 27439/1558083. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 27440/1558092. ------ 1. ==[ start ]==> (((a b) a)(b (a (a a)))) REDUCED to normal form. ------ 27441/1558110. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(^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. ------ 27442/1558119. ------ 1. ==[ start ]==> (((a a)(^a.b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 27443/1558173. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 27444/1558200. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a (^y.y)) a)) REDUCED to normal form. ------ 27445/1558227. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(a (a a)))) 5. ==[ beta ]==> ((^y.a)((a a)(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((a a)(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27446/1558272. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(y y))(a a))) 3. ==[ beta ]==> (b ((^y.(y y))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 27447/1558299. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 27448/1558317. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 27449/1558344. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a a)(^y.(y y)))) REDUCED to normal form. ------ 27450/1558371. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (a a)) a)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a)) a)) 5. ==[ beta ]==> ((a (^y.y))((a (a a)) a)) 6. ==[ alpha ]==> ((a (^x.x))((a (a a)) a)) REDUCED to normal form. ------ 27451/1558398. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a) b)) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a b)) REDUCED to normal form. ------ 27452/1558470. ------ 1. ==[ start ]==> (((^a.b) b)(a (a (a a)))) 2. ==[ alpha ]==> (((^x.b) b)(a (a (a a)))) 3. ==[ beta ]==> (b (a (a (a a)))) REDUCED to normal form. ------ 27453/1558479. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x)) a)) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 27454/1558506. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a) b)) 3. ==[ beta ]==> ((a (a a))((^y.a) b)) 4. ==[ alpha ]==> ((a (a a))((^x.a) b)) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 27455/1558515. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(c (^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27456/1558542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(b (^x1.a))) 3. ==[ beta ]==> ((^y.y)(b (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 27457/1558596. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(a a))) 5. ==[ beta ]==> ((^y.y)((^y1.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. ------ 27458/1558677. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 27459/1558686. ------ 1. ==[ start ]==> (((a b) b)(c (a a))) REDUCED to normal form. ------ 27460/1558713. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(b (a (^y.y)))) 3. ==[ beta ]==> (((a a) a)(b (a (^y.y)))) 4. ==[ alpha ]==> (((a a) a)(b (a (^x.x)))) REDUCED to normal form. ------ 27461/1558731. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(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))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 27462/1558740. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 27463/1558758. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c (^z.z))) 3. ==[ beta ]==> ((^y.y)(c (^z.z))) 4. ==[ alpha ]==> ((^x.x)(c (^y.y))) 5. ==[ beta ]==> (c (^y.y)) 6. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 27464/1558767. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))(a a))) REDUCED to normal form. ------ 27465/1558812. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(a (^x1.a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(a (^x1.a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a (^y1.a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a (^y1.a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.a))) 9. ==[ beta ]==> ((^y.y)(a (^z.a))) 10. ==[ alpha ]==> ((^x.x)(a (^y.a))) 11. ==[ beta ]==> (a (^y.a)) 12. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 27466/1558821. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(c a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c a)) REDUCED to normal form. ------ 27467/1558848. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b b)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b b)) 5. ==[ beta ]==> ((^y.(y y))(b b)) 6. ==[ alpha ]==> ((^x.(x x))(b b)) 7. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 27468/1558875. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a c)) REDUCED to normal form. ------ 27469/1558893. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 27470/1558902. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 27471/1558929. ------ 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)))) REDUCED to normal form. ------ 27472/1558965. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y) b)) 3. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 4. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 27473/1558992. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(^y.y))) REDUCED to normal form. ------ 27474/1559019. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a a) a)) 3. ==[ beta ]==> ((a ((a a) a))((a a) a)) REDUCED to normal form. ------ 27475/1559046. ------ 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))(^y.y))((^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. ------ 27476/1559072. ------ 1. ==[ start ]==> (^a.(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (^x.(((^y.y)(^z.z))(x (x x)))) 3. ==[ beta ]==> (^x.((^z.z)(x (x x)))) 4. ==[ alpha ]==> (^x.((^y.y)(x (x x)))) 5. ==[ beta ]==> (^x.(x (x x))) REDUCED to normal form. ------ 27477/1559073. ------ 1. ==[ start ]==> (a (((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> (a ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (a ((^x.x)(a (a a)))) 5. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 27478/1562130. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a))) a) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a))) a) 3. ==[ beta ]==> (((^y.y)(a (a a))) a) 4. ==[ alpha ]==> (((^x.x)(a (a a))) a) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 27479/1562136. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a a))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 27480/1562163. ------ 1. ==[ start ]==> ((^a.(a a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((^y.y)(^z.z)))((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a (a a))(^x.x))((a (a a))(^z.z))) 8. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 27481/1562190. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 27482/1562388. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (^x.((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 27483/1562472. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27484/1562706. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a (a a))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> ((a (a a))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 27485/1562730. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a b)(a a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a b)(a a))) 3. ==[ beta ]==> (((a b)(a a))(((a b)(a a))((a b)(a a)))) REDUCED to normal form. ------ 27486/1562913. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 27487/1562955. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27488/1563093. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27489/1563291. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(^x1.z))) 3. ==[ beta ]==> ((a (^y.a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 27490/1563642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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))) REDUCED to normal form. ------ 27491/1563804. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27492/1563846. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27493/1564236. ------ 1. ==[ start ]==> (((a a)(^a.b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 27494/1564371. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 27495/1564413. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.((((^z.z) a)(^x1.(^y1.y1)))(((^z.z) a)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((((^y.y) a)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.((a (^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (^x.((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1))))) 7. ==[ beta ]==> (^x.((a (^y.(^z.z)))(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (^x.((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 27496/1564587. ------ 1. ==[ start ]==> (((^a.b) b)(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 27497/1564596. ------ 1. ==[ start ]==> (((a b)(a a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(x (x x)))) REDUCED to normal form. ------ 27498/1564620. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)(a a))(((^z.z) a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)(a a))(((^z.z) a)(a a)))) 5. ==[ beta ]==> ((((^y.y) a)(a a))(((^z.z) a)(a a))) 6. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) a)(a a))) 7. ==[ beta ]==> ((a (a a))(((^y.y) a)(a a))) 8. ==[ alpha ]==> ((a (a a))(((^x.x) a)(a a))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27499/1564857. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 27500/1564929. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.c)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.c)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.c)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.c)) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.c)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.c)) 9. ==[ beta ]==> ((^y.y)(^z.c)) 10. ==[ alpha ]==> ((^x.x)(^y.c)) 11. ==[ beta ]==> (^y.c) 12. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 27501/1564938. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 27502/1564992. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 27503/1565046. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 27504/1565136. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.b)) 3. ==[ beta ]==> ((a ((a a) a))(^y.b)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.b)) REDUCED to normal form. ------ 27505/1565163. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(z z))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(z z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y y))) REDUCED to normal form. ------ 27506/1565190. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.z)) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.y)) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 27507/1565202. ------ 1. ==[ start ]==> ((a a)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 27508/1565229. ------ 1. ==[ start ]==> ((a (a a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((a (a a))((^x.x)(^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. ------ 27509/1565256. ------ 1. ==[ start ]==> ((a b)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a b)(((^x.x) a)((a a) a))) 3. ==[ beta ]==> ((a b)(a ((a a) a))) REDUCED to normal form. ------ 27510/1565301. ------ 1. ==[ start ]==> (((^a.a) b)(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(b (^y.(a a)))) 3. ==[ beta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 27511/1565310. ------ 1. ==[ start ]==> (((a a)(a a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 27512/1565346. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27513/1565355. ------ 1. ==[ start ]==> (((a a) b)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(a a))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 27514/1565373. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(^y1.y1)))) 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. ------ 27515/1565382. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 27516/1565400. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((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. ------ 27517/1565427. ------ 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.(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. ------ 27518/1565436. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 27519/1565454. ------ 1. ==[ start ]==> ((a (^b.a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 27520/1565490. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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 REDUCED to normal form. ------ 27521/1565535. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((^y.a)((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.a)((a a)(^y.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27522/1565562. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(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. ------ 27523/1565571. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 27524/1565598. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 27525/1565625. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 27526/1565652. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 27527/1565679. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27528/1565742. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (a b))) REDUCED to normal form. ------ 27529/1565769. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a a))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (a a))(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27530/1565796. ------ 1. ==[ start ]==> ((a (a (a a)))((a b)(a a))) REDUCED to normal form. ------ 27531/1565805. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b) b)) 3. ==[ beta ]==> ((^y.(y y))((^z.b) b)) 4. ==[ alpha ]==> ((^x.(x x))((^y.b) b)) 5. ==[ beta ]==> (((^y.b) b)((^y.b) b)) 6. ==[ alpha ]==> (((^x.b) b)((^y.b) b)) 7. ==[ beta ]==> (b ((^y.b) b)) 8. ==[ alpha ]==> (b ((^x.b) b)) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 27532/1565832. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.a) c)) 3. ==[ beta ]==> ((^y.y)((^x1.a) c)) 4. ==[ alpha ]==> ((^x.x)((^y.a) c)) 5. ==[ beta ]==> ((^y.a) c) 6. ==[ alpha ]==> ((^x.a) c) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27533/1565949. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(b (^z.b))) REDUCED to normal form. ------ 27534/1565976. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 27535/1565994. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(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. ------ 27536/1566003. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 27537/1566021. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 27538/1566111. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 27539/1566156. ------ 1. ==[ start ]==> (((^a.a)(^b.(^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) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27540/1566183. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((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. ------ 27541/1566246. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 27542/1566273. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (a ((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> (a ((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> (a ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 27543/1566300. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 27544/1566354. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.b))) 5. ==[ beta ]==> ((a (^x.a))(^z.b)) 6. ==[ alpha ]==> ((a (^x.a))(^y.b)) REDUCED to normal form. ------ 27545/1566372. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.b) a)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b) a)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 27546/1566444. ------ 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))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 27547/1566471. ------ 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 (^x.x))(a (a a)))(a (a (a a)))) REDUCED to normal form. ------ 27548/1566498. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 27549/1566525. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 27550/1566615. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^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 a))(^y1.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. ------ 27551/1566669. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 27552/1566705. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)((a a) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)((^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. ------ 27553/1566750. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^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. ------ 27554/1566786. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 27555/1566813. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 27556/1566840. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(^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. ------ 27557/1566912. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 27558/1566930. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 27559/1566957. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z) a))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 27560/1566984. ------ 1. ==[ start ]==> ((((^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)))) 3. ==[ beta ]==> ((a (a (a a)))((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 27561/1567011. ------ 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.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. ------ 27562/1567083. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (b ((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 27563/1567101. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27564/1567182. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1)) a)) IRREDUCIBLE: cycle. ------ 27565/1567245. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 27566/1567272. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 27567/1567299. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 27568/1567317. ------ 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)((^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. ------ 27569/1567371. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.a) c)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.a) c)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a) c)) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 27570/1567407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(b (^z.(z z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.(z z)))) 6. ==[ alpha ]==> ((^x.a)(b (^y.(y y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27571/1567434. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 27572/1567452. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 27573/1567461. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 27574/1567479. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) 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. ------ 27575/1567497. ------ 1. ==[ start ]==> (((a a)(a b))(c c)) REDUCED to normal form. ------ 27576/1567632. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b a)) REDUCED to normal form. ------ 27577/1567650. ------ 1. ==[ start ]==> (((^a.b) b)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 27578/1567659. ------ 1. ==[ start ]==> (((a b)(a a))(a (a (a a)))) REDUCED to normal form. ------ 27579/1567686. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)(a a))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(a a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)(a a))) 5. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27580/1567695. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a) b)) 3. ==[ beta ]==> ((^y.(a a))((^z.a) b)) 4. ==[ alpha ]==> ((^x.(a a))((^y.a) b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27581/1567722. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 5. ==[ beta ]==> ((^y.(^z.z)) c) 6. ==[ alpha ]==> ((^x.(^y.y)) c) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27582/1567776. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.z1))) 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. ------ 27583/1567857. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a) a)) 3. ==[ beta ]==> (b (((^x1.x1) a) a)) 4. ==[ alpha ]==> (b (((^x.x) a) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 27584/1567866. ------ 1. ==[ start ]==> (((a b) b)((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.y))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 27585/1567893. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 27586/1567920. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 27587/1567938. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a) a)) 3. ==[ beta ]==> ((^y.y)((^z.a) a)) 4. ==[ alpha ]==> ((^x.x)((^y.a) a)) 5. ==[ beta ]==> ((^y.a) a) 6. ==[ alpha ]==> ((^x.a) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27588/1567947. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c (^z.z))) REDUCED to normal form. ------ 27589/1568001. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 27590/1568028. ------ 1. ==[ start ]==> ((((^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))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(a a))) 7. ==[ beta ]==> (((^y.(^z.z))(a a))((^y.(^z.z))(a a))) 8. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(a a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 11. ==[ beta ]==> ((^y.(^z.z))(a a)) 12. ==[ alpha ]==> ((^x.(^y.y))(a a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27591/1568055. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(a (^a.a)))) 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. ------ 27592/1568073. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.z)) a)) 3. ==[ beta ]==> (b ((a (^z.z)) a)) 4. ==[ alpha ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 27593/1568082. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 27594/1568109. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^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. ------ 27595/1568145. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a a)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(a a))) 3. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 27596/1568172. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b a)) REDUCED to normal form. ------ 27597/1568199. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a b)) 3. ==[ beta ]==> ((a ((a a) a))(a b)) REDUCED to normal form. ------ 27598/1568226. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a (a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a (a a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(a (a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (a a))) REDUCED to normal form. ------ 27599/1568253. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(a a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(a a)) 3. ==[ beta ]==> (((^y.y)(a (a a)))(a a)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(a a)) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 27600/1571319. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a))) b) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a))) b) 3. ==[ beta ]==> (((^y.y)(a (a a))) b) 4. ==[ alpha ]==> (((^x.x)(a (a a))) b) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 27601/1571343. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27602/1571424. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27603/1571658. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(a b))) 3. ==[ eta ]==> ((^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. ------ 27604/1571904. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 27605/1572279. ------ 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. ------ 27606/1572507. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(z b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(z b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z b))) REDUCED to normal form. ------ 27607/1572687. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.b))) 5. ==[ beta ]==> ((a a)(^y.(^z.b))) 6. ==[ alpha ]==> ((a a)(^x.(^y.b))) REDUCED to normal form. ------ 27608/1572840. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 27609/1573044. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27610/1573224. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(a (^z.z))) b) 4. ==[ alpha ]==> (((^x.(x x))(a (^y.y))) b) 5. ==[ beta ]==> (((a (^y.y))(a (^y.y))) b) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 27611/1573452. ------ 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)(^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 ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27612/1573686. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a (a a)))) REDUCED to normal form. ------ 27613/1573785. ------ 1. ==[ start ]==> (((^a.b) b)(^c.d)) 2. ==[ alpha ]==> (((^x.b) b)(^y.d)) 3. ==[ beta ]==> (b (^y.d)) 4. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 27614/1573794. ------ 1. ==[ start ]==> (((a b)(a a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 27615/1574055. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 27616/1574073. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(^y.y))(a b))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27617/1574136. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 27618/1574190. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 27619/1574208. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.c)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.c)) 3. ==[ beta ]==> (b (^z.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 27620/1574307. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 27621/1574334. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(a a))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(a a))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(a a))) REDUCED to normal form. ------ 27622/1574361. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 27623/1574388. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.z))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 27624/1574418. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 27625/1574445. ------ 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))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 27626/1574472. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((a a)(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)((a a) a))) 5. ==[ beta ]==> ((a a)(a ((a a) a))) REDUCED to normal form. ------ 27627/1574499. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a b))) REDUCED to normal form. ------ 27628/1574517. ------ 1. ==[ start ]==> (((a a)(a a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a a))(b (^x.(a a)))) REDUCED to normal form. ------ 27629/1574562. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> (((a a) b)((a a)(^y.y))) 4. ==[ alpha ]==> (((a a) b)((a a)(^x.x))) REDUCED to normal form. ------ 27630/1574589. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 27631/1574616. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 27632/1574643. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^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. ------ 27633/1574679. ------ 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.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 10. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 27634/1574697. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 27635/1574706. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 27636/1574733. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) 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)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 27637/1574778. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x)) b)((a a) a)) REDUCED to normal form. ------ 27638/1574805. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b) b)) 2. ==[ alpha ]==> ((((^x.x) a) a)((a b) b)) 3. ==[ beta ]==> ((a a)((a b) b)) REDUCED to normal form. ------ 27639/1574832. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a) c)) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a) c)) REDUCED to normal form. ------ 27640/1574922. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.a))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 27641/1574949. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 27642/1574976. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 27643/1574994. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(a a)) a)) 3. ==[ beta ]==> ((a a)((^y.(a a)) a)) 4. ==[ alpha ]==> ((a a)((^x.(a a)) a)) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27644/1575012. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(a a))) 3. ==[ beta ]==> ((^y.(y y))((a b)(a a))) 4. ==[ alpha ]==> ((^x.(x x))((a b)(a a))) 5. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 27645/1575039. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.x1)))) 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. ------ 27646/1575093. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (a a)))) 7. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27647/1575120. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 27648/1575147. ------ 1. ==[ start ]==> (((^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))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((a (^y.y))((a a) a)) 6. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 27649/1575210. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 27650/1575273. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 27651/1575300. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 27652/1575318. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 27653/1575327. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 27654/1575354. ------ 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)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27655/1575453. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y)) c)) 3. ==[ beta ]==> (((a (a a)) b)((^y.y) c)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x) c)) 5. ==[ beta ]==> (((a (a a)) b) c) REDUCED to normal form. ------ 27656/1575579. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(a (a b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(a (a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a b))) REDUCED to normal form. ------ 27657/1575588. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 27658/1575732. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 27659/1575759. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(a (^z.b))) 3. ==[ beta ]==> (((^y.y)(a a))(a (^z.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. ------ 27660/1575912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 27661/1575939. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a) a) a)) REDUCED to normal form. ------ 27662/1575993. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a)) c)) REDUCED to normal form. ------ 27663/1576119. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 27664/1576218. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 27665/1576272. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^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)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 27666/1576290. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 27667/1576299. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> ((a (a b))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> ((a (a b))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 27668/1576452. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a) c)) 3. ==[ beta ]==> ((((a a) a) b)(a c)) REDUCED to normal form. ------ 27669/1576470. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c ((^z.z) a))) 3. ==[ beta ]==> (b (c ((^z.z) a))) 4. ==[ alpha ]==> (b (c ((^x.x) a))) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 27670/1576497. ------ 1. ==[ start ]==> (((^a.a)(a b))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(b (a (a a)))) 3. ==[ beta ]==> ((a b)(b (a (a a)))) REDUCED to normal form. ------ 27671/1576524. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (a ((^y.y)(^z.z))) 6. ==[ alpha ]==> (a ((^x.x)(^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27672/1576560. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z)) b)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 27673/1576578. ------ 1. ==[ start ]==> (((^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.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) 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. ------ 27674/1576587. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.a) c)) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 27675/1576668. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 27676/1576704. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 27677/1576731. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 27678/1576758. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 27679/1576785. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^y.y))) 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. ------ 27680/1576812. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a ((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27681/1576839. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 27682/1576866. ------ 1. ==[ start ]==> (((a b)(a a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(y y))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(x x))) REDUCED to normal form. ------ 27683/1576902. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27684/1576929. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 27685/1577073. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) a) a)) 2. ==[ alpha ]==> (((a b) b)(((^x.x) a) a)) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 27686/1577100. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (^y.y)) b)) 3. ==[ beta ]==> (((a a) a)((a (^y.y)) b)) 4. ==[ alpha ]==> (((a a) a)((a (^x.x)) b)) REDUCED to normal form. ------ 27687/1577118. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (a (^y.y)))) 5. ==[ beta ]==> ((a a)(b (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(b (a (^x.x)))) REDUCED to normal form. ------ 27688/1577127. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a) c)) REDUCED to normal form. ------ 27689/1577145. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(a ((^z.z) a))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a))) 5. ==[ beta ]==> (a ((^y.y) a)) 6. ==[ alpha ]==> (a ((^x.x) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27690/1577154. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 27691/1577199. ------ 1. ==[ start ]==> (((^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.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)(a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(a (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (^z.z)))) 9. ==[ beta ]==> ((^y.y)((a a)(a (^z.z)))) 10. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y)))) 11. ==[ beta ]==> ((a a)(a (^y.y))) 12. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 27692/1577208. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) c) REDUCED to normal form. ------ 27693/1577235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.y))(^z.z))) 7. ==[ beta ]==> (((a (^y.y))(^z.z))((a (^y.y))(^z.z))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 27694/1577262. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 27695/1577280. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a c)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a c)) 3. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 27696/1577289. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 27697/1577316. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a a) b)) 3. ==[ beta ]==> (((a a)(^y.y))((a a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((a a) b)) REDUCED to normal form. ------ 27698/1577352. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(b (^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (^y.y))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 27699/1577379. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 27700/1577406. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y)(a a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(a a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a a))) 5. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 27701/1577433. ------ 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))(^y.y))((^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. ------ 27702/1577460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(a (^z.z))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(a (^z.z))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(a (^y.y))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 27703/1580811. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27704/1580883. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))(^x1.b))) 3. ==[ eta ]==> ((^y.y)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 27705/1580922. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (^y.((^z.z)(a a))) 6. ==[ alpha ]==> (^x.((^y.y)(a a))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 27706/1581054. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 27707/1581147. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(x x)))) 5. ==[ beta ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 27708/1581153. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((^y.(a a)) a)(((^y.(a a)) a)((^y.(a a)) a))) 4. ==[ alpha ]==> (((^x.(a a)) a)(((^y.(a a)) a)((^z.(a a)) a))) 5. ==[ beta ]==> ((a a)(((^y.(a a)) a)((^z.(a a)) a))) 6. ==[ alpha ]==> ((a a)(((^x.(a a)) a)((^y.(a a)) a))) 7. ==[ beta ]==> ((a a)((a a)((^y.(a a)) a))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a)) a))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 27709/1581354. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 27710/1581378. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27711/1581543. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.(z z))) a) 4. ==[ beta ]==> ((^y.y) a) 5. ==[ alpha ]==> ((^x.x) a) 6. ==[ beta ]==> a REDUCED to normal form. ------ 27712/1581732. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 27713/1581741. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 27714/1581936. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a) a)(^y.y))) 3. ==[ beta ]==> (((((a a) a)(^y.y))(((a a) a)(^y.y)))(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 27715/1582254. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((y y) y))) REDUCED to normal form. ------ 27716/1582449. ------ 1. ==[ start ]==> ((^a.(a b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^y.(^z.z))) b) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 27717/1582542. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.x1)(^y1.y1)))) IRREDUCIBLE: cycle. ------ 27718/1582677. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 27719/1582812. ------ 1. ==[ start ]==> (((^a.b)(a a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27720/1582836. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))(a a))) 3. ==[ beta ]==> (^y.(((^z.(z z))(a a))((^z.(z z))(a a)))) 4. ==[ alpha ]==> (^x.(((^y.(y y))(a a))((^z.(z z))(a a)))) 5. ==[ beta ]==> (^x.(((a a)(a a))((^z.(z z))(a a)))) 6. ==[ alpha ]==> (^x.(((a a)(a a))((^y.(y y))(a a)))) 7. ==[ beta ]==> (^x.(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 27721/1583019. ------ 1. ==[ start ]==> (((a b)(a a))(^c.d)) 2. ==[ alpha ]==> (((a b)(a a))(^x.d)) REDUCED to normal form. ------ 27722/1583043. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z)) a)) 3. ==[ beta ]==> ((^y.y)(((^z.(z z)) a)((^z.(z z)) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y)) a)((^z.(z z)) a))) 5. ==[ beta ]==> (((^y.(y y)) a)((^z.(z z)) a)) 6. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y y)) a)) 7. ==[ beta ]==> ((a a)((^y.(y y)) a)) 8. ==[ alpha ]==> ((a a)((^x.(x x)) a)) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27723/1583136. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 27724/1583217. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (b (^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 27725/1583298. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 27726/1583307. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 27727/1583361. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 27728/1583433. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 27729/1583442. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 27730/1583532. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 27731/1583613. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 27732/1583661. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (a (((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (a ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (a ((^x.x)(a (a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 27733/1583688. ------ 1. ==[ start ]==> (((a a) a)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((a (a a))((^x.x)(^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. ------ 27734/1583715. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a a)(^x.x))(a ((a a) a))) REDUCED to normal form. ------ 27735/1583742. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a b))) 3. ==[ beta ]==> (b ((a (^y.y))(a b))) 4. ==[ alpha ]==> (b ((a (^x.x))(a b))) REDUCED to normal form. ------ 27736/1583769. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27737/1583814. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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 a) REDUCED to normal form. ------ 27738/1583841. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 27739/1583895. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 27740/1583913. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 27741/1583967. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(^z.b))) 3. ==[ beta ]==> ((a a)((a (^y.y))(^z.b))) 4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 27742/1583976. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27743/1584003. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1)(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. ------ 27744/1584057. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 27745/1584138. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 27746/1584228. ------ 1. ==[ start ]==> (((^a.(a a)) a)(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a a)(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 27747/1584237. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(a a)) a)) 3. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 27748/1584309. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a b)((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((a b)((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((a b)((^y.y) a)) 8. ==[ alpha ]==> ((a b)((^x.x) a)) 9. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 27749/1584336. ------ 1. ==[ start ]==> (((a (a a)) a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 27750/1584363. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 27751/1584390. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 27752/1584417. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 27753/1584435. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(a (^y.(a a)))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 27754/1584462. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 27755/1584480. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 27756/1584507. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.a))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.a)) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.a)) REDUCED to normal form. ------ 27757/1584534. ------ 1. ==[ start ]==> ((((^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 z)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 27758/1584561. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) a)(^y.(^z.z)))) 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. ------ 27759/1584597. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^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. ------ 27760/1584624. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a b))) 5. ==[ beta ]==> ((^y.y)(a b)) 6. ==[ alpha ]==> ((^x.x)(a b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 27761/1584732. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 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. ------ 27762/1584759. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27763/1584795. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(b ((a a) a))) 3. ==[ beta ]==> ((a (^y.a))(b ((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))(b ((a a) a))) REDUCED to normal form. ------ 27764/1584813. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.b)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.b)) REDUCED to normal form. ------ 27765/1584822. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 27766/1584849. ------ 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 ]==> ((^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. ------ 27767/1584885. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 27768/1585020. ------ 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. ------ 27769/1585056. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^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. ------ 27770/1585110. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(a (a a)))) 5. ==[ beta ]==> (a ((^z.a)(a (a a)))) 6. ==[ alpha ]==> (a ((^x.a)(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27771/1585218. ------ 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.(^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. ------ 27772/1585272. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(^z.(z z)))) 7. ==[ beta ]==> ((a a)((^y.a)(^z.(z z)))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.(y y)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 27773/1585281. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(c (a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(c (a (a a)))) REDUCED to normal form. ------ 27774/1585308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27775/1585335. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(a ((a a) a))) REDUCED to normal form. ------ 27776/1585371. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 27777/1585506. ------ 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))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 27778/1585533. ------ 1. ==[ start ]==> ((a (a b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 27779/1585542. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27780/1585623. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) IRREDUCIBLE: cycle. ------ 27781/1585704. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 27782/1585713. ------ 1. ==[ start ]==> (((a b) a)(c ((^a.a) a))) 2. ==[ alpha ]==> (((a b) a)(c ((^x.x) a))) 3. ==[ beta ]==> (((a b) a)(c a)) REDUCED to normal form. ------ 27783/1585731. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 27784/1585740. ------ 1. ==[ start ]==> (((a a)(^a.b))(b (a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(b (a (a a)))) REDUCED to normal form. ------ 27785/1585758. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27786/1585794. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 27787/1585821. ------ 1. ==[ start ]==> (((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.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 27788/1585848. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.a)((a (^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.a)((a (^y.y))((^z.z) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27789/1585875. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 27790/1585893. ------ 1. ==[ start ]==> (((^a.b)(a a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 27791/1585920. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(a a))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 27792/1585938. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 27793/1585965. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 27794/1585992. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)(^z.(z z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 27795/1586019. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a)) a)) REDUCED to normal form. ------ 27796/1586046. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a) b)) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a) b)) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a) b)) 7. ==[ beta ]==> (a (((^y.y) a) b)) 8. ==[ alpha ]==> (a (((^x.x) a) b)) 9. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 27797/1586091. ------ 1. ==[ start ]==> (((^a.b) b)(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) b)(b ((^y.y) a))) 3. ==[ beta ]==> (b (b ((^y.y) a))) 4. ==[ alpha ]==> (b (b ((^x.x) a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 27798/1586127. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y)) a)) 3. ==[ beta ]==> ((a (a a))((^y.(y y)) a)) 4. ==[ alpha ]==> ((a (a a))((^x.(x x)) a)) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 27799/1586163. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 27800/1586217. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)(a (^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 27801/1586298. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 27802/1586352. ------ 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))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 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)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 27803/1586361. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b (a (^y.y)))) REDUCED to normal form. ------ 27804/1586379. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 27805/1586388. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 27806/1586433. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 11. ==[ beta ]==> (b (^y.(^z.z))) 12. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 27807/1586442. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 27808/1586496. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b b)) REDUCED to normal form. ------ 27809/1586514. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 27810/1586523. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a c)) REDUCED to normal form. ------ 27811/1586550. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b (a a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (a a))) REDUCED to normal form. ------ 27812/1586586. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 27813/1586613. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y) b)) 3. ==[ beta ]==> (((a (^x.x))(a b)) b) REDUCED to normal form. ------ 27814/1586640. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a a)(^a.a))) 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. ------ 27815/1586667. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a a) a)) 3. ==[ beta ]==> (((a (a a))(^y.y))((a a) a)) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a a) a)) REDUCED to normal form. ------ 27816/1586694. ------ 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)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 27817/1586720. ------ 1. ==[ start ]==> (^a.(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (^x.(((x x) x)((^y.y) x))) 3. ==[ beta ]==> (^x.(((x x) x) x)) REDUCED to normal form. ------ 27818/1586721. ------ 1. ==[ start ]==> (a (((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (a (((a a) a)((^x.x) a))) 3. ==[ beta ]==> (a (((a a) a) a)) REDUCED to normal form. ------ 27819/1587318. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((^y.((^z.z)(y y)))((^y.((^z.z)(y y)))(^y.((^z.z)(y y))))) 4. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.((^x1.x1)(z z)))(^y1.((^z1.z1)(y1 y1))))) 5. ==[ beta ]==> ((^y.y)(((^z.((^x1.x1)(z z)))(^y1.((^z1.z1)(y1 y1))))((^z.((^x1.x1)(z z)))(^y1.((^z1.z1)(y1 y1)))))) 6. ==[ alpha ]==> ((^x.x)(((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))((^z1.((^x2.x2)(z1 z1)))(^y2.((^z2.z2)(y2 y2)))))) 7. ==[ beta ]==> (((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))((^z1.((^x2.x2)(z1 z1)))(^y2.((^z2.z2)(y2 y2))))) 8. ==[ alpha ]==> (((^x.((^y.y)(x x)))(^z.((^x1.x1)(z z))))((^y1.((^z1.z1)(y1 y1)))(^x2.((^y2.y2)(x2 x2))))) 9. ==[ beta ]==> (((^y.y)((^z.((^x1.x1)(z z)))(^z.((^x1.x1)(z z)))))((^y1.((^z1.z1)(y1 y1)))(^x2.((^y2.y2)(x2 x2))))) 10. ==[ alpha ]==> (((^x.x)((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1)))))((^z1.((^x2.x2)(z1 z1)))(^y2.((^z2.z2)(y2 y2))))) 11. ==[ beta ]==> (((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))((^z1.((^x2.x2)(z1 z1)))(^y2.((^z2.z2)(y2 y2))))) IRREDUCIBLE: cycle. ------ 27820/1589208. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(z (z z)))) 3. ==[ beta ]==> ((^y.y)((^z.(z (z z)))(^z.(z (z z))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (y y)))(^z.(z (z z))))) 5. ==[ beta ]==> ((^y.(y (y y)))(^z.(z (z z)))) 6. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y (y y)))) 7. ==[ beta ]==> ((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y))))) 8. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z))))) 9. ==[ beta ]==> (((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z)))))) 10. ==[ alpha ]==> (((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1)))))) 11. ==[ beta ]==> (((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1)))))) 12. ==[ alpha ]==> (((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2)))))) 13. ==[ beta ]==> ((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2)))))) 14. ==[ alpha ]==> ((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3)))))) 15. ==[ beta ]==> ((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3)))))) 16. ==[ alpha ]==> ((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3)))))) 17. ==[ beta ]==> (((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3)))))) 18. ==[ alpha ]==> (((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4)))))) 19. ==[ beta ]==> (((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4)))))) 20. ==[ alpha ]==> (((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4)))))) 21. ==[ beta ]==> ((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4)))))) 22. ==[ alpha ]==> ((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5)))))) 23. ==[ beta ]==> ((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5)))))) 24. ==[ alpha ]==> ((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6)))))) 25. ==[ beta ]==> (((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6)))))) 26. ==[ alpha ]==> (((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7)))))) 27. ==[ beta ]==> (((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7)))))) 28. ==[ alpha ]==> (((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7)))))) 29. ==[ beta ]==> ((((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7)))))) 30. ==[ alpha ]==> ((((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8)))))) 31. ==[ beta ]==> ((((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8)))))) 32. ==[ alpha ]==> ((((((((^x.(x (x x)))((^y.(y (y y)))(^z.(z (z z)))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8)))))) 33. ==[ beta ]==> (((((((((^y.(y (y y)))(^z.(z (z z))))(((^y.(y (y y)))(^z.(z (z z))))((^y.(y (y y)))(^z.(z (z z))))))(((^x1.(x1 (x1 x1)))(^y1.(y1 (y1 y1))))((^z1.(z1 (z1 z1)))(^x2.(x2 (x2 x2))))))(((^y2.(y2 (y2 y2)))(^z2.(z2 (z2 z2))))((^x3.(x3 (x3 x3)))(^y3.(y3 (y3 y3))))))(((^z3.(z3 (z3 z3)))(^x4.(x4 (x4 x4))))((^y4.(y4 (y4 y4)))(^z4.(z4 (z4 z4))))))(((^x5.(x5 (x5 x5)))(^y5.(y5 (y5 y5))))((^z5.(z5 (z5 z5)))(^x6.(x6 (x6 x6))))))(((^y6.(y6 (y6 y6)))(^z6.(z6 (z6 z6))))((^x7.(x7 (x7 x7)))(^y7.(y7 (y7 y7))))))(((^z7.(z7 (z7 z7)))(^x8.(x8 (x8 x8))))((^y8.(y8 (y8 y8)))(^z8.(z8 (z8 z8)))))) 34. ==[ alpha ]==> (((((((((^x.(x (x x)))(^y.(y (y y))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))(((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9)))))) 35. ==[ beta ]==> (((((((((^y.(y (y y)))((^y.(y (y y)))(^y.(y (y y)))))(((^z.(z (z z)))(^x1.(x1 (x1 x1))))((^y1.(y1 (y1 y1)))(^z1.(z1 (z1 z1))))))(((^x2.(x2 (x2 x2)))(^y2.(y2 (y2 y2))))((^z2.(z2 (z2 z2)))(^x3.(x3 (x3 x3))))))(((^y3.(y3 (y3 y3)))(^z3.(z3 (z3 z3))))((^x4.(x4 (x4 x4)))(^y4.(y4 (y4 y4))))))(((^z4.(z4 (z4 z4)))(^x5.(x5 (x5 x5))))((^y5.(y5 (y5 y5)))(^z5.(z5 (z5 z5))))))(((^x6.(x6 (x6 x6)))(^y6.(y6 (y6 y6))))((^z6.(z6 (z6 z6)))(^x7.(x7 (x7 x7))))))(((^y7.(y7 (y7 y7)))(^z7.(z7 (z7 z7))))((^x8.(x8 (x8 x8)))(^y8.(y8 (y8 y8))))))(((^z8.(z8 (z8 z8)))(^x9.(x9 (x9 x9))))((^y9.(y9 (y9 y9)))(^z9.(z9 (z9 z9)))))) UNREDUCED: maximal number of reductions reached. ------ 27821/1589805. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a)) a) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a)) a) 3. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 27822/1589811. ------ 1. ==[ start ]==> ((^a.a)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a a) a)((^y.y) a)) 4. ==[ alpha ]==> (((a a) a)((^x.x) a)) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 27823/1589838. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(a (a a)))(((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))(a (a a)))) 7. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(a (a a)))) 8. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(a (a a)))) 9. ==[ beta ]==> ((a (a a))((^y.y)(a (a a)))) 10. ==[ alpha ]==> ((a (a a))((^x.x)(a (a a)))) 11. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27824/1589865. ------ 1. ==[ start ]==> ((^a.b)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 27825/1589946. ------ 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)((^z.z)(a a)))(^y.y)) 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. ------ 27826/1589967. ------ 1. ==[ start ]==> (((a a) b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27827/1590063. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^x.((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(z z)))) 7. ==[ beta ]==> (^x.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 27828/1590183. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^y.(a a))) REDUCED to normal form. ------ 27829/1590399. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 27830/1590405. ------ 1. ==[ start ]==> ((^a.(a (a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a ((^y.y)(a a)))(a ((^y.y)(a a))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a ((^y.y)(a a)))(a ((^z.z)(a a))))) 5. ==[ beta ]==> ((a (a a))((a ((^y.y)(a a)))(a ((^z.z)(a a))))) 6. ==[ alpha ]==> ((a (a a))((a ((^x.x)(a a)))(a ((^y.y)(a a))))) 7. ==[ beta ]==> ((a (a a))((a (a a))(a ((^y.y)(a a))))) 8. ==[ alpha ]==> ((a (a a))((a (a a))(a ((^x.x)(a a))))) 9. ==[ beta ]==> ((a (a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 27831/1590408. ------ 1. ==[ start ]==> ((a (a (a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.((^y.y)(x x)))) 3. ==[ beta ]==> ((a (a (a a)))(^x.(x x))) REDUCED to normal form. ------ 27832/1590615. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 27833/1590630. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.x1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27834/1590993. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 27835/1591344. ------ 1. ==[ start ]==> ((((a a) a) a)(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.((a a) a))) REDUCED to normal form. ------ 27836/1591506. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 27837/1591521. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.a) a)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a) a)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27838/1592073. ------ 1. ==[ start ]==> (((a b)(^a.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 27839/1592088. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a))(^z.z))) 3. ==[ beta ]==> (^y.(((a (a a))(^z.z))((a (a a))(^z.z)))) 4. ==[ alpha ]==> (^x.(((a (a a))(^y.y))((a (a a))(^z.z)))) REDUCED to normal form. ------ 27840/1592295. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(a (a (a a)))) 3. ==[ beta ]==> ((^y.y)((a (a (a a)))(a (a (a a))))) 4. ==[ alpha ]==> ((^x.x)((a (a (a a)))(a (a (a a))))) 5. ==[ beta ]==> ((a (a (a a)))(a (a (a a)))) REDUCED to normal form. ------ 27841/1592298. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(y (y y)))) 3. ==[ beta ]==> ((a (a a))(^y.(y (y y)))) 4. ==[ alpha ]==> ((a (a a))(^x.(x (x x)))) REDUCED to normal form. ------ 27842/1592469. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (b (^x1.(^y1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 27843/1592478. ------ 1. ==[ start ]==> (((a b) b)(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)(^x.((^y.y) a))) 3. ==[ beta ]==> (((a b) b)(^x.a)) REDUCED to normal form. ------ 27844/1592550. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.z)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27845/1592559. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.a))) REDUCED to normal form. ------ 27846/1592640. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.y))) 7. ==[ beta ]==> ((^y.(^z.y))(^y.(^z.y))) 8. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.z))) 9. ==[ beta ]==> (^y.(^z.(^x1.z))) 10. ==[ alpha ]==> (^x.(^y.(^z.y))) REDUCED to normal form. ------ 27847/1592685. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(^a.(^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. ------ 27848/1592694. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 27849/1592757. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(y (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 27850/1592784. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(a a))) REDUCED to normal form. ------ 27851/1592838. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.b)) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.b)) REDUCED to normal form. ------ 27852/1592865. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(z z))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(z z))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(y y))) 5. ==[ beta ]==> ((a (a a))(^y.(y y))) 6. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 27853/1592892. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.y)) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 27854/1592904. ------ 1. ==[ start ]==> ((a a)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a a)(((a a) a)((^x.x) a))) 3. ==[ beta ]==> ((a a)(((a a) a) a)) REDUCED to normal form. ------ 27855/1592931. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 27856/1592958. ------ 1. ==[ start ]==> ((a b)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((a (a a))((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a b)((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a b)((a (a a))(^x.x))) REDUCED to normal form. ------ 27857/1593003. ------ 1. ==[ start ]==> (((^a.a) b)(c (^a.b))) 2. ==[ alpha ]==> (((^x.x) b)(c (^y.b))) 3. ==[ beta ]==> (b (c (^y.b))) 4. ==[ alpha ]==> (b (c (^x.b))) REDUCED to normal form. ------ 27858/1593012. ------ 1. ==[ start ]==> (((a a)(a a))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a b))) REDUCED to normal form. ------ 27859/1593030. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 27860/1593039. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 27861/1593057. ------ 1. ==[ start ]==> (((a a) b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 27862/1593075. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 27863/1593084. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 27864/1593102. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 27865/1593111. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 27866/1593129. ------ 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)(^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. ------ 27867/1593156. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(y y))) REDUCED to normal form. ------ 27868/1593192. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 27869/1593237. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.a)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.a)((a (^y.y))(^z.b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 27870/1593264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 27871/1593273. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 27872/1593300. ------ 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))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27873/1593318. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b) b)) 3. ==[ beta ]==> (((^y.y) a)((a b) b)) 4. ==[ alpha ]==> (((^x.x) a)((a b) b)) 5. ==[ beta ]==> (a ((a b) b)) REDUCED to normal form. ------ 27874/1593327. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 27875/1593381. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 27876/1593471. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(b (a b))) 3. ==[ beta ]==> ((a (a a))(b (a b))) REDUCED to normal form. ------ 27877/1593489. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a a)(^y.(a a))) 6. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 27878/1593498. ------ 1. ==[ start ]==> ((a (a (a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(a ((^x.x)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(a (a a))) REDUCED to normal form. ------ 27879/1593507. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a)) a)) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a)) a)) 5. ==[ beta ]==> (((^y.(a a)) a)((^y.(a a)) a)) 6. ==[ alpha ]==> (((^x.(a a)) a)((^y.(a a)) a)) 7. ==[ beta ]==> ((a a)((^y.(a a)) a)) 8. ==[ alpha ]==> ((a a)((^x.(a a)) a)) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 27880/1593534. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.b) b)) 3. ==[ beta ]==> ((^y.y)((^x1.b) b)) 4. ==[ alpha ]==> ((^x.x)((^y.b) b)) 5. ==[ beta ]==> ((^y.b) b) 6. ==[ alpha ]==> ((^x.b) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 27881/1593651. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(c (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(c (^z.a))) REDUCED to normal form. ------ 27882/1593678. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b (^x1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.b))) REDUCED to normal form. ------ 27883/1593705. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 27884/1593723. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 27885/1593813. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((b b)((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(a (a a)))) 5. ==[ beta ]==> ((b b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 27886/1593858. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27887/1593885. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.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. ------ 27888/1593939. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 27889/1593948. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 27890/1593975. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 27891/1594002. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 27892/1594029. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 27893/1594056. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 27894/1594083. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 27895/1594146. ------ 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)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 27896/1594173. ------ 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.y) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a (a a)) a)) REDUCED to normal form. ------ 27897/1594200. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a (a a)))) REDUCED to normal form. ------ 27898/1594227. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 27899/1594254. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(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. ------ 27900/1594317. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 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. ------ 27901/1594371. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (a (((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a (((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> (a (a (^y.(y y)))) 8. ==[ alpha ]==> (a (a (^x.(x x)))) REDUCED to normal form. ------ 27902/1594407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 27903/1594434. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.x)((a a) a))) 3. ==[ beta ]==> ((((a a) a) a)((a a) a)) REDUCED to normal form. ------ 27904/1594452. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a) a)) 3. ==[ beta ]==> (((a a) a)(((a a) a) a)) REDUCED to normal form. ------ 27905/1594479. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((^y.y)(^z.z)) b) 6. ==[ alpha ]==> (((^x.x)(^y.y)) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 27906/1594488. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^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. ------ 27907/1594515. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(^z.a))) 7. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 27908/1594542. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 27909/1594569. ------ 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))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27910/1594614. ------ 1. ==[ start ]==> ((a (^a.b))((^c.a) a)) 2. ==[ alpha ]==> ((a (^x.b))((^y.a) a)) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 27911/1594632. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))(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. ------ 27912/1594659. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 27913/1594686. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((a (a (a a)))(a ((^y.y) a))) 6. ==[ alpha ]==> ((a (a (a a)))(a ((^x.x) a))) 7. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 27914/1594713. ------ 1. ==[ start ]==> (((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)))) 3. ==[ beta ]==> (((a (a a)) a)((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 27915/1594740. ------ 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)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 27916/1594785. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.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. ------ 27917/1594803. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 27918/1594884. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)(^z.(^x1.x1)))) IRREDUCIBLE: cycle. ------ 27919/1594947. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) b)((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a) b)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 27920/1594965. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) a) c)) 3. ==[ beta ]==> (b (((^z.z) a) c)) 4. ==[ alpha ]==> (b (((^x.x) a) c)) 5. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 27921/1594974. ------ 1. ==[ start ]==> (((a b) a)((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 27922/1595001. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 27923/1595073. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y)) b)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y)) b)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x)) b)) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b b)) REDUCED to normal form. ------ 27924/1595109. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(c (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c (^z.a))) 5. ==[ beta ]==> ((^y.a)(c (^z.a))) 6. ==[ alpha ]==> ((^x.a)(c (^y.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27925/1595136. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 27926/1595163. ------ 1. ==[ start ]==> (((a b)(^a.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 27927/1595181. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(^y.y))) REDUCED to normal form. ------ 27928/1595352. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 27929/1595361. ------ 1. ==[ start ]==> (((a b)(a a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))(b ((^x.x) a))) 3. ==[ beta ]==> (((a b)(a a))(b a)) REDUCED to normal form. ------ 27930/1595388. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(a (a (a a)))) 3. ==[ beta ]==> ((a (a a))(a (a (a a)))) REDUCED to normal form. ------ 27931/1595397. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z)) a)) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z)) a)) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y)) a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27932/1595424. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a) b)) 3. ==[ beta ]==> ((^y.y)((^x1.a) b)) 4. ==[ alpha ]==> ((^x.x)((^y.a) b)) 5. ==[ beta ]==> ((^y.a) b) 6. ==[ alpha ]==> ((^x.a) b) 7. ==[ beta ]==> a REDUCED to normal form. ------ 27933/1595559. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> (b ((a a)(^x1.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 27934/1595568. ------ 1. ==[ start ]==> (((a b) b)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a b) b)((^y.y) a)) 4. ==[ alpha ]==> (((a b) b)((^x.x) a)) 5. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 27935/1595595. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.y))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 27936/1595613. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(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)) REDUCED to normal form. ------ 27937/1595622. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 27938/1595640. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a a) c)) 3. ==[ beta ]==> ((^y.y)((a a) c)) 4. ==[ alpha ]==> ((^x.x)((a a) c)) 5. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 27939/1595649. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 27940/1595694. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1)) b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) b)) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) b)) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 11. ==[ beta ]==> ((^y.(^z.z)) b) 12. ==[ alpha ]==> ((^x.(^y.y)) b) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27941/1595703. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 27942/1595730. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.a))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.a))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.a))) 7. ==[ beta ]==> ((a (^y.a))(a (^y.a))) 8. ==[ alpha ]==> ((a (^x.a))(a (^y.a))) REDUCED to normal form. ------ 27943/1595757. ------ 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)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 27944/1595775. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 27945/1595784. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 27946/1595811. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^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))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 27947/1595847. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (a (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(a (a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(a (a (^x.x)))) REDUCED to normal form. ------ 27948/1595874. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(a a))) REDUCED to normal form. ------ 27949/1595901. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(b a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(b a)) 3. ==[ beta ]==> ((a ((a a) a))(b a)) REDUCED to normal form. ------ 27950/1595928. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a b)) 3. ==[ beta ]==> (((a (a a))(^y.y))(a b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a b)) REDUCED to normal form. ------ 27951/1595955. ------ 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 ]==> (((^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. ------ 27952/1595982. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(a a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(a a)) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 27953/1596588. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(a a)))((^y.(^z.(a a)))(^y.(^z.(a a))))) 4. ==[ alpha ]==> ((^x.(^y.(a a)))((^z.(^x1.(a a)))(^y1.(^z1.(a a))))) 5. ==[ beta ]==> (^y.(a a)) 6. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 27954/1597371. ------ 1. ==[ start ]==> ((^a.((a a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.(^z.b))) 3. ==[ beta ]==> (((^y.(^z.b))(^y.(^z.b)))(^y.(^z.b))) 4. ==[ alpha ]==> (((^x.(^y.b))(^z.(^x1.b)))(^y1.(^z1.b))) 5. ==[ beta ]==> ((^y.b)(^y1.(^z1.b))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 27955/1597704. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((z z) z))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27956/1598478. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(x1 x1)))(^z.(^x1.(x1 x1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(z z)))(^x1.(^y1.(y1 y1))))) 5. ==[ beta ]==> ((^y.(^z.(z z)))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 27957/1599075. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a)) b) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a)) b) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 27958/1599099. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27959/1599180. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 27960/1599225. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> ((b (^z.(a a)))(^y.y)) 4. ==[ alpha ]==> ((b (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 27961/1599414. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)((a a) a))) 3. ==[ eta ]==> ((^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 REDUCED to normal form. ------ 27962/1599462. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(a a)))) REDUCED to normal form. ------ 27963/1599684. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^y.y)(^z.(a a)))((^y.y)(^z.(a a))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.(a a)))((^y1.y1)(^z1.(a a))))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.(a a)))((^y1.y1)(^z1.(a a))))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.(a a)))((^x1.x1)(^y1.(a a))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27964/1599687. ------ 1. ==[ start ]==> ((a (a (a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(a a)))) REDUCED to normal form. ------ 27965/1599696. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((^y.(y y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((^x.(x x))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((^y.((^z.z)(y y)))(^y.((^z.z)(y y)))) 6. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.((^x1.x1)(z z)))) 7. ==[ beta ]==> ((^y.y)((^z.((^x1.x1)(z z)))(^z.((^x1.x1)(z z))))) 8. ==[ alpha ]==> ((^x.x)((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1))))) 9. ==[ beta ]==> ((^y.((^z.z)(y y)))(^x1.((^y1.y1)(x1 x1)))) 10. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.((^x1.x1)(z z)))) IRREDUCIBLE: cycle. ------ 27966/1600035. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 27967/1600467. ------ 1. ==[ start ]==> ((^a.((a a) a))(a (^a.b))) 2. ==[ alpha ]==> ((^x.((x x) x))(a (^y.b))) 3. ==[ beta ]==> (((a (^y.b))(a (^y.b)))(a (^y.b))) 4. ==[ alpha ]==> (((a (^x.b))(a (^y.b)))(a (^z.b))) REDUCED to normal form. ------ 27968/1600470. ------ 1. ==[ start ]==> ((a ((a a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.b))) REDUCED to normal form. ------ 27969/1600800. ------ 1. ==[ start ]==> ((^a.(^a.b))(a ((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(a ((a a) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 27970/1600803. ------ 1. ==[ start ]==> ((a (^a.b))(^a.((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((y y) y))) REDUCED to normal form. ------ 27971/1600980. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(a a)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(a a)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 27972/1601343. ------ 1. ==[ start ]==> (((^a.b)(a a))(^c.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(a (a a)))) 3. ==[ beta ]==> (b (^y.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 27973/1601469. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(a (a a)))) REDUCED to normal form. ------ 27974/1601574. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) 5. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(z z)))) 9. ==[ beta ]==> (((^y.y)(^z.(z z)))((^y.y)(^z.(z z)))) 10. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 27975/1601577. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 27976/1601586. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(z (z z)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(z (z z)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(y (y y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 27977/1601667. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 5. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1) 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. ------ 27978/1601757. ------ 1. ==[ start ]==> (((a b) b)(^c.(^b.a))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.a))) REDUCED to normal form. ------ 27979/1601838. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 27980/1601919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.c)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.c)) 5. ==[ beta ]==> ((^y.(y y))(^z.c)) 6. ==[ alpha ]==> ((^x.(x x))(^y.c)) 7. ==[ beta ]==> ((^y.c)(^y.c)) 8. ==[ alpha ]==> ((^x.c)(^y.c)) 9. ==[ beta ]==> c REDUCED to normal form. ------ 27981/1601973. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 27982/1602036. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27983/1602090. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 27984/1602117. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(a a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a a))) REDUCED to normal form. ------ 27985/1602144. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^b.(^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. ------ 27986/1602171. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.(^z.z))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 27987/1602201. ------ 1. ==[ start ]==> ((a (^a.a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((a (^x.x))(((a a) a) a)) REDUCED to normal form. ------ 27988/1602228. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (a a))) 7. ==[ beta ]==> ((^y.y)(a (a a))) 8. ==[ alpha ]==> ((^x.x)(a (a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 27989/1602255. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a a))((^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)))) 5. ==[ beta ]==> ((a a)((a (a a))(^y.y))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.x))) REDUCED to normal form. ------ 27990/1602282. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 27991/1602327. ------ 1. ==[ start ]==> ((a (a (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 27992/1602336. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1)(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. ------ 27993/1602372. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 27994/1602399. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 27995/1602426. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.a))) REDUCED to normal form. ------ 27996/1602462. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 27997/1602480. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) 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. ------ 27998/1602489. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 10. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 27999/1602516. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a a)((^y.a)((a a) a))) 4. ==[ alpha ]==> ((a a)((^x.a)((a a) a))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 28000/1602561. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(a a)))) REDUCED to normal form. ------ 28001/1602588. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((a a)(((^y.y)(a a)) a)) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a)) a)) 5. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 28002/1602615. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b) b)) 2. ==[ alpha ]==> (((a a)(^x.a))((a b) b)) REDUCED to normal form. ------ 28003/1602705. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 28004/1602732. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 28005/1602759. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 28006/1602786. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(a a))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(a a))) REDUCED to normal form. ------ 28007/1602795. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.(y y))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((a ((^y.y)(a a)))(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x)(a a)))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((a (a a))(a ((^y.y)(a a)))) 8. ==[ alpha ]==> ((a (a a))(a ((^x.x)(a a)))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 28008/1602822. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a b)(a a))) 3. ==[ beta ]==> ((^y.y)((a b)(a a))) 4. ==[ alpha ]==> ((^x.x)((a b)(a a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 28009/1602858. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a) c)) 3. ==[ beta ]==> ((a b)((^y.a) c)) 4. ==[ alpha ]==> ((a b)((^x.a) c)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 28010/1602876. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a)) 9. ==[ beta ]==> ((^y.y)((^z.z) a)) 10. ==[ alpha ]==> ((^x.x)((^y.y) a)) 11. ==[ beta ]==> ((^y.y) a) 12. ==[ alpha ]==> ((^x.x) a) 13. ==[ beta ]==> a REDUCED to normal form. ------ 28011/1602903. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 28012/1602930. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 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))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 28013/1602984. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a a)(a b))) 3. ==[ beta ]==> (((a a)(a a))((a a)(a b))) REDUCED to normal form. ------ 28014/1603029. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(a a))) 3. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 28015/1603083. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 28016/1603101. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (a a))(^y.(y y)))) 3. ==[ beta ]==> ((b b)((a (a a))(^y.(y y)))) 4. ==[ alpha ]==> ((b b)((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 28017/1603110. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 28018/1603137. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^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. ------ 28019/1603236. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a) a) b)) REDUCED to normal form. ------ 28020/1603362. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(b ((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(b ((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 28021/1603398. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.b) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) a)) 5. ==[ beta ]==> ((^y.y)((^z.b) a)) 6. ==[ alpha ]==> ((^x.x)((^y.b) a)) 7. ==[ beta ]==> ((^y.b) a) 8. ==[ alpha ]==> ((^x.b) a) 9. ==[ beta ]==> b REDUCED to normal form. ------ 28022/1603542. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(b (^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.a))) 5. ==[ beta ]==> ((a a)(b (^y.a))) 6. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 28023/1603569. ------ 1. ==[ start ]==> ((a ((a a) a))(a (^a.b))) 2. ==[ alpha ]==> ((a ((a a) a))(a (^x.b))) REDUCED to normal form. ------ 28024/1603695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) 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. ------ 28025/1603776. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1)) 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. ------ 28026/1603902. ------ 1. ==[ start ]==> ((a (^a.b))(a ((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))(a ((a a) a))) REDUCED to normal form. ------ 28027/1604028. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 28028/1604073. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^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. ------ 28029/1604082. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(a a))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 28030/1604235. ------ 1. ==[ start ]==> ((((a a) a) b)((a (a a)) b)) REDUCED to normal form. ------ 28031/1604262. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a) c)) 2. ==[ alpha ]==> (((a b) a)(((^x.x) a) c)) 3. ==[ beta ]==> (((a b) a)(a c)) REDUCED to normal form. ------ 28032/1604280. ------ 1. ==[ start ]==> (((^a.a)(a b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(c ((^y.y) a))) 3. ==[ beta ]==> ((a b)(c ((^y.y) a))) 4. ==[ alpha ]==> ((a b)(c ((^x.x) a))) 5. ==[ beta ]==> ((a b)(c a)) REDUCED to normal form. ------ 28033/1604307. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(b (a (a a)))) 3. ==[ beta ]==> ((^y.y)(b (a (a a)))) 4. ==[ alpha ]==> ((^x.x)(b (a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 28034/1604343. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 28035/1604361. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(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. ------ 28036/1604370. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y)) b)) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(b b)) REDUCED to normal form. ------ 28037/1604397. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a) c)) 5. ==[ beta ]==> ((^y.a)((^z.a) c)) 6. ==[ alpha ]==> ((^x.a)((^y.a) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 28038/1604442. ------ 1. ==[ start ]==> (((^a.b)(a a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a a)(a (a a)))) 3. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 28039/1604487. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(a a))) 3. ==[ beta ]==> (((a a)(a b))((a a)(a a))) REDUCED to normal form. ------ 28040/1604514. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 28041/1604541. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 28042/1604568. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 28043/1604595. ------ 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 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.z))) 7. ==[ beta ]==> (a ((^y.(y y))(^z.z))) 8. ==[ alpha ]==> (a ((^x.(x x))(^y.y))) 9. ==[ beta ]==> (a ((^y.y)(^y.y))) 10. ==[ alpha ]==> (a ((^x.x)(^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 28044/1604622. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 28045/1604640. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.y)) c)) 3. ==[ beta ]==> (b ((a (^y.y)) c)) 4. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 28046/1604649. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 28047/1604676. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a (a a))(^y.(y y))) 6. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 28048/1604685. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (a (a a)))) 3. ==[ beta ]==> ((^y.(a a))(a (a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))(a (a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 28049/1604712. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a))) 5. ==[ beta ]==> (((^y.y) a)(a a)) 6. ==[ alpha ]==> (((^x.x) a)(a a)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 28050/1604766. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 28051/1604847. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 28052/1604856. ------ 1. ==[ start ]==> (((a b) b)((a a)(^b.a))) 2. ==[ alpha ]==> (((a b) b)((a a)(^x.a))) REDUCED to normal form. ------ 28053/1604883. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) a) a)) 3. ==[ beta ]==> (((a a) a)(((^y.y) a) a)) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a) a)) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 28054/1604910. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 28055/1604928. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b (a (^z.z)))) 3. ==[ beta ]==> ((^y.y)(b (a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 28056/1604937. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a) c)) REDUCED to normal form. ------ 28057/1604982. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a a))) 9. ==[ beta ]==> ((^y.y)((a (^z.z))(a a))) 10. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a))) 11. ==[ beta ]==> ((a (^y.y))(a a)) 12. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 28058/1604991. ------ 1. ==[ start ]==> (((a (a a))(^b.(^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)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 28059/1605045. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 28060/1605063. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b b)) 3. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 28061/1605072. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 28062/1605099. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 28063/1605135. ------ 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)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^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. ------ 28064/1605162. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.y))) REDUCED to normal form. ------ 28065/1605189. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a (^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 28066/1605216. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 28067/1605243. ------ 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))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 28068/1605270. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 28069/1605287. ------ 1. ==[ start ]==> (^a.((^a.b) c)) 2. ==[ alpha ]==> (^x.((^y.b) c)) 3. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 28070/1605288. ------ 1. ==[ start ]==> (a ((^a.b) c)) 2. ==[ alpha ]==> (a ((^x.b) c)) 3. ==[ beta ]==> (a b) REDUCED to normal form. ------ 28071/1606110. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 28072/1607001. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 28073/1607568. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 28074/1608390. ------ 1. ==[ start ]==> (((^a.b) c) a) 2. ==[ alpha ]==> (((^x.b) c) a) 3. ==[ beta ]==> (b a) REDUCED to normal form. ------ 28075/1608396. ------ 1. ==[ start ]==> ((^a.a)((^a.b) c)) 2. ==[ alpha ]==> ((^x.x)((^y.b) c)) 3. ==[ beta ]==> ((^y.b) c) 4. ==[ alpha ]==> ((^x.b) c) 5. ==[ beta ]==> b REDUCED to normal form. ------ 28076/1608552. ------ 1. ==[ start ]==> (((a a) b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)(^x.(a a))) REDUCED to normal form. ------ 28077/1608648. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (^y.((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (^x.((^y.a)((^z.z) a))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 28078/1608891. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 28079/1609002. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((^y.(^z.(a a)))(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.(a a)))(^z.(^x1.(a a)))) 7. ==[ beta ]==> (^y.(a a)) 8. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 28080/1609215. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 28081/1609218. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 28082/1609341. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 28083/1609605. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(x1 b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z b))) 5. ==[ beta ]==> ((^y.y)(^z.(z b))) 6. ==[ alpha ]==> ((^x.x)(^y.(y b))) 7. ==[ beta ]==> (^y.(y b)) 8. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 28084/1609947. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.((a a) a))) 3. ==[ beta ]==> (((a a) a)(^y.((a a) a))) 4. ==[ alpha ]==> (((a a) a)(^x.((a a) a))) REDUCED to normal form. ------ 28085/1610106. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 28086/1610109. ------ 1. ==[ start ]==> ((a (^a.b))(^b.(^c.a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 28087/1610286. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1)) b) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z)) b) 5. ==[ beta ]==> (((^y.y)(^z.z)) b) 6. ==[ alpha ]==> (((^x.x)(^y.y)) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 28088/1610550. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.((^a.a)(^a.a)))) 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)))(^z.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 28089/1610658. ------ 1. ==[ start ]==> (((a b)(^a.a))(^c.(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.(a (a a)))) REDUCED to normal form. ------ 28090/1610673. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 28091/1610676. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 28092/1610892. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(^z.(z z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 28093/1611396. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.b)) 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. ------ 28094/1611477. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.a)) 3. ==[ beta ]==> ((((a a) a) a)(^y.a)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.a)) REDUCED to normal form. ------ 28095/1611495. ------ 1. ==[ start ]==> (((^a.b) c)(^a.a)) 2. ==[ alpha ]==> (((^x.b) c)(^y.y)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 28096/1611507. ------ 1. ==[ start ]==> ((a a)((^a.b) c)) 2. ==[ alpha ]==> ((a a)((^x.b) c)) 3. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 28097/1611525. ------ 1. ==[ start ]==> (((^a.a) a)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x) a)(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (a (((a a) a)((^y.y) a))) 4. ==[ alpha ]==> (a (((a a) a)((^x.x) a))) 5. ==[ beta ]==> (a (((a a) a) a)) REDUCED to normal form. ------ 28098/1611552. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a a) a)(a (a a))) REDUCED to normal form. ------ 28099/1611579. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y)(^z.z)))) 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. ------ 28100/1611606. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (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. ------ 28101/1611633. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))(a b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a b))) 5. ==[ beta ]==> ((a (^y.y))(a b)) 6. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 28102/1611651. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 28103/1611660. ------ 1. ==[ start ]==> (((a a) b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a) b)((a a)(a a))) REDUCED to normal form. ------ 28104/1611705. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^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 a)) REDUCED to normal form. ------ 28105/1611732. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 28106/1611759. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 28107/1611777. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 28108/1611804. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 28109/1611840. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)((a a) a))) 3. ==[ beta ]==> ((^y.a)((^z.a)((a a) a))) 4. ==[ alpha ]==> ((^x.a)((^y.a)((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 28110/1611867. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^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. ------ 28111/1611921. ------ 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))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 28112/1611948. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(^z1.z1)))) 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. ------ 28113/1612002. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 28114/1612092. ------ 1. ==[ start ]==> (((^a.(a a)) a)(b (a b))) 2. ==[ alpha ]==> (((^x.(x x)) a)(b (a b))) 3. ==[ beta ]==> ((a a)(b (a b))) REDUCED to normal form. ------ 28115/1612110. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.(a a)))((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.(a a)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.(a a)))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.(a a)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 28116/1612173. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a) a)(a (^y.y)))) 3. ==[ beta ]==> ((a b)(((a a) a)(a (^y.y)))) 4. ==[ alpha ]==> ((a b)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 28117/1612200. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)((^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. ------ 28118/1612227. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 28119/1612254. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.z))) REDUCED to normal form. ------ 28120/1612281. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 28121/1612299. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(b (^y.b))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.b))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.b))) REDUCED to normal form. ------ 28122/1612308. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(a b))) REDUCED to normal form. ------ 28123/1612326. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 28124/1612344. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a b)(^x.x))) REDUCED to normal form. ------ 28125/1612371. ------ 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.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 28126/1612398. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.a))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.a)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.a)) REDUCED to normal form. ------ 28127/1612425. ------ 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. ------ 28128/1612452. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^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. ------ 28129/1612461. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^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. ------ 28130/1612488. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(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. ------ 28131/1612542. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.z1))) 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. ------ 28132/1612596. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.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. ------ 28133/1612623. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 7. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 28134/1612659. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.a))(c (^z.z))) 6. ==[ alpha ]==> ((a (^x.a))(c (^y.y))) REDUCED to normal form. ------ 28135/1612686. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 28136/1612713. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a b))) 5. ==[ beta ]==> ((^y.y)(a (a b))) 6. ==[ alpha ]==> ((^x.x)(a (a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 28137/1612776. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 28138/1612920. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.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. ------ 28139/1612974. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> (a ((^z.(z z))((^x1.x1) 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. ------ 28140/1613055. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a a) a)((^y.y)((a a) a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 28141/1613136. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))(^x1.a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))(^z.a))) 7. ==[ beta ]==> ((a a)((^y.(y y))(^z.a))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(^y.a))) 9. ==[ beta ]==> ((a a)((^y.a)(^y.a))) 10. ==[ alpha ]==> ((a a)((^x.a)(^y.a))) 11. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 28142/1613199. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 28143/1613217. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (^x.b))(^z.a)) 4. ==[ alpha ]==> ((a (^x.b))(^y.a)) REDUCED to normal form. ------ 28144/1613262. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 28145/1613397. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^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. ------ 28146/1613406. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 28147/1613487. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (a a)))) IRREDUCIBLE: cycle. ------ 28148/1613568. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.y1)))) 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. ------ 28149/1613595. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 28150/1613604. ------ 1. ==[ start ]==> (((a a)(^a.b))(c ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(c ((^y.y) a))) 3. ==[ beta ]==> (((a a)(^x.b))(c a)) REDUCED to normal form. ------ 28151/1613622. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) 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. ------ 28152/1613658. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 28153/1613685. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (a a))(a a))) REDUCED to normal form. ------ 28154/1613712. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(((^z.z) a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a)(a (^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 28155/1613739. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 28156/1613757. ------ 1. ==[ start ]==> (((^a.b)(a a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(b (^y.(y y)))) 3. ==[ beta ]==> (b (b (^y.(y y)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 28157/1613766. ------ 1. ==[ start ]==> (((a b)(^a.a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 28158/1613784. ------ 1. ==[ start ]==> ((a (^b.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 28159/1613802. ------ 1. ==[ start ]==> (((a a)(a b))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a b))((a (a a))(^x.x))) REDUCED to normal form. ------ 28160/1613829. ------ 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)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 28161/1613856. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 28162/1613883. ------ 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. ------ 28163/1613910. ------ 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 ]==> (((^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. ------ 28164/1613937. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) a) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a b)) REDUCED to normal form. ------ 28165/1613955. ------ 1. ==[ start ]==> (((^a.b) b)(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(c (a (^y.y)))) 3. ==[ beta ]==> (b (c (a (^y.y)))) 4. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 28166/1613964. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x)) c)) REDUCED to normal form. ------ 28167/1614000. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 28168/1614081. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.a))) 5. ==[ beta ]==> ((^y.y)(b (^y1.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 28169/1614162. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 28170/1614171. ------ 1. ==[ start ]==> (((a b) b)(b c)) REDUCED to normal form. ------ 28171/1614216. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.y))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 28172/1614225. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c (a a))) REDUCED to normal form. ------ 28173/1614243. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 28174/1614252. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (a (^z.z)))) REDUCED to normal form. ------ 28175/1614306. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 28176/1614333. ------ 1. ==[ start ]==> ((((^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.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a (^y.y)))) 7. ==[ beta ]==> (((a a)(a (^y.y)))((a a)(a (^y.y)))) 8. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 28177/1614360. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c a)) REDUCED to normal form. ------ 28178/1614378. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 28179/1614387. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 28180/1614450. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a a) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a) b)) 3. ==[ beta ]==> (((a a)(a a))((a a) b)) REDUCED to normal form. ------ 28181/1614477. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 28182/1614504. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y) b)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) b)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) b)) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 28183/1614531. ------ 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))(^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 28184/1614558. ------ 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 ]==> (((^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. ------ 28185/1614585. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.a) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y) a)) 3. ==[ beta ]==> ((((a a) a) a)((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x) a)) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 28186/1614603. ------ 1. ==[ start ]==> (((^a.b) c)(a a)) 2. ==[ alpha ]==> (((^x.b) c)(a a)) 3. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 28187/1614611. ------ 1. ==[ start ]==> (^a.((a b)(a (^a.a)))) 2. ==[ alpha ]==> (^x.((x b)(x (^y.y)))) REDUCED to normal form. ------ 28188/1614612. ------ 1. ==[ start ]==> (a ((a b)(a (^a.a)))) 2. ==[ alpha ]==> (a ((a b)(a (^x.x)))) REDUCED to normal form. ------ 28189/1617714. ------ 1. ==[ start ]==> (((^a.b) c) b) 2. ==[ alpha ]==> (((^x.b) c) b) 3. ==[ beta ]==> (b b) REDUCED to normal form. ------ 28190/1617723. ------ 1. ==[ start ]==> (((a b)(a (^a.a))) a) 2. ==[ alpha ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 28191/1617729. ------ 1. ==[ start ]==> ((^a.a)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.x)((a b)(a (^y.y)))) 3. ==[ beta ]==> ((a b)(a (^y.y))) 4. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 28192/1617738. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.b) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 28193/1617756. ------ 1. ==[ start ]==> ((^a.(a a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x x))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)((^y.y) a))(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a) a)(((a a) a)((^y.y) a))) 6. ==[ alpha ]==> ((((a a) a) a)(((a a) a)((^x.x) a))) 7. ==[ beta ]==> ((((a a) a) a)(((a a) a) a)) REDUCED to normal form. ------ 28194/1617783. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 28195/1617864. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(a b))) 3. ==[ beta ]==> (((a (^z.z))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 28196/1617981. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a)(^z.a))) 3. ==[ beta ]==> (^y.(((a a) a)(^z.a))) 4. ==[ alpha ]==> (^x.(((a a) a)(^y.a))) REDUCED to normal form. ------ 28197/1618128. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 28198/1618323. ------ 1. ==[ start ]==> ((^a.(a (a a)))(b (a b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(b (a b))) 3. ==[ beta ]==> ((b (a b))((b (a b))(b (a b)))) REDUCED to normal form. ------ 28199/1618938. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^b.(^a.b))) 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. ------ 28200/1619106. ------ 1. ==[ start ]==> ((^a.((a a) a))((a a)((a a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((a a)((a a) a))) 3. ==[ beta ]==> ((((a a)((a a) a))((a a)((a a) a)))((a a)((a a) a))) REDUCED to normal form. ------ 28201/1619460. ------ 1. ==[ start ]==> (((a a)((a a) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.((x x) x))) REDUCED to normal form. ------ 28202/1619613. ------ 1. ==[ start ]==> (((^a.b) a)(^a.(^c.a))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(^z.y))) 3. ==[ beta ]==> (b (^y.(^z.y))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 28203/1619883. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 28204/1620213. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b ((^z.z) a))) 3. ==[ beta ]==> ((^y.y)((b ((^z.z) a))(b ((^z.z) a)))) 4. ==[ alpha ]==> ((^x.x)((b ((^y.y) a))(b ((^z.z) a)))) 5. ==[ beta ]==> ((b ((^y.y) a))(b ((^z.z) a))) 6. ==[ alpha ]==> ((b ((^x.x) a))(b ((^y.y) a))) 7. ==[ beta ]==> ((b a)(b ((^y.y) a))) 8. ==[ alpha ]==> ((b a)(b ((^x.x) a))) 9. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 28205/1620225. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.d)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.d)) 3. ==[ beta ]==> ((^y.(a a))(^z.d)) 4. ==[ alpha ]==> ((^x.(a a))(^y.d)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 28206/1620423. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.((^z.z) a))) 3. ==[ beta ]==> (((a a) a)(^y.((^z.z) a))) 4. ==[ alpha ]==> (((a a) a)(^x.((^y.y) a))) 5. ==[ beta ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 28207/1620585. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 28208/1620639. ------ 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)))) REDUCED to normal form. ------ 28209/1620702. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 28210/1620783. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.b)) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.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. ------ 28211/1620810. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.(y y))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(y y))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(x x))) REDUCED to normal form. ------ 28212/1620828. ------ 1. ==[ start ]==> (((^a.b) c)(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 28213/1620837. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^a.a)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 28214/1620849. ------ 1. ==[ start ]==> ((a a)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((a a)((a b)(a (^x.x)))) REDUCED to normal form. ------ 28215/1620858. ------ 1. ==[ start ]==> ((a (^a.a))((^a.b) c)) 2. ==[ alpha ]==> ((a (^x.x))((^y.b) c)) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 28216/1620876. ------ 1. ==[ start ]==> ((a (a a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a a))(((a a) a)((^x.x) a))) 3. ==[ beta ]==> ((a (a a))(((a a) a) a)) REDUCED to normal form. ------ 28217/1620903. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> ((a b)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a b)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 28218/1620957. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(a ((a a) a))) REDUCED to normal form. ------ 28219/1620984. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 28220/1621002. ------ 1. ==[ start ]==> (((a a) b)(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a) b)(b (^x.(a a)))) REDUCED to normal form. ------ 28221/1621047. ------ 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. ------ 28222/1621056. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 28223/1621074. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(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. ------ 28224/1621083. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 28225/1621101. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 28226/1621137. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^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. ------ 28227/1621182. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((^y.a)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 28228/1621209. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 28229/1621218. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 28230/1621245. ------ 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)((^y.y)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 28231/1621263. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a)) a)) 5. ==[ beta ]==> (a (((^y.y)(a a)) a)) 6. ==[ alpha ]==> (a (((^x.x)(a a)) a)) 7. ==[ beta