Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 125001/12534753. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a b)(^x.x))(a (b a))) REDUCED to normal form. ------ 125002/12534771. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125003/12534843. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 125004/12534870. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 125005/12534897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(^z.a))) 5. ==[ beta ]==> (((^y.y) a)((b a)(^z.a))) 6. ==[ alpha ]==> (((^x.x) a)((b a)(^y.a))) 7. ==[ beta ]==> (a ((b a)(^y.a))) 8. ==[ alpha ]==> (a ((b a)(^x.a))) REDUCED to normal form. ------ 125006/12534924. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 125007/12534951. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 125008/12534978. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)(^y.a))) 3. ==[ beta ]==> ((a (a a))((a b)(^y.a))) 4. ==[ alpha ]==> ((a (a a))((a b)(^x.a))) REDUCED to normal form. ------ 125009/12534987. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((^y.(a a))((^z.b)((a a) a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.b)((a a) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125010/12535014. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a b))) 5. ==[ beta ]==> ((^y.a)(a b)) 6. ==[ alpha ]==> ((^x.a)(a b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 125011/12535068. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 9. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 10. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 125012/12535149. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 125013/12535203. ------ 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.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 125014/12535284. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 11. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 12. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125015/12535365. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125016/12535491. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b) 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. ------ 125017/12535518. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 125018/12535590. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 125019/12535824. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 125020/12535905. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 125021/12535932. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125022/12535986. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 125023/12536067. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125024/12536409. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 125025/12536643. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 125026/12536688. ------ 1. ==[ start ]==> (((^a.a)(b a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 125027/12536769. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 125028/12536850. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a 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. ------ 125029/12536958. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(b a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 125030/12536976. ------ 1. ==[ start ]==> (((a a)(b a))((b a) a)) REDUCED to normal form. ------ 125031/12537003. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 125032/12537237. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(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. ------ 125033/12537552. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 125034/12537579. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((^y.b)((^z.z) a)) 6. ==[ alpha ]==> ((^x.b)((^y.y) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125035/12537633. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 125036/12537714. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125037/12537822. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125038/12537849. ------ 1. ==[ start ]==> ((a (^b.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 125039/12538029. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a)) b)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a)) b)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a)) b)) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 125040/12538056. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.b) c)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.b) c)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.b) c)) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 125041/12538128. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125042/12538173. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(c (^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.b))) 3. ==[ beta ]==> ((^y.y)(c (^z.b))) 4. ==[ alpha ]==> ((^x.x)(c (^y.b))) 5. ==[ beta ]==> (c (^y.b)) 6. ==[ alpha ]==> (c (^x.b)) REDUCED to normal form. ------ 125043/12538200. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(b (^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(b (^z1.(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. ------ 125044/12538335. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(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. ------ 125045/12538443. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125046/12538497. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 125047/12538578. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 125048/12538614. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c ((a a) a))) 5. ==[ beta ]==> ((^y.(a a))(c ((a a) a))) 6. ==[ alpha ]==> ((^x.(a a))(c ((a a) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125049/12538641. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(b (a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(b (a b))) REDUCED to normal form. ------ 125050/12538659. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 125051/12538668. ------ 1. ==[ start ]==> (((a b)(^c.a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(a (a a))) REDUCED to normal form. ------ 125052/12538695. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 125053/12538722. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 125054/12538776. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 125055/12538803. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 125056/12538893. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(^y.y))) 3. ==[ beta ]==> ((a (b a))((a b)(^y.y))) 4. ==[ alpha ]==> ((a (b a))((a b)(^x.x))) REDUCED to normal form. ------ 125057/12538920. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 125058/12538947. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.a))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.a))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.a))) 11. ==[ beta ]==> ((a a)(^y.a)) 12. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 125059/12538974. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 125060/12539001. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 125061/12539055. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.b))) REDUCED to normal form. ------ 125062/12539109. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a) b)) REDUCED to normal form. ------ 125063/12539136. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z)) c)) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y)) c)) 5. ==[ beta ]==> ((b (a a))((^y.y) c)) 6. ==[ alpha ]==> ((b (a a))((^x.x) c)) 7. ==[ beta ]==> ((b (a a)) c) REDUCED to normal form. ------ 125064/12539199. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 125065/12539442. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(a (^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125066/12539523. ------ 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))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) 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. ------ 125067/12539550. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^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. ------ 125068/12539604. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.y)((a a) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.y)((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.x)((a a) a))) 5. ==[ beta ]==> (((b a)(b a))((a a) a)) REDUCED to normal form. ------ 125069/12539685. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125070/12539748. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 125071/12539802. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 125072/12539829. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 125073/12539856. ------ 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) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 125074/12539946. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 125075/12539973. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 125076/12540000. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.a))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.a))) REDUCED to normal form. ------ 125077/12540027. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 125078/12540054. ------ 1. ==[ start ]==> (((a b)(a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 125079/12540081. ------ 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)) a)) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^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. ------ 125080/12540108. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (a a)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a)) b)) REDUCED to normal form. ------ 125081/12540216. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 125082/12540243. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y)) b)) 3. ==[ beta ]==> ((a (b (^x.x)))(b b)) REDUCED to normal form. ------ 125083/12540333. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a (^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125084/12540414. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125085/12540522. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125086/12540558. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (a (a a)))) 3. ==[ beta ]==> ((b c)(a (a (a a)))) REDUCED to normal form. ------ 125087/12540585. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) a)(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a (a a))) REDUCED to normal form. ------ 125088/12540630. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b (^z.a))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.a))) REDUCED to normal form. ------ 125089/12540657. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(a (^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 5. ==[ beta ]==> (a (^y.(y y))) 6. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 125090/12540693. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c b)) 3. ==[ beta ]==> ((a (^y.y))(c b)) 4. ==[ alpha ]==> ((a (^x.x))(c b)) REDUCED to normal form. ------ 125091/12540711. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 125092/12540720. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b c)) REDUCED to normal form. ------ 125093/12540792. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125094/12540801. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b (a (^y.y)))) REDUCED to normal form. ------ 125095/12540828. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.b))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 125096/12540900. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(a (^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125097/12540936. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b b)) 3. ==[ beta ]==> ((b (^y.a))(b b)) 4. ==[ alpha ]==> ((b (^x.a))(b b)) REDUCED to normal form. ------ 125098/12541026. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 125099/12541053. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 125100/12541080. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(^z.z))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(^z.z))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.y))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 125101/12541107. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 125102/12541134. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y) a)) 5. ==[ beta ]==> ((b a)((^y.y) a)) 6. ==[ alpha ]==> ((b a)((^x.x) a)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 125103/12541160. ------ 1. ==[ start ]==> (^a.(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (^x.(((x x) x)((x x)(^y.y)))) REDUCED to normal form. ------ 125104/12541161. ------ 1. ==[ start ]==> (a (((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (a (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 125105/12545079. ------ 1. ==[ start ]==> ((^a.(b a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(y (^z.(^x1.x1))))) 3. ==[ eta ]==> (b (^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 125106/12545916. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(b x1))) 3. ==[ eta ]==> ((^x.(x (^y.(^z.z)))) b) 4. ==[ beta ]==> (b (^y.(^z.z))) 5. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 125107/12549834. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a))) a) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 125108/12549840. ------ 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. ------ 125109/12549867. ------ 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))(b a))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(b a))) 8. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(b a))) 9. ==[ beta ]==> ((b a)((^y.y)(b a))) 10. ==[ alpha ]==> ((b a)((^x.x)(b a))) 11. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 125110/12549894. ------ 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 REDUCED to normal form. ------ 125111/12549975. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(b (^z.z)))(^y.y)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 125112/12550092. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((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)))) REDUCED to normal form. ------ 125113/12550761. ------ 1. ==[ start ]==> (((a (a a))(a a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 125114/12550785. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(a 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. ------ 125115/12551481. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 125116/12551550. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 125117/12552498. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (b (^x1.(^y1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 125118/12552507. ------ 1. ==[ start ]==> (((a b) b)(^b.((^a.a) b))) 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. ------ 125119/12552840. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a ((a a) a))(^y.((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.((^y.y) b))) 5. ==[ beta ]==> ((a ((a a) a))(^x.b)) REDUCED to normal form. ------ 125120/12552999. ------ 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 ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))(^y.y)) 4. ==[ alpha ]==> (((((a a) a)((a a) a))(((a a) a)((a a) a)))(^x.x)) REDUCED to normal form. ------ 125121/12553452. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 125122/12553755. ------ 1. ==[ start ]==> ((^a.(b a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(a (a (^y.(^z.z))))) 3. ==[ eta ]==> (b (a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 125123/12553758. ------ 1. ==[ start ]==> ((a (b a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 125124/12554592. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a (b a))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 125125/12554595. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(b z))) 3. ==[ eta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 125126/12555099. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 125127/12555351. ------ 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)))) REDUCED to normal form. ------ 125128/12555510. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 125129/12555801. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^z.(a a))) REDUCED to normal form. ------ 125130/12556017. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 125131/12556953. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.a))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 125132/12557268. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 125133/12557565. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 125134/12557589. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125135/12557907. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(y y)))) REDUCED to normal form. ------ 125136/12558177. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 125137/12558249. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.c)) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.c)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125138/12558258. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.x1))) REDUCED to normal form. ------ 125139/12558312. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 125140/12558375. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 125141/12558456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 125142/12558483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(z z))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(z z))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(y y))) 5. ==[ beta ]==> ((b a)(^y.(y y))) 6. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 125143/12558510. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 125144/12558522. ------ 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. ------ 125145/12558549. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> ((a (a a))((^y.y)(b a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(b a))) 5. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 125146/12558576. ------ 1. ==[ start ]==> ((a b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 125147/12558621. ------ 1. ==[ start ]==> (((^a.a) b)(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 125148/12558630. ------ 1. ==[ start ]==> (((a a)(a a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 125149/12558657. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 125150/12558693. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 125151/12558720. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 125152/12558747. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^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. ------ 125153/12558756. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 125154/12558774. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 125155/12558855. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 125156/12558882. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 125157/12558891. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 125158/12558945. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 125159/12558963. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125160/12558972. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a (^y1.(^z1.z1)))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.(^x2.x2))))) REDUCED to normal form. ------ 125161/12558999. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 125162/12559125. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b) c)) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) b) c)) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) b) c)) 5. ==[ beta ]==> ((((^y.y) b) c)(((^y.y) b) c)) 6. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) b) c)) 7. ==[ beta ]==> ((b c)(((^y.y) b) c)) 8. ==[ alpha ]==> ((b c)(((^x.x) b) c)) 9. ==[ beta ]==> ((b c)(b c)) REDUCED to normal form. ------ 125163/12559242. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 125164/12559269. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 125165/12559413. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b ((a a)(a a)))) REDUCED to normal form. ------ 125166/12559440. ------ 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. ------ 125167/12559467. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^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))) REDUCED to normal form. ------ 125168/12559476. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125169/12559503. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1) c)) 3. ==[ beta ]==> ((^y.y)((^x1.x1) 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. ------ 125170/12559764. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 125171/12559791. ------ 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 a)(a a)))) REDUCED to normal form. ------ 125172/12559935. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 125173/12559989. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b)(^z.b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b)(^z.b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b)(^z.b))) 5. ==[ beta ]==> (a ((a b)(^z.b))) 6. ==[ alpha ]==> (a ((a b)(^x.b))) REDUCED to normal form. ------ 125174/12560025. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.a)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125175/12560052. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 125176/12560097. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125177/12560106. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 125178/12560133. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 125179/12560160. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a a)(a a))) REDUCED to normal form. ------ 125180/12560214. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 125181/12560232. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 125182/12560403. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125183/12560583. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 125184/12560817. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 125185/12560844. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a a) b)) REDUCED to normal form. ------ 125186/12560970. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) 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. ------ 125187/12561015. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.(a a))((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.(a a))((a b)(^y.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125188/12561042. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a) a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 5. ==[ beta ]==> (((a a) a)(^y.b)) 6. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 125189/12561096. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^y1.(^z1.z1)))) 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. ------ 125190/12561177. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> (b ((a a)(^x1.x1))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 125191/12561186. ------ 1. ==[ start ]==> (((a b) b)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) b)((^x.x)((^y.y) b))) 3. ==[ beta ]==> (((a b) b)((^y.y) b)) 4. ==[ alpha ]==> (((a b) b)((^x.x) b)) 5. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 125192/12561213. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b)(^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. ------ 125193/12561231. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z))) b)) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 125194/12561240. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 125195/12561258. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 125196/12561321. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 125197/12561348. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((^y.(y y))((^z.b)(^x1.a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.b)(^z.a))) 7. ==[ beta ]==> (((^y.b)(^z.a))((^y.b)(^z.a))) 8. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(^x1.a))) 9. ==[ beta ]==> (b ((^z.b)(^x1.a))) 10. ==[ alpha ]==> (b ((^x.b)(^y.a))) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 125198/12561375. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 125199/12561402. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 125200/12561492. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 125201/12561519. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a ((^y.y) b))) 3. ==[ beta ]==> ((a ((a a) a))(a ((^y.y) b))) 4. ==[ alpha ]==> ((a ((a a) a))(a ((^x.x) b))) 5. ==[ beta ]==> ((a ((a a) a))(a b)) REDUCED to normal form. ------ 125202/12561546. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 125203/12561573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b a)(a (^y.y)))) 5. ==[ beta ]==> ((a (a a))((b a)(a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))((b a)(a (^x.x)))) REDUCED to normal form. ------ 125204/12561600. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> ((((a a) a) a)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 125205/12561627. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 125206/12561654. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))((a b)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((a b)(^x.x))) REDUCED to normal form. ------ 125207/12561681. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 125208/12561852. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 125209/12561861. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 125210/12561933. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 125211/12561960. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((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. ------ 125212/12561969. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 125213/12561996. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)((a a) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)((a a) a))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 125214/12562014. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(^z.b))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.b))) 7. ==[ beta ]==> ((((a a) a)((a a) a))(^y.b)) 8. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.b)) REDUCED to normal form. ------ 125215/12562050. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125216/12562077. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 125217/12562104. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 125218/12562131. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 125219/12562158. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 125220/12562410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (b a))) REDUCED to normal form. ------ 125221/12562437. ------ 1. ==[ start ]==> ((a (b a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 125222/12562671. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (^y.(^z.z)))) REDUCED to normal form. ------ 125223/12562743. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((b a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 125224/12562779. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 125225/12562797. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((a b)(a b))((a a)(^y.a))) 6. ==[ alpha ]==> (((a b)(a b))((a a)(^x.a))) REDUCED to normal form. ------ 125226/12562806. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 125227/12562860. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 125228/12562878. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^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. ------ 125229/12562887. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 125230/12562914. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(z z))(a b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(a b))) 5. ==[ beta ]==> (((a a)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 125231/12562941. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 125232/12563274. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (b a))) REDUCED to normal form. ------ 125233/12563553. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((a a)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125234/12563580. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125235/12563589. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 125236/12563607. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 125237/12563661. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 11. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 12. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 125238/12563670. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 125239/12563697. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((^y.b)((^z.(z z))((a a) a))) 6. ==[ alpha ]==> ((^x.b)((^y.(y y))((a a) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125240/12563742. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 125241/12563751. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 125242/12563778. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 125243/12563805. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 125244/12563850. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125245/12563859. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 125246/12564003. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(b ((^y.y)(a a)))) 6. ==[ alpha ]==> ((a b)(b ((^x.x)(a a)))) 7. ==[ beta ]==> ((a b)(b (a a))) REDUCED to normal form. ------ 125247/12564030. ------ 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. ------ 125248/12564057. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 125249/12564084. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a b)(a (^x.x)))) REDUCED to normal form. ------ 125250/12564111. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a) a) a)) REDUCED to normal form. ------ 125251/12564165. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (a a))(^z.z))) REDUCED to normal form. ------ 125252/12564192. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((a b)(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)((a a) a))) 5. ==[ beta ]==> ((a b)(a ((a a) a))) REDUCED to normal form. ------ 125253/12564363. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(y1 y1)))) 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. ------ 125254/12564471. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125255/12564480. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 125256/12564507. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.y))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 125257/12564525. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b) b)) 3. ==[ beta ]==> (((^y.y) b)((a b) b)) 4. ==[ alpha ]==> (((^x.x) b)((a b) b)) 5. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 125258/12564534. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 125259/12564642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125260/12564669. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 125261/12564696. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(a a))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 125262/12564867. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 125263/12564894. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(a b))) REDUCED to normal form. ------ 125264/12565362. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125265/12565506. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(a a))) 3. ==[ beta ]==> ((b b)((^y.a)(a a))) 4. ==[ alpha ]==> ((b b)((^x.a)(a a))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 125266/12565533. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 125267/12565551. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a (a a))(^y.a))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.a))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.a))) REDUCED to normal form. ------ 125268/12565578. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 125269/12565587. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^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. ------ 125270/12565614. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 125271/12565632. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a a)(^y.a))) 3. ==[ beta ]==> (((b a)(b a))((a a)(^y.a))) 4. ==[ alpha ]==> (((b a)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 125272/12565695. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 125273/12565713. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((a (a a)) c)) 3. ==[ beta ]==> (b ((a (a a)) c)) REDUCED to normal form. ------ 125274/12565722. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 125275/12565776. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 125276/12565920. ------ 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 (a a)))) REDUCED to normal form. ------ 125277/12565947. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 125278/12566217. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b (a (a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(b (a (a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 125279/12566244. ------ 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. ------ 125280/12566271. ------ 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. ------ 125281/12566442. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 125282/12566586. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((b c)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((b c)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((b c)(^y.(y y))) 6. ==[ alpha ]==> ((b c)(^x.(x x))) REDUCED to normal form. ------ 125283/12566658. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 125284/12566721. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 125285/12566739. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 125286/12566748. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 125287/12566820. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z)) b)) 3. ==[ beta ]==> (b ((a (^z.z)) b)) 4. ==[ alpha ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 125288/12566829. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 125289/12566856. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.a)) REDUCED to normal form. ------ 125290/12566937. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.a))) REDUCED to normal form. ------ 125291/12566964. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 125292/12566991. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 125293/12567054. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 125294/12567081. ------ 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. ------ 125295/12567108. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b a)) 3. ==[ beta ]==> ((a ((^y.y) b))(b a)) 4. ==[ alpha ]==> ((a ((^x.x) b))(b a)) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 125296/12567135. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 125297/12567162. ------ 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. ------ 125298/12567189. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 125299/12571116. ------ 1. ==[ start ]==> ((^a.(b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125300/12575871. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a))) b) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 125301/12575895. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125302/12575976. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125303/12576429. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 125304/12577263. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))((^y1.y1) a))((^y.(^z.(^x1.x1)))((^y1.y1) a)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.(^x2.x2)))((^y2.y2) a)))((^z2.(^x3.(^y3.y3)))((^z3.z3) a))) 5. ==[ beta ]==> (((^y.(^z.z))((^y1.(^z1.(^x2.x2)))((^y2.y2) a)))((^z2.(^x3.(^y3.y3)))((^z3.z3) a))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a)))((^x2.(^y2.(^z2.z2)))((^x3.x3) a))) 7. ==[ beta ]==> ((^y.y)((^x2.(^y2.(^z2.z2)))((^x3.x3) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125305/12577527. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 125306/12577776. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125307/12578163. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (^y.((((^z.z) a)(b a))(((^z.z) a)(b a)))) 4. ==[ alpha ]==> (^x.((((^y.y) a)(b a))(((^z.z) a)(b a)))) 5. ==[ beta ]==> (^x.((a (b a))(((^z.z) a)(b a)))) 6. ==[ alpha ]==> (^x.((a (b a))(((^y.y) a)(b a)))) 7. ==[ beta ]==> (^x.((a (b a))(a (b a)))) REDUCED to normal form. ------ 125308/12578370. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(a a))((^x1.x1)(^y1.y1)))((^z.(a a))((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(a a))((^z.z)(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> (((^y.(a a))((^z.z)(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((^x.(a a))((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a a)((^x1.(a a))((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(^z.z)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 125309/12578553. ------ 1. ==[ start ]==> (((a b) b)(^c.(^b.b))) 2. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 125310/12578886. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.(^b.b))) 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. ------ 125311/12579801. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125312/12579804. ------ 1. ==[ start ]==> ((a (b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125313/12580083. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(b a))) 3. ==[ beta ]==> ((b a)(^y.(b a))) 4. ==[ alpha ]==> ((b a)(^x.(b a))) REDUCED to normal form. ------ 125314/12580371. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(b a))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(x a))) REDUCED to normal form. ------ 125315/12580650. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.x)(^y.(^z.(^x1.x1)))) b) 4. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 5. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 6. ==[ beta ]==> (^y.(^z.z)) 7. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125316/12581397. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125317/12581847. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(a a)))) REDUCED to normal form. ------ 125318/12582288. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.(y y)))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 125319/12582555. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a)))(((^y.(^z.z))(^x1.a))((^y.(^z.z))(^x1.a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a)))(((^x2.(^y2.y2))(^z2.a))((^x3.(^y3.y3))(^z3.a)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(^z1.a)))(((^x2.(^y2.y2))(^z2.a))((^x3.(^y3.y3))(^z3.a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.a)))(((^y1.(^z1.z1))(^x2.a))((^y2.(^z2.z2))(^x3.a)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.a))(((^y1.(^z1.z1))(^x2.a))((^y2.(^z2.z2))(^x3.a)))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.a))((^x2.(^y2.y2))(^z2.a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a)))) 11. ==[ beta ]==> (((^y.(^z.z))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.a))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 15. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125320/12582837. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125321/12583188. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.((y1 y1) y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((y1 y1) y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z) z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125322/12583476. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))(^x.(^z.z))) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 125323/12583611. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125324/12583953. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.d)) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.d)) 3. ==[ beta ]==> ((b c)(^y.d)) 4. ==[ alpha ]==> ((b c)(^x.d)) REDUCED to normal form. ------ 125325/12584223. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 125326/12584304. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.c)) REDUCED to normal form. ------ 125327/12584421. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 125328/12584475. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125329/12584502. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 125330/12584529. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.z))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 125331/12584556. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125332/12584586. ------ 1. ==[ start ]==> ((a (^a.a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 125333/12584613. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 7. ==[ beta ]==> ((^y.y)(b a)) 8. ==[ alpha ]==> ((^x.x)(b a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125334/12584640. ------ 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. ------ 125335/12584667. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 125336/12584721. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(b (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125337/12584757. ------ 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. ------ 125338/12584784. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 125339/12584811. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.a))) REDUCED to normal form. ------ 125340/12584847. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125341/12584865. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 125342/12584946. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.(a a)))) REDUCED to normal form. ------ 125343/12585027. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 125344/12585054. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 125345/12585090. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 125346/12585117. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 125347/12585162. ------ 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)) b)) REDUCED to normal form. ------ 125348/12585414. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 125349/12585441. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 125350/12585531. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125351/12585558. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 125352/12585612. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 7. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 125353/12585666. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 7. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 8. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 9. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 125354/12585693. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a b)(a b))) 3. ==[ beta ]==> ((^y.y)((a b)(a b))) 4. ==[ alpha ]==> ((^x.x)((a b)(a b))) 5. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 125355/12585747. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)((a a)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 125356/12585846. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 125357/12585927. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.b)(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. ------ 125358/12585954. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 125359/12586080. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> (b (((a a) a)(^y.(a a)))) 6. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 125360/12586161. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 125361/12586188. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 125362/12586215. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 125363/12586242. ------ 1. ==[ start ]==> ((((^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)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a)) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125364/12586269. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a) a)(^x.x))(b b)) REDUCED to normal form. ------ 125365/12586305. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 125366/12586386. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 125367/12586413. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.b)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.b))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 125368/12586467. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 125369/12586557. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(b ((^z.z) b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(b ((^z.z) b))) IRREDUCIBLE: cycle. ------ 125370/12586620. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x) b)) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 125371/12586638. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 125372/12586647. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 125373/12586665. ------ 1. ==[ start ]==> (((^a.a)(a b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))((b a)((^y.y) a))) 3. ==[ beta ]==> ((a b)((b a)((^y.y) a))) 4. ==[ alpha ]==> ((a b)((b a)((^x.x) a))) 5. ==[ beta ]==> ((a b)((b a) a)) REDUCED to normal form. ------ 125374/12586692. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((a a)(^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))) REDUCED to normal form. ------ 125375/12586746. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a b)((a a) a))) REDUCED to normal form. ------ 125376/12586827. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (a a))((a a)(^y.y)))) 3. ==[ beta ]==> (b ((a (a a))((a a)(^y.y)))) 4. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 125377/12586854. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (b a))) REDUCED to normal form. ------ 125378/12586872. ------ 1. ==[ start ]==> (((a a)(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 125379/12586899. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(b (^y.y))) REDUCED to normal form. ------ 125380/12586953. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.b)(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. ------ 125381/12586980. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 7. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 8. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(a (^x1.x1)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 125382/12587025. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 125383/12587034. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 125384/12587061. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 125385/12587241. ------ 1. ==[ start ]==> (((a b) b)((a a)(^b.b))) 2. ==[ alpha ]==> (((a b) b)((a a)(^x.x))) REDUCED to normal form. ------ 125386/12587268. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) b) a)) 3. ==[ beta ]==> (((a a) a)(((^y.y) b) a)) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b) a)) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 125387/12587295. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 125388/12587322. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b a) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a) c)) REDUCED to normal form. ------ 125389/12587547. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 125390/12587574. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.a)(^b.b))) 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. ------ 125391/12587673. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z)) d)) 3. ==[ beta ]==> (b ((^y.(^z.z)) d)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) d)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125392/12587772. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a b)) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 125393/12587916. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 125394/12587943. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 125395/12587970. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 125396/12588024. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125397/12588051. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((a (^y.b))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.b))(((a a) a)(^y.a))) REDUCED to normal form. ------ 125398/12588105. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125399/12588186. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 125400/12588213. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 125401/12588303. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 125402/12588330. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 125403/12588384. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 125404/12588411. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((a b) a)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 125405/12588438. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 125406/12588492. ------ 1. ==[ start ]==> ((a (b a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125407/12588582. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y) a))) 7. ==[ beta ]==> (b ((a a)((^y.y) a))) 8. ==[ alpha ]==> (b ((a a)((^x.x) a))) 9. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 125408/12588663. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (b ((^y.y)((a a) a))) 6. ==[ alpha ]==> (b ((^x.x)((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 125409/12588771. ------ 1. ==[ start ]==> (((^a.a)(b a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)(b a))((a a)(b a))) 3. ==[ beta ]==> ((b a)((a a)(b a))) REDUCED to normal form. ------ 125410/12588834. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 125411/12588861. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 125412/12588915. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125413/12588942. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.(x x)))(^z.a)) 6. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 125414/12588969. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^y.a))((a (a a))(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(^y.b))) REDUCED to normal form. ------ 125415/12588996. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 125416/12589059. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(b a))) 3. ==[ beta ]==> (((a a)(b a))(b a)) REDUCED to normal form. ------ 125417/12589140. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 125418/12589167. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.(z z)))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.(y y)))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 125419/12589221. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 125420/12589248. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))(^z.b))) 5. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.b))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.b))) 7. ==[ beta ]==> (((a a) a)((^y.b)(^y.b))) 8. ==[ alpha ]==> (((a a) a)((^x.b)(^y.b))) 9. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 125421/12589275. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 125422/12589338. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125423/12589419. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)((^z.z) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)((^z.z) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)((^z.z) a))) 5. ==[ beta ]==> ((a a)((a b)((^z.z) a))) 6. ==[ alpha ]==> ((a a)((a b)((^x.x) a))) 7. ==[ beta ]==> ((a a)((a b) a)) REDUCED to normal form. ------ 125424/12589500. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))((a a) a))) 3. ==[ beta ]==> (b ((a (a a))((a a) a))) REDUCED to normal form. ------ 125425/12589617. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 125426/12589644. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 125427/12589725. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 125428/12589752. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.a))) 5. ==[ beta ]==> ((^y.b)((a (a a))(^z.a))) 6. ==[ alpha ]==> ((^x.b)((a (a a))(^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125429/12589806. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 125430/12589860. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 125431/12589914. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b) c)) REDUCED to normal form. ------ 125432/12589977. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 125433/12590031. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 125434/12590058. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 125435/12590256. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^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. ------ 125436/12590283. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.y)((a (^z1.z1))(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. ------ 125437/12590535. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.(a a)))) REDUCED to normal form. ------ 125438/12590562. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((b a)(((^y.y)(a a)) a)) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a)) a)) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 125439/12590589. ------ 1. ==[ start ]==> (((a a)(^b.b))((a b) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((a b) b)) REDUCED to normal form. ------ 125440/12590742. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(b (a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(b (a b))) 3. ==[ beta ]==> (b (b (a b))) REDUCED to normal form. ------ 125441/12590778. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 125442/12590805. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 125443/12590850. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125444/12590922. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c (^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(c (^y.a))) 3. ==[ beta ]==> (((a a) b)(c (^y.a))) 4. ==[ alpha ]==> (((a a) b)(c (^x.a))) REDUCED to normal form. ------ 125445/12590949. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(b (^x1.b))) REDUCED to normal form. ------ 125446/12590976. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(a (^y.(a a)))) 3. ==[ beta ]==> ((a (b a))(a (^y.(a a)))) 4. ==[ alpha ]==> ((a (b a))(a (^x.(a a)))) REDUCED to normal form. ------ 125447/12591003. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.b)(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 125448/12591057. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 125449/12591084. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))(a (a a)))) 3. ==[ beta ]==> (((a b)((a a) a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 125450/12591111. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 125451/12591138. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 125452/12591192. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 125453/12591219. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 125454/12591246. ------ 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. ------ 125455/12591417. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 125456/12591525. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125457/12591561. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)(^y.y))) 3. ==[ beta ]==> ((b b)(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((b b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 125458/12591588. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 125459/12591642. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(z z)))) REDUCED to normal form. ------ 125460/12591669. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 125461/12591750. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y) b)) 5. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 125462/12591777. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a)) c)) REDUCED to normal form. ------ 125463/12591876. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(a ((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125464/12591885. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 125465/12591912. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 125466/12592002. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(^z.z)))) REDUCED to normal form. ------ 125467/12592056. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 125468/12592083. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))((a (^z.z))(a (^z.z)))) 8. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 125469/12592110. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 125470/12592137. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 125471/12592164. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 8. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 125472/12592191. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 125473/12592245. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 125474/12592272. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 125475/12592299. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)(^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. ------ 125476/12592416. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125477/12592497. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c c)) 3. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 125478/12592641. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a) d)) 3. ==[ beta ]==> ((b c)((a a) d)) REDUCED to normal form. ------ 125479/12592668. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x)) a)) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 125480/12592713. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 125481/12592740. ------ 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)((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 5. ==[ beta ]==> ((a a)((^y.y) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 125482/12592776. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 125483/12592803. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 125484/12592875. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c (a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c (a a))) 3. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 125485/12592884. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 125486/12592911. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a) c)) 3. ==[ beta ]==> (((a a)(^y.b))((a a) c)) 4. ==[ alpha ]==> (((a a)(^x.b))((a a) c)) REDUCED to normal form. ------ 125487/12592983. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125488/12593019. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 125489/12593046. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125490/12593109. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125491/12593136. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (^y.y))) REDUCED to normal form. ------ 125492/12593163. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 125493/12593190. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 125494/12593217. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 125495/12593244. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 125496/12602115. ------ 1. ==[ start ]==> (((a a) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a a) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 125497/12602211. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (^y.((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (^x.((^y.y)((^z.z) a))) 5. ==[ beta ]==> (^x.((^z.z) a)) 6. ==[ alpha ]==> (^x.((^y.y) a)) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 125498/12602454. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 125499/12602553. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) b)((((a a)(a a)) b)(((a a)(a a)) b))) REDUCED to normal form. ------ 125500/12603336. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((((a (^y.(^z.z)))(^x1.a))((a (^y.(^z.z)))(^x1.a)))((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.a))((a (^x1.(^y1.y1)))(^z1.a)))((a (^x2.(^y2.y2)))(^z2.a))) REDUCED to normal form. ------ 125501/12603669. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 125502/12604443. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(a a))(^x1.(^y1.y1)))(((^z.z)(a a))(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(a a))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((^y.y)(a a))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 9. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 10. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125503/12605292. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 125504/12606183. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 125505/12606423. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 125506/12606444. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 125507/12607314. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125508/12608136. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(a b))) REDUCED to normal form. ------ 125509/12608163. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 125510/12609261. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125511/12609270. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.((x1 x1) x1))) REDUCED to normal form. ------ 125512/12609708. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125513/12610026. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((^z.z) a))) 3. ==[ beta ]==> ((b c)(^y.((^z.z) a))) 4. ==[ alpha ]==> ((b c)(^x.((^y.y) a))) 5. ==[ beta ]==> ((b c)(^x.a)) REDUCED to normal form. ------ 125514/12610053. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(x (x x)))) REDUCED to normal form. ------ 125515/12610494. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.b)) REDUCED to normal form. ------ 125516/12610548. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.z)) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.z)) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.y)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 125517/12610602. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.a)) 3. ==[ beta ]==> (((^y.y)(b a))(^z.a)) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.a)) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 125518/12610629. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 125519/12610677. ------ 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. ------ 125520/12610704. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a a) a)((^y.y)(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 125521/12610731. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 125522/12610758. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 125523/12610785. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^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. ------ 125524/12610812. ------ 1. ==[ start ]==> (((a a) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a) b)((a a)(b (^x.x)))) REDUCED to normal form. ------ 125525/12610911. ------ 1. ==[ start ]==> ((a (^b.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.a))((^z.z) a)) 4. ==[ alpha ]==> ((a (^x.a))((^y.y) a)) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 125526/12610929. ------ 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)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 125527/12610956. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 125528/12610992. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 125529/12611019. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125530/12611100. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125531/12611154. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 125532/12611226. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b (^y.y)) a)) 3. ==[ beta ]==> ((a (a a))((b (^y.y)) a)) 4. ==[ alpha ]==> ((a (a a))((b (^x.x)) a)) REDUCED to normal form. ------ 125533/12611253. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 125534/12611289. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 125535/12611397. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((^y.(a a))(^z.b)) 6. ==[ alpha ]==> ((^x.(a a))(^y.b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125536/12611568. ------ 1. ==[ start ]==> (((^a.(a a)) b)(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(b ((a a)(a a)))) 3. ==[ beta ]==> ((b b)(b ((a a)(a a)))) REDUCED to normal form. ------ 125537/12611703. ------ 1. ==[ start ]==> (((a (a a)) b)((b a)(a (a a)))) REDUCED to normal form. ------ 125538/12611730. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((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. ------ 125539/12611757. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 125540/12611784. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a b)(a b))) REDUCED to normal form. ------ 125541/12611811. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 125542/12611838. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 125543/12611865. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(b a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(b a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(b a))) 7. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 125544/12611982. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 125545/12612009. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 125546/12612036. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 125547/12612126. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))((a a) a))) 5. ==[ beta ]==> (a ((^z.(a a))((a a) a))) 6. ==[ alpha ]==> (a ((^x.(a a))((a a) a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 125548/12612207. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 125549/12612234. ------ 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))(b a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(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. ------ 125550/12612288. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) b))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 125551/12612369. ------ 1. ==[ start ]==> ((a (^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 125552/12612558. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 125553/12612639. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))(^b.b))) 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. ------ 125554/12612702. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) b)(a a))) 3. ==[ beta ]==> ((((a a) a) b)(b (a a))) REDUCED to normal form. ------ 125555/12612729. ------ 1. ==[ start ]==> (((a b) a)((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 125556/12612756. ------ 1. ==[ start ]==> (((a a)(^a.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a a)(^x.b))((b a) a)) REDUCED to normal form. ------ 125557/12612810. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 125558/12612837. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a b)((a a) a))) REDUCED to normal form. ------ 125559/12612864. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(a b))) 5. ==[ beta ]==> ((^y.a)(((a a) a)(a b))) 6. ==[ alpha ]==> ((^x.a)(((a a) a)(a b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 125560/12612891. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 125561/12612918. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 125562/12613035. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 125563/12613062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x) a)((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)))) REDUCED to normal form. ------ 125564/12613089. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b a)(^y.a))) REDUCED to normal form. ------ 125565/12613116. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 125566/12613143. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(a 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. ------ 125567/12613152. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125568/12613179. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.b)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((a a) a)) 6. ==[ alpha ]==> ((^x.b)((a a) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125569/12613233. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125570/12613314. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125571/12613368. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 125572/12613395. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125573/12613530. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b ((^z.a)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125574/12613683. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.b) 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. ------ 125575/12613710. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 125576/12613755. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 125577/12613764. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 125578/12613989. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(a (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a (^z.z))) 3. ==[ beta ]==> (b (a (^z.z))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 125579/12614097. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125580/12614232. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125581/12614331. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b a) b)) REDUCED to normal form. ------ 125582/12614808. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)(a (a a))) REDUCED to normal form. ------ 125583/12614880. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 125584/12614934. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 125585/12615015. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125586/12615123. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 125587/12615168. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((b a) a)) REDUCED to normal form. ------ 125588/12615195. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(^y.y)) b)) 5. ==[ beta ]==> ((a (a a))(((a a)(^y.y)) b)) 6. ==[ alpha ]==> ((a (a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 125589/12615222. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(a a)) c)) 3. ==[ beta ]==> (((a (a a))(a b))((a a) c)) REDUCED to normal form. ------ 125590/12615402. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125591/12615744. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125592/12615879. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (b ((^x1.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125593/12615987. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125594/12616014. ------ 1. ==[ start ]==> ((a (^b.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.a))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 125595/12616194. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 125596/12616221. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a)) b)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a)) b)) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 125597/12616248. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.b) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.b) c)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b) c)) 5. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 125598/12616293. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125599/12616500. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125600/12616608. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125601/12616662. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.z))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.z))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 125602/12616689. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125603/12616743. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 125604/12616806. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c ((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c ((a a) a))) REDUCED to normal form. ------ 125605/12616824. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125606/12616833. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (a b))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (a b))) REDUCED to normal form. ------ 125607/12616860. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 125608/12616887. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(a a))) REDUCED to normal form. ------ 125609/12616941. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)((^x2.x2) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1) a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) a)) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 125610/12616968. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 125611/12617085. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 125612/12617112. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(((a a) a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 125613/12617139. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a) a)(a b))(^y.a)) 6. ==[ alpha ]==> ((((a a) a)(a b))(^x.a)) REDUCED to normal form. ------ 125614/12617166. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 125615/12617193. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 125616/12617274. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b) a)) REDUCED to normal form. ------ 125617/12617301. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a) b)) 3. ==[ beta ]==> ((b (a a))(((a a) a) b)) REDUCED to normal form. ------ 125618/12617364. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 125619/12617607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(b (^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125620/12617688. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 125621/12617715. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 7. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125622/12617769. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 125623/12617850. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125624/12617913. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (a (a a)))) REDUCED to normal form. ------ 125625/12617967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a ((a a) a))) REDUCED to normal form. ------ 125626/12617994. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 125627/12618021. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 125628/12618138. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 125629/12618165. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 125630/12618192. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (^y.a))) 6. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.a))) REDUCED to normal form. ------ 125631/12618219. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 125632/12618246. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a a)(^b.(^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. ------ 125633/12618273. ------ 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.y1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1) a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z) a)) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 125634/12618408. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 125635/12618498. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b (^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b (^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125636/12618579. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125637/12618687. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125638/12618723. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b ((^y.y) a))) 3. ==[ beta ]==> ((b c)(b ((^y.y) a))) 4. ==[ alpha ]==> ((b c)(b ((^x.x) a))) 5. ==[ beta ]==> ((b c)(b a)) REDUCED to normal form. ------ 125639/12618750. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a (a (a a)))) REDUCED to normal form. ------ 125640/12618795. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 125641/12618822. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b (^z.a))) 3. ==[ beta ]==> ((^y.y)(b (^z.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 125642/12618876. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 125643/12618957. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125644/12618966. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c (a a))) REDUCED to normal form. ------ 125645/12618993. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.b))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (a (^y.y)))) REDUCED to normal form. ------ 125646/12619065. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125647/12619074. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 125648/12619101. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c a)) 3. ==[ beta ]==> ((b (^y.a))(c a)) 4. ==[ alpha ]==> ((b (^x.a))(c a)) REDUCED to normal form. ------ 125649/12619128. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 125650/12619191. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a) b)) REDUCED to normal form. ------ 125651/12619218. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 125652/12619245. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y) b)) 5. ==[ beta ]==> ((a b)((^y.y) b)) 6. ==[ alpha ]==> ((a b)((^x.x) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 125653/12619272. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 125654/12619299. ------ 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. ------ 125655/12619326. ------ 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)(^x.x))) a) REDUCED to normal form. ------ 125656/12619352. ------ 1. ==[ start ]==> (^a.((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (^x.((x b)((^y.y)(x x)))) 3. ==[ beta ]==> (^x.((x b)(x x))) REDUCED to normal form. ------ 125657/12619353. ------ 1. ==[ start ]==> (a ((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (a ((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (a ((a b)(a a))) REDUCED to normal form. ------ 125658/12620301. ------ 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. ------ 125659/12627105. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125660/12628053. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a))) a) 2. ==[ alpha ]==> (((a b)((^x.x)(a a))) a) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 125661/12628059. ------ 1. ==[ start ]==> ((^a.a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)((^y.y)(a a))) 4. ==[ alpha ]==> ((a b)((^x.x)(a a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 125662/12628086. ------ 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)(^y.y)))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 125663/12628113. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 125664/12628194. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^z.z))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 125665/12628311. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (^x.(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (^x.(b (^z.a))) 6. ==[ alpha ]==> (^x.(b (^y.a))) REDUCED to normal form. ------ 125666/12628554. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 125667/12629004. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125668/12629007. ------ 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)))) REDUCED to normal form. ------ 125669/12629727. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125670/12629769. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) b) b)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 125671/12630753. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^b.((^a.a) b))) 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. ------ 125672/12631086. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^y.b)) REDUCED to normal form. ------ 125673/12631218. ------ 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 ]==> ((((a b)((^z.z)(^x1.x1)))((a b)((^z.z)(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((((a b)((^x.x)(^y.y)))((a b)((^z.z)(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((((a b)(^y.y))((a b)((^z.z)(^x1.x1))))(^y1.y1)) 6. ==[ alpha ]==> ((((a b)(^x.x))((a b)((^y.y)(^z.z))))(^x1.x1)) 7. ==[ beta ]==> ((((a b)(^x.x))((a b)(^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((((a b)(^x.x))((a b)(^y.y)))(^z.z)) REDUCED to normal form. ------ 125674/12631401. ------ 1. ==[ start ]==> (((a b) c)(^a.(^b.b))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 125675/12631698. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 125676/12631974. ------ 1. ==[ start ]==> ((^a.(b a))(b (b a))) 2. ==[ alpha ]==> ((^x.(b x))(b (b a))) 3. ==[ eta ]==> (b (b (b a))) REDUCED to normal form. ------ 125677/12632811. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b ((a a)(^x1.x1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((b ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125678/12633345. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 125679/12633414. ------ 1. ==[ start ]==> ((^a.(^b.b))((a b) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((a b) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125680/12633597. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 125681/12633729. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 125682/12634047. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 125683/12634263. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 125684/12634461. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(a b))) 3. ==[ beta ]==> ((a (b a))(^y.(a b))) 4. ==[ alpha ]==> ((a (b a))(^x.(a b))) REDUCED to normal form. ------ 125685/12635046. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(^z.b))) 3. ==[ beta ]==> ((b b)(^y.(^z.b))) 4. ==[ alpha ]==> ((b b)(^x.(^y.b))) REDUCED to normal form. ------ 125686/12635370. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.a))) REDUCED to normal form. ------ 125687/12635808. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125688/12635811. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125689/12636153. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 125690/12636261. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 125691/12636504. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.z))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 125692/12636621. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 125693/12636648. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(a a))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 125694/12636702. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.b)) 3. ==[ beta ]==> (((^y.y)(b a))(^z.b)) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.b)) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 125695/12636729. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 125696/12636756. ------ 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. ------ 125697/12636768. ------ 1. ==[ start ]==> ((a a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a a)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((a a)((a b)(a a))) REDUCED to normal form. ------ 125698/12636795. ------ 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. ------ 125699/12636822. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> ((a b)((^y.y)(b a))) 4. ==[ alpha ]==> ((a b)((^x.x)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 125700/12636876. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a a)(a a))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) b))) 5. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 125701/12636903. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 125702/12636966. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 125703/12636993. ------ 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.(^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. ------ 125704/12637020. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a (^x.a))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.a))) REDUCED to normal form. ------ 125705/12637056. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125706/12637101. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 125707/12637128. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 125708/12637137. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 125709/12637164. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 125710/12637191. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 125711/12637218. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 125712/12637245. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 125713/12637263. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 125714/12637371. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.(y y))(((a a)(a a)) b)) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(a a)) b)) 5. ==[ beta ]==> ((((a a)(a a)) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 125715/12637398. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 5. ==[ beta ]==> (((^y.y) b) c) 6. ==[ alpha ]==> (((^x.x) b) c) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 125716/12637434. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 125717/12637515. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 125718/12637542. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 125719/12637677. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 125720/12637686. ------ 1. ==[ start ]==> (((a (a a))(a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 125721/12637713. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 125722/12638010. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 125723/12638037. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 125724/12638064. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a a)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((a a)((a a)(a a)))) REDUCED to normal form. ------ 125725/12638181. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(y y)))) 5. ==[ beta ]==> ((b a)(^y.(y y))) 6. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 125726/12638235. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (a (((^z.z)(a a))(^x1.a))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.a))) 7. ==[ beta ]==> (a ((a a)(^y.a))) 8. ==[ alpha ]==> (a ((a a)(^x.a))) REDUCED to normal form. ------ 125727/12638271. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.b)(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(a b))) 5. ==[ beta ]==> (b ((^y.b)(a b))) 6. ==[ alpha ]==> (b ((^x.b)(a b))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 125728/12638352. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((b a)(b a))) REDUCED to normal form. ------ 125729/12638379. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 125730/12638397. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.z))(^x1.x1))) 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 a)((a (^y.y))(^z.z))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 125731/12638406. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 125732/12638433. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125733/12638478. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) b) b)) 3. ==[ beta ]==> ((a (^x.b))(b b)) REDUCED to normal form. ------ 125734/12638649. ------ 1. ==[ start ]==> (((^a.b) a)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125735/12638829. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(^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. ------ 125736/12638856. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 125737/12639063. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a a)(a b))(a (b a))) REDUCED to normal form. ------ 125738/12639090. ------ 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))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 125739/12639117. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)((^z.z) b))) 5. ==[ beta ]==> ((a (^y.y))((a a)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) b))) 7. ==[ beta ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 125740/12639261. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125741/12639288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 125742/12639342. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a))) 9. ==[ beta ]==> ((^y.y)(^z.(a a))) 10. ==[ alpha ]==> ((^x.x)(^y.(a a))) 11. ==[ beta ]==> (^y.(a a)) 12. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 125743/12639423. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125744/12639432. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 125745/12639459. ------ 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. ------ 125746/12639477. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) b) a)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b) a)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b) a)) 5. ==[ beta ]==> ((a a)(((^y.y) b) a)) 6. ==[ alpha ]==> ((a a)(((^x.x) b) a)) 7. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 125747/12639486. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 125748/12639504. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a (^y.(^z.z))) b) 6. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 125749/12639513. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 125750/12639567. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(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. ------ 125751/12639594. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 9. ==[ beta ]==> ((a a)((^x1.(a a))(^y1.(^z1.z1)))) 10. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 125752/12639621. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 125753/12639648. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 125754/12639675. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 125755/12639738. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c (b a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c (b a))) REDUCED to normal form. ------ 125756/12639765. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a ((a a) a))(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a ((a a) a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 125757/12639792. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a b)) REDUCED to normal form. ------ 125758/12639819. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a a))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 125759/12639846. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a) a)((b a)(a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a) a)((b a)(a (^x.x)))) REDUCED to normal form. ------ 125760/12639873. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 125761/12639900. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a (a a)))) REDUCED to normal form. ------ 125762/12639927. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a b)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 125763/12640107. ------ 1. ==[ start ]==> (((a b) c)(a (^b.b))) 2. ==[ alpha ]==> (((a b) c)(a (^x.x))) REDUCED to normal form. ------ 125764/12640134. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 125765/12640179. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 125766/12640206. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(y1 y1)))) 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. ------ 125767/12640215. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 125768/12640242. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 125769/12640296. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125770/12640323. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 125771/12640341. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 125772/12640350. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 125773/12640377. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 125774/12640404. ------ 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 (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 125775/12640683. ------ 1. ==[ start ]==> ((a (b a))(b (b a))) REDUCED to normal form. ------ 125776/12640773. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (b ((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125777/12641043. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 125778/12641052. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 125779/12641106. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 125780/12641124. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a 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. ------ 125781/12641133. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 125782/12641160. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 125783/12641187. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(a b))) REDUCED to normal form. ------ 125784/12641520. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 125785/12641610. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a)) c)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a)) c)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a)) c)) 5. ==[ beta ]==> ((a a)((^z.(a a)) c)) 6. ==[ alpha ]==> ((a a)((^x.(a a)) c)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 125786/12641826. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 125787/12641853. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 125788/12641907. ------ 1. ==[ start ]==> (((^a.(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 z)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.(y y)))) 8. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 125789/12641916. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 125790/12641943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125791/12641988. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.b))) 5. ==[ beta ]==> (b (a (^y.b))) 6. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 125792/12641997. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 125793/12642024. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 125794/12642051. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.z))) REDUCED to normal form. ------ 125795/12642096. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125796/12642105. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 125797/12642123. ------ 1. ==[ start ]==> ((a (^b.b))((a b) c)) 2. ==[ alpha ]==> ((a (^x.x))((a b) c)) REDUCED to normal form. ------ 125798/12642249. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c (a b))) 3. ==[ beta ]==> (((^y.y)(a b))(c (a b))) 4. ==[ alpha ]==> (((^x.x)(a b))(c (a b))) 5. ==[ beta ]==> ((a b)(c (a b))) REDUCED to normal form. ------ 125799/12642276. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(b ((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(b (a a))) REDUCED to normal form. ------ 125800/12642303. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.y))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 125801/12642330. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 125802/12642357. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(a (^y.y)))) REDUCED to normal form. ------ 125803/12642411. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a (a a))) REDUCED to normal form. ------ 125804/12642438. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a b)((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a b)((a (a a))(^y.y))) 6. ==[ alpha ]==> ((a b)((a (a a))(^x.x))) REDUCED to normal form. ------ 125805/12642609. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a) a)(^z.a))) 3. ==[ beta ]==> (b (((a a) a)(^z.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 125806/12642717. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125807/12642726. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 125808/12642753. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)((^y.y)(a a))) 6. ==[ alpha ]==> ((b a)((^x.x)(a a))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 125809/12642771. ------ 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. ------ 125810/12642780. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 125811/12642798. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 125812/12642807. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 125813/12642888. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 125814/12642915. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 125815/12642942. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 125816/12642969. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 125817/12643113. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a) b)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a) b)(a (^y.y))) 8. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 125818/12643140. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (^x1.x1))((a a) a))) REDUCED to normal form. ------ 125819/12643167. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a a)(a b))) 3. ==[ beta ]==> ((a (b a))((a a)(a b))) REDUCED to normal form. ------ 125820/12643608. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a) b)) 3. ==[ beta ]==> (b ((^z.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125821/12643752. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)(a (^y.b))) 3. ==[ beta ]==> ((b b)(a (^y.b))) 4. ==[ alpha ]==> ((b b)(a (^x.b))) REDUCED to normal form. ------ 125822/12643797. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 125823/12643824. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 125824/12643833. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(((^x1.x1) a)((^x1.x1) 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. ------ 125825/12643860. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 125826/12643878. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 125827/12643941. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 125828/12643959. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (b (((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) b)) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 125829/12643968. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 125830/12644022. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 125831/12644076. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.a)) REDUCED to normal form. ------ 125832/12644166. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x) a)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a ((^y.y) a))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(a ((^x.x) a))) 5. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 125833/12644193. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 125834/12644220. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 125835/12644328. ------ 1. ==[ start ]==> (((a b)(a b))(c d)) REDUCED to normal form. ------ 125836/12644463. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c ((^z.z) a))) 3. ==[ beta ]==> ((b (a (^y.y)))(c ((^z.z) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c ((^y.y) a))) 5. ==[ beta ]==> ((b (a (^x.x)))(c a)) REDUCED to normal form. ------ 125837/12644490. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b (a (a a)))) REDUCED to normal form. ------ 125838/12644517. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 125839/12644688. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 125840/12644796. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125841/12644832. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 125842/12644859. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.(y y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(x x))) REDUCED to normal form. ------ 125843/12644904. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) b)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 125844/12644967. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 125845/12644985. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.y1))) REDUCED to normal form. ------ 125846/12644994. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 125847/12645066. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^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. ------ 125848/12645075. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 125849/12645102. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 125850/12645174. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125851/12645183. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 125852/12645210. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a (^z.a))) 3. ==[ beta ]==> ((b (^y.a))(a (^z.a))) 4. ==[ alpha ]==> ((b (^x.a))(a (^y.a))) REDUCED to normal form. ------ 125853/12645237. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 125854/12645300. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (a a))) REDUCED to normal form. ------ 125855/12645327. ------ 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. ------ 125856/12645354. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(a a))) 5. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 125857/12645381. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 125858/12645408. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a b)) 3. ==[ beta ]==> (((^y.y)(b a))(a b)) 4. ==[ alpha ]==> (((^x.x)(b a))(a b)) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 125859/12645435. ------ 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. ------ 125860/12645462. ------ 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. ------ 125861/12653223. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125862/12654171. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a))) b) 2. ==[ alpha ]==> (((a b)((^x.x)(a a))) b) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 125863/12654195. ------ 1. ==[ start ]==> ((^a.(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125864/12654276. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125865/12654756. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((a (a a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a (a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 125866/12655143. ------ 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. ------ 125867/12655563. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((((^y.y)(a (^z.z)))((^y.y)(a (^z.z))))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x)(a (^y.y)))((^z.z)(a (^x1.x1))))((^y1.y1)(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^y.y))((^z.z)(a (^x1.x1))))((^y1.y1)(a (^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))((^y.y)(a (^z.z))))((^x1.x1)(a (^y1.y1)))) 7. ==[ beta ]==> (((a (^x.x))(a (^z.z)))((^x1.x1)(a (^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.x1)))) 9. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 10. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 125868/12656076. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.a)(^z.(a a))) b) 4. ==[ alpha ]==> (((^x.a)(^y.(a a))) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 125869/12656463. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (^y.(((a (a a))((a a)(^z.z)))((a (a a))((a a)(^z.z))))) 4. ==[ alpha ]==> (^x.(((a (a a))((a a)(^y.y)))((a (a a))((a a)(^z.z))))) REDUCED to normal form. ------ 125870/12657213. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^b.(^b.b))) 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. ------ 125871/12657519. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 125872/12658698. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(z a))) REDUCED to normal form. ------ 125873/12659472. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 125874/12659724. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 125875/12660174. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.(a a)))) 3. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 125876/12660615. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 125877/12660804. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 125878/12661668. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.x))) REDUCED to normal form. ------ 125879/12661803. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^z.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 125880/12661935. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125881/12661938. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 125882/12662280. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.d)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.d)) REDUCED to normal form. ------ 125883/12662631. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.c)) 3. ==[ beta ]==> ((b (^y.a))(^z.c)) 4. ==[ alpha ]==> ((b (^x.a))(^y.c)) REDUCED to normal form. ------ 125884/12662748. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 125885/12662802. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 125886/12662829. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(a a))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(a a))) 5. ==[ beta ]==> ((b a)(^y.(a a))) 6. ==[ alpha ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 125887/12662856. ------ 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. ------ 125888/12662883. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 125889/12662913. ------ 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. ------ 125890/12662940. ------ 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. ------ 125891/12662967. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> ((a a)((^y.y)(b a))) 6. ==[ alpha ]==> ((a a)((^x.x)(b a))) 7. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 125892/12662994. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 125893/12663048. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125894/12663075. ------ 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 a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 125895/12663111. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 125896/12663138. ------ 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)))) REDUCED to normal form. ------ 125897/12663174. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 125898/12663192. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((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))) REDUCED to normal form. ------ 125899/12663201. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 125900/12663273. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.b))) REDUCED to normal form. ------ 125901/12663300. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a b)(^y.(a a)))) 3. ==[ beta ]==> ((a a)((a b)(^y.(a a)))) 4. ==[ alpha ]==> ((a a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 125902/12663327. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 125903/12663381. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125904/12663417. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a) a)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)((^x.a)((^y.y) b))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 125905/12663444. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 125906/12663471. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a))(b (^y.y))) 6. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 125907/12663489. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)((b (^y.y)) a)) 3. ==[ beta ]==> ((a a)((b (^y.y)) a)) 4. ==[ alpha ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 125908/12663768. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 125909/12663795. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 125910/12663858. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (b (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125911/12663885. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((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. ------ 125912/12663939. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 125913/12663993. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^y.y))((^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. ------ 125914/12664020. ------ 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)(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. ------ 125915/12664074. ------ 1. ==[ start ]==> (((^a.(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 a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 125916/12664200. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b (^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.(a a)))) 5. ==[ beta ]==> ((a a)(b (^y.(a a)))) 6. ==[ alpha ]==> ((a a)(b (^x.(a a)))) REDUCED to normal form. ------ 125917/12664281. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> ((a ((a a) a))(a (^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))(a (^x.x))) REDUCED to normal form. ------ 125918/12664407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a b)(^z.b))) 3. ==[ beta ]==> (((^y.y) b)((a b)(^z.b))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(^y.b))) 5. ==[ beta ]==> (b ((a b)(^y.b))) 6. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 125919/12664434. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 125920/12664515. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125921/12664542. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 125922/12664596. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 125923/12664632. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^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. ------ 125924/12664659. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 125925/12664740. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 125926/12664767. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.b))) 3. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 125927/12664794. ------ 1. ==[ start ]==> ((a (a b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 125928/12664947. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a)) a)) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 125929/12664965. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) b)(a a))) 3. ==[ beta ]==> (b (((^z.z) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 125930/12664974. ------ 1. ==[ start ]==> (((a b) a)((^b.b) b)) 2. ==[ alpha ]==> (((a b) a)((^x.x) b)) 3. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 125931/12664992. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 125932/12665001. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 125933/12665019. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b a)((^z.z) a))) 3. ==[ beta ]==> ((^y.y)((b a)((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y) a))) 5. ==[ beta ]==> ((b a)((^y.y) a)) 6. ==[ alpha ]==> ((b a)((^x.x) a)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 125934/12665073. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(^y.y))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 125935/12665154. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 125936/12665181. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 125937/12665253. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (^z.z))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 125938/12665307. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(a a))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 125939/12665334. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125940/12665352. ------ 1. ==[ start ]==> (((^a.b) b)((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)((b a)(^y.a))) 3. ==[ beta ]==> (b ((b a)(^y.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 125941/12665568. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 125942/12665595. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a a)(^b.b))) 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. ------ 125943/12665622. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b) a)) 3. ==[ beta ]==> (((a a)(^x.(a a)))(b a)) REDUCED to normal form. ------ 125944/12665649. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 125945/12665901. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 125946/12665928. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^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. ------ 125947/12666000. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a) c)) 2. ==[ alpha ]==> (((^x.b) c)((^y.a) c)) 3. ==[ beta ]==> (b ((^y.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 125948/12666099. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a 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. ------ 125949/12666234. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 125950/12666270. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 125951/12666297. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 125952/12666351. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 125953/12666378. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 125954/12666432. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125955/12666459. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 125956/12666486. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 125957/12666540. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 125958/12666576. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 125959/12666630. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 125960/12666657. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a a)) REDUCED to normal form. ------ 125961/12666684. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 11. ==[ beta ]==> b REDUCED to normal form. ------ 125962/12666738. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 125963/12666765. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 125964/12666792. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 125965/12666909. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (b (((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 125966/12666990. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (((a a) a)(^y.y))) 6. ==[ alpha ]==> (b (((a a) a)(^x.x))) REDUCED to normal form. ------ 125967/12667098. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((b a)((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b a)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 125968/12667125. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a a)(b a))) 3. ==[ beta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 125969/12667161. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((b a)(^z.z))) 3. ==[ beta ]==> ((a (^y.(a a)))((b a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.y))) REDUCED to normal form. ------ 125970/12667188. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 125971/12667242. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.(z z)))) REDUCED to normal form. ------ 125972/12667269. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 125973/12667296. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.a))(^z.a)) 8. ==[ alpha ]==> (((a a)(^x.a))(^y.a)) REDUCED to normal form. ------ 125974/12667323. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))(^x1.b))) REDUCED to normal form. ------ 125975/12667386. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 125976/12667413. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b a)) REDUCED to normal form. ------ 125977/12667467. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 125978/12667494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 125979/12667521. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 125980/12667548. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 125981/12667575. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 125982/12667602. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 125983/12667665. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 125984/12667746. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^z.z)(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(a (^y.y)))) 7. ==[ beta ]==> ((a a)((a a)(a (^y.y)))) 8. ==[ alpha ]==> ((a a)((a a)(a (^x.x)))) REDUCED to normal form. ------ 125985/12667827. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 125986/12667935. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 125987/12667971. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 125988/12668052. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 125989/12668079. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 125990/12668133. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 125991/12668160. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 125992/12668187. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 125993/12668241. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a) b)) REDUCED to normal form. ------ 125994/12668277. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 125995/12668304. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 125996/12668331. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 125997/12668385. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.b))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.b))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.b))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 125998/12668412. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(^z.(a 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. ------ 125999/12668439. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 126000/12668538. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a) d)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a) d)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a) d)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126001/12668583. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((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. ------ 126002/12668610. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1) 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. ------ 126003/12668862. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 126004/12668889. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a a)(^y.(a a)))) 3. ==[ beta ]==> ((b a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((b a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 126005/12668916. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 126006/12668943. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b) b)) REDUCED to normal form. ------ 126007/12669069. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c ((a a) a))) 3. ==[ beta ]==> (b (c ((a a) a))) REDUCED to normal form. ------ 126008/12669132. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 126009/12669177. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126010/12669303. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(b (^y.b))) 3. ==[ beta ]==> ((a (b a))(b (^y.b))) 4. ==[ alpha ]==> ((a (b a))(b (^x.b))) REDUCED to normal form. ------ 126011/12669330. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 126012/12669357. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.b)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(a a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(a a))) 7. ==[ beta ]==> ((a a)((^y.b)(a a))) 8. ==[ alpha ]==> ((a a)((^x.b)(a a))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 126013/12669384. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 126014/12669411. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 126015/12669438. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a (a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 126016/12669465. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) a) REDUCED to normal form. ------ 126017/12669519. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a b)) REDUCED to normal form. ------ 126018/12669546. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(^z.z))) 3. ==[ beta ]==> ((b (a a))((^y.b)(^z.z))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(^y.y))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 126019/12669744. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(a a))) 3. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 126020/12669852. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126021/12669915. ------ 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. ------ 126022/12669969. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.a))) REDUCED to normal form. ------ 126023/12669996. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 126024/12670077. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a) a)) REDUCED to normal form. ------ 126025/12670104. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z) b)) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y) b)) 5. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 126026/12670203. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126027/12670239. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a) a)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 126028/12670266. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 126029/12670329. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c (^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.(y y)))) REDUCED to normal form. ------ 126030/12670356. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 126031/12670383. ------ 1. ==[ start ]==> (((a (a a))(b a))(a (^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(a (^x.a))) REDUCED to normal form. ------ 126032/12670410. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 126033/12670437. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 126034/12670464. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 126035/12670491. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 126036/12670518. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 126037/12670572. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 126038/12670599. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 126039/12670626. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 126040/12670653. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 126041/12670743. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))((^y2.y2) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))((^y2.y2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126042/12670968. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y)) c)) 3. ==[ beta ]==> ((b c)((a (^y.y)) c)) 4. ==[ alpha ]==> ((b c)((a (^x.x)) c)) REDUCED to normal form. ------ 126043/12671040. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(a a))) 5. ==[ beta ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 126044/12671067. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 126045/12671130. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 126046/12671211. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a) a)) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 126047/12671238. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z)) b)) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y)) b)) REDUCED to normal form. ------ 126048/12671310. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126049/12671319. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 126050/12671346. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z) c)) 3. ==[ beta ]==> ((b (^y.a))((^z.z) c)) 4. ==[ alpha ]==> ((b (^x.a))((^y.y) c)) 5. ==[ beta ]==> ((b (^x.a)) c) REDUCED to normal form. ------ 126051/12671373. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 126052/12671436. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 126053/12671463. ------ 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)(^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. ------ 126054/12671490. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (^z.z))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (^z.z))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.y))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 126055/12671517. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 126056/12671544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(a a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(a a))) 5. ==[ beta ]==> ((b a)((^y.y)(a a))) 6. ==[ alpha ]==> ((b a)((^x.x)(a a))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 126057/12671571. ------ 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)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 126058/12671598. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 126059/12680316. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a))) c) 2. ==[ alpha ]==> (((a b)((^x.x)(a a))) c) 3. ==[ beta ]==> (((a b)(a a)) c) REDUCED to normal form. ------ 126060/12680592. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (^x.((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 126061/12680664. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)(^z.(^x1.x1)))) 3. ==[ eta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 126062/12680835. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 126063/12680934. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x (x x)))((b (^y.y)) a)) 3. ==[ beta ]==> (((b (^y.y)) a)(((b (^y.y)) a)((b (^y.y)) a))) 4. ==[ alpha ]==> (((b (^x.x)) a)(((b (^y.y)) a)((b (^z.z)) a))) REDUCED to normal form. ------ 126064/12681159. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126065/12681717. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((((^y.y) b)(^z.(^x1.x1)))(((^y.y) b)(^z.(^x1.x1))))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((((^x.x) b)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1))))(((^x2.x2) b)(^y2.(^z2.z2)))) 5. ==[ beta ]==> (((b (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1))))(((^x2.x2) b)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((b (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1))))(((^z1.z1) b)(^x2.(^y2.y2)))) 7. ==[ beta ]==> (((b (^x.(^y.y)))(b (^x1.(^y1.y1))))(((^z1.z1) b)(^x2.(^y2.y2)))) 8. ==[ alpha ]==> (((b (^x.(^y.y)))(b (^z.(^x1.x1))))(((^y1.y1) b)(^z1.(^x2.x2)))) 9. ==[ beta ]==> (((b (^x.(^y.y)))(b (^z.(^x1.x1))))(b (^z1.(^x2.x2)))) 10. ==[ alpha ]==> (((b (^x.(^y.y)))(b (^z.(^x1.x1))))(b (^y1.(^z1.z1)))) REDUCED to normal form. ------ 126066/12682050. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126067/12682386. ------ 1. ==[ start ]==> ((((a a) a) b)(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((x x)(x x)))) REDUCED to normal form. ------ 126068/12682824. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((((a a)(^z.z))(^x1.(x1 x1)))(((a a)(^z.z))(^x1.(x1 x1))))) 4. ==[ alpha ]==> ((^x.x)((((a a)(^y.y))(^z.(z z)))(((a a)(^x1.x1))(^y1.(y1 y1))))) 5. ==[ beta ]==> ((((a a)(^y.y))(^z.(z z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 126069/12683052. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^b.((^a.a) b))) 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. ------ 126070/12683682. ------ 1. ==[ start ]==> (((a b) c)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 126071/12684804. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 126072/12685695. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126073/12686346. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.((^z.z)(a a)))) 6. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 7. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 126074/12686571. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(z z))) REDUCED to normal form. ------ 126075/12687009. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a) b)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a) a) b)) 3. ==[ beta ]==> (((((a a) a) b)(((a a) a) b))((((a a) a) b)(((a a) a) b))) REDUCED to normal form. ------ 126076/12687327. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.((a a) a))) 3. ==[ beta ]==> ((b b)(^y.((a a) a))) 4. ==[ alpha ]==> ((b b)(^x.((a a) a))) REDUCED to normal form. ------ 126077/12687678. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((z z) z))) REDUCED to normal form. ------ 126078/12688542. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 126079/12688560. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) REDUCED to normal form. ------ 126080/12688641. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (b (^z.((^x1.x1) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 126081/12688785. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 126082/12688956. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 126083/12688983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.z))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 126084/12689037. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.a)) 3. ==[ beta ]==> (((a b)(a a))(^y.a)) 4. ==[ alpha ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 126085/12689085. ------ 1. ==[ start ]==> (((^a.a) a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) a)((a b)((^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. ------ 126086/12689112. ------ 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. ------ 126087/12689139. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b a))) 5. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 126088/12689166. ------ 1. ==[ start ]==> (((^a.a) b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (b ((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 126089/12689193. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 126090/12689220. ------ 1. ==[ start ]==> (((a a) b)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 126091/12689247. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(b (^y.y)))) REDUCED to normal form. ------ 126092/12689319. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 126093/12689337. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 126094/12689364. ------ 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 x1)))) REDUCED to normal form. ------ 126095/12689391. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a a)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 126096/12689481. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> (a ((^y.b)((^z.z)(a a)))) 6. ==[ alpha ]==> (a ((^x.b)((^y.y)(a a)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 126097/12689562. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.(x x)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 126098/12689580. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 126099/12689661. ------ 1. ==[ start ]==> ((a (a (a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((a (a (a a)))((b (^x.x)) a)) REDUCED to normal form. ------ 126100/12689697. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126101/12689751. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126102/12689859. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 126103/12689886. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 126104/12689976. ------ 1. ==[ start ]==> (((^a.(a a)) b)(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(c ((^y.y) b))) 3. ==[ beta ]==> ((b b)(c ((^y.y) b))) 4. ==[ alpha ]==> ((b b)(c ((^x.x) b))) 5. ==[ beta ]==> ((b b)(c b)) REDUCED to normal form. ------ 126105/12690111. ------ 1. ==[ start ]==> (((a (a a)) b)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 126106/12690138. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(a (a a)))) 5. ==[ beta ]==> (a ((b a)(a (a a)))) REDUCED to normal form. ------ 126107/12690165. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 126108/12690192. ------ 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)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)((a a) a))) REDUCED to normal form. ------ 126109/12690219. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)(a b))) 3. ==[ beta ]==> ((a (^y.a))((a b)(a b))) 4. ==[ alpha ]==> ((a (^x.a))((a b)(a b))) REDUCED to normal form. ------ 126110/12690246. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 126111/12690273. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 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. ------ 126112/12690417. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^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. ------ 126113/12690444. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 126114/12690480. ------ 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.(^x2.x2)))((^y2.y2) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126115/12690534. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(^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. ------ 126116/12690642. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126117/12690696. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.a)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.a)(a (^y.(^z.z))))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 126118/12690777. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 126119/12690795. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) b) b)) 3. ==[ beta ]==> (((a a)((a a) a))(b b)) REDUCED to normal form. ------ 126120/12690966. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 126121/12691047. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(^y1.(^z1.z1))))) IRREDUCIBLE: cycle. ------ 126122/12691110. ------ 1. ==[ start ]==> ((((a a) a) b)(a ((a a)(a a)))) REDUCED to normal form. ------ 126123/12691137. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a b) a)(b (a a))) REDUCED to normal form. ------ 126124/12691164. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 126125/12691218. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 126126/12691245. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 126127/12691272. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a b)((a a) a))) 5. ==[ beta ]==> ((^y.a)((a b)((a a) a))) 6. ==[ alpha ]==> ((^x.a)((a b)((a a) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 126128/12691299. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 126129/12691326. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 126130/12691470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.z))) 7. ==[ beta ]==> (a (((^y.y) b)(^z.z))) 8. ==[ alpha ]==> (a (((^x.x) b)(^y.y))) 9. ==[ beta ]==> (a (b (^y.y))) 10. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 126131/12691497. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 126132/12691524. ------ 1. ==[ start ]==> (((a b)(a a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))((b a)(^x.a))) REDUCED to normal form. ------ 126133/12691551. ------ 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))(^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. ------ 126134/12691560. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126135/12691587. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126136/12691641. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(a b))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a b))) 7. ==[ beta ]==> ((^y.a)(a b)) 8. ==[ alpha ]==> ((^x.a)(a b)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 126137/12691722. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (b ((^x1.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 126138/12691776. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 126139/12691803. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b)(^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)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126140/12691938. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (b ((^z.b)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126141/12692118. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.b) 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. ------ 126142/12692145. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 126143/12692163. ------ 1. ==[ start ]==> (((^a.b) c)((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((b a)(a (^y.y)))) 3. ==[ beta ]==> (b ((b a)(a (^y.y)))) 4. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 126144/12692397. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 126145/12692406. ------ 1. ==[ start ]==> (((a b) c)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 126146/12692559. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 126147/12692640. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 126148/12692739. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 126149/12692766. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b a) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a) b)) REDUCED to normal form. ------ 126150/12692793. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x)) c)) REDUCED to normal form. ------ 126151/12693216. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (a a))(a b))) REDUCED to normal form. ------ 126152/12693261. ------ 1. ==[ start ]==> (((^a.a)(b a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b a)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b a)(c (^x.(^y.y)))) REDUCED to normal form. ------ 126153/12693423. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.b)(a (a a)))) 3. ==[ beta ]==> (b ((^y.b)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.b)(a (a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126154/12693531. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 126155/12693549. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 126156/12693603. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((b a) a)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a) a)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a) a)) 5. ==[ beta ]==> ((a (a a))((b a) a)) REDUCED to normal form. ------ 126157/12693630. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 126158/12694098. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126159/12694107. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 126160/12694152. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126161/12694206. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)((^z.z) a))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)((^z.z) a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)((^y.y) a))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 126162/12694287. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a) a))) 5. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 126163/12694422. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 126164/12694440. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b) c)) REDUCED to normal form. ------ 126165/12694656. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a)) b)) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 126166/12694701. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126167/12694908. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126168/12695016. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.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. ------ 126169/12695070. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126170/12695097. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 126171/12695232. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 126172/12695241. ------ 1. ==[ start ]==> (((a b)(^c.a))(c ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))(c ((a a) a))) REDUCED to normal form. ------ 126173/12695268. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a b))) REDUCED to normal form. ------ 126174/12695295. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a (a a))) REDUCED to normal form. ------ 126175/12695349. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a)(a (^y1.y1)))) REDUCED to normal form. ------ 126176/12695376. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((b (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 126177/12695520. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.z))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.y))) 7. ==[ beta ]==> ((a a)((a b)(^y.y))) 8. ==[ alpha ]==> ((a a)((a b)(^x.x))) REDUCED to normal form. ------ 126178/12695547. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 126179/12695574. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)((a a) a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a b)((a a) a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a b)((a a) a))(^y.a)) 6. ==[ alpha ]==> (((a b)((a a) a))(^x.a)) REDUCED to normal form. ------ 126180/12695601. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 126181/12695628. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 126182/12695682. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.b))) REDUCED to normal form. ------ 126183/12695709. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b) a)) 3. ==[ beta ]==> ((b (a a))((a b) a)) REDUCED to normal form. ------ 126184/12695736. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a) a) b)) REDUCED to normal form. ------ 126185/12695772. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 126186/12696015. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126187/12696051. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a a)((a a) a))) 3. ==[ beta ]==> ((b b)((a a)((a a) a))) REDUCED to normal form. ------ 126188/12696123. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 126189/12696177. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(a (a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(a (a a)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 126190/12696258. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> (b ((^y.a)(^z.z))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 126191/12696366. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126192/12696375. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b (^x1.x1))) REDUCED to normal form. ------ 126193/12696402. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a ((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a ((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 126194/12696429. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 126195/12696573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a a)(^y.y))(((^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. ------ 126196/12696600. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 126197/12696627. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.a))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.a))) REDUCED to normal form. ------ 126198/12696654. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 126199/12696681. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 126200/12696735. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (a a)) b)) REDUCED to normal form. ------ 126201/12696762. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) a) c)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a) c)) 5. ==[ beta ]==> ((b (a (^x.x)))(a c)) REDUCED to normal form. ------ 126202/12696987. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(z z))(a a))) 3. ==[ beta ]==> (b ((^z.(z z))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 126203/12697095. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(y1 y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126204/12697131. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (a (^y.y)))) 3. ==[ beta ]==> ((b c)(c (a (^y.y)))) 4. ==[ alpha ]==> ((b c)(c (a (^x.x)))) REDUCED to normal form. ------ 126205/12697158. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b ((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(b a)) REDUCED to normal form. ------ 126206/12697266. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 126207/12697284. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.(y1 y1)))) REDUCED to normal form. ------ 126208/12697365. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1) 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. ------ 126209/12697401. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c (a a))) 3. ==[ beta ]==> (((a a)(^y.b))(c (a a))) 4. ==[ alpha ]==> (((a a)(^x.b))(c (a a))) REDUCED to normal form. ------ 126210/12697482. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 126211/12697509. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.a))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(a (^y.y)))) REDUCED to normal form. ------ 126212/12697599. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 126213/12697626. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a) b)) REDUCED to normal form. ------ 126214/12697653. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 126215/12697680. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 126216/12697707. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(^z.z))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(^y.y))) 5. ==[ beta ]==> ((b a)((a a)(^y.y))) 6. ==[ alpha ]==> ((b a)((a a)(^x.x))) REDUCED to normal form. ------ 126217/12697734. ------ 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. ------ 126218/12697761. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^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. ------ 126219/12697787. ------ 1. ==[ start ]==> (^a.(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (^x.(((^y.y)(x x))(x b))) 3. ==[ beta ]==> (^x.((x x)(x b))) REDUCED to normal form. ------ 126220/12697788. ------ 1. ==[ start ]==> (a (((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (a (((^x.x)(a a))(a b))) 3. ==[ beta ]==> (a ((a a)(a b))) REDUCED to normal form. ------ 126221/12706515. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b)) a) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b)) a) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 126222/12706521. ------ 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. ------ 126223/12706548. ------ 1. ==[ start ]==> ((^a.(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x x))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((^y.y)(a a)))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a a))((a b)((^y.y)(a a)))) 6. ==[ alpha ]==> (((a b)(a a))((a b)((^x.x)(a a)))) 7. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 126224/12706575. ------ 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 REDUCED to normal form. ------ 126225/12706656. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((((^z.z) a)((^x1.x1) b))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.z)) 5. ==[ beta ]==> ((a ((^y.y) b))(^z.z)) 6. ==[ alpha ]==> ((a ((^x.x) b))(^y.y)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 126226/12706773. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 126227/12707016. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 126228/12707109. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(y (^z.z)))) 3. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 126229/12707466. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(b ((a 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. ------ 126230/12708216. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((a a)(a a)))) REDUCED to normal form. ------ 126231/12708231. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a)) a)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126232/12708567. ------ 1. ==[ start ]==> ((((a a) a) b)(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 126233/12709242. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^b.((^a.a) b))) 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. ------ 126234/12709575. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a (a a))(^y.((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))(^x.((^y.y) b))) 7. ==[ beta ]==> ((a (a a))(^x.b)) REDUCED to normal form. ------ 126235/12709680. ------ 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 (a a)))) 3. ==[ beta ]==> (((((^z.z)(a a))(a (a a)))(((^z.z)(a a))(a (a a))))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(a a))(a (a a)))(((^y.y)(a a))(a (a a))))(^z.z)) 5. ==[ beta ]==> ((((a a)(a (a a)))(((^y.y)(a a))(a (a a))))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a (a a)))(((^x.x)(a a))(a (a a))))(^y.y)) 7. ==[ beta ]==> ((((a a)(a (a a)))((a a)(a (a a))))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a (a a)))((a a)(a (a a))))(^x.x)) REDUCED to normal form. ------ 126236/12709863. ------ 1. ==[ start ]==> (((a b) c)(^d.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126237/12709890. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^a.(^b.b))) 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. ------ 126238/12710436. ------ 1. ==[ start ]==> ((^a.(b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(c ((a a)(^y.y)))) 3. ==[ eta ]==> (b (c ((a a)(^y.y)))) 4. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 126239/12710781. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 126240/12710985. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 126241/12711876. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126242/12712086. ------ 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 y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 126243/12712191. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 126244/12712527. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(a a)))) 5. ==[ beta ]==> (b (^y.(^z.(a a)))) 6. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 126245/12712536. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 126246/12712752. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 126247/12713535. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.b))) REDUCED to normal form. ------ 126248/12713697. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 126249/12713859. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 126250/12714003. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))(^x.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.y))) REDUCED to normal form. ------ 126251/12714270. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b (a (a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126252/12714750. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 126253/12714822. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 126254/12714831. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 126255/12714993. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 126256/12715056. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.c)) REDUCED to normal form. ------ 126257/12715110. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(y (^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 126258/12715191. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 126259/12715218. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^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. ------ 126260/12715245. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.y)) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 126261/12715257. ------ 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. ------ 126262/12715284. ------ 1. ==[ start ]==> ((a (a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a a))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((a (a a))((a b)(a a))) REDUCED to normal form. ------ 126263/12715311. ------ 1. ==[ start ]==> ((a b)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a b)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 126264/12715365. ------ 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. ------ 126265/12715392. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a (a (^x.x)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a (a (^x.x)))(a b)) REDUCED to normal form. ------ 126266/12715410. ------ 1. ==[ start ]==> (((a a) b)(c (^c.(a a)))) 2. ==[ alpha ]==> (((a a) b)(c (^x.(a a)))) REDUCED to normal form. ------ 126267/12715482. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 126268/12715509. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 126269/12715545. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 126270/12715590. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 126271/12715626. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 126272/12715653. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a))(a b))) 3. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 4. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 126273/12715671. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y) a)((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(^y.(a a)))) 5. ==[ beta ]==> (a ((a b)(^y.(a a)))) 6. ==[ alpha ]==> (a ((a b)(^x.(a a)))) REDUCED to normal form. ------ 126274/12715680. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 126275/12715734. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 126276/12715752. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126277/12715842. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 126278/12715860. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z)) a)) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z)) a)) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) a)) 5. ==[ beta ]==> (((b (^y.y)) a)((b (^y.y)) a)) 6. ==[ alpha ]==> (((b (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 126279/12715887. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((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. ------ 126280/12715923. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 126281/12715950. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 126282/12716004. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 126283/12716031. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 126284/12716058. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 126285/12716166. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)(^z.z))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.z))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.y))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 126286/12716202. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(b ((a a)(a a)))) REDUCED to normal form. ------ 126287/12716292. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1) c)) 5. ==[ beta ]==> ((^y.y)((^y1.y1) c)) 6. ==[ alpha ]==> ((^x.x)((^y.y) c)) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 126288/12716499. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(b a))) REDUCED to normal form. ------ 126289/12716526. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 126290/12716553. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z) b))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y) b))) 7. ==[ beta ]==> ((a a)((a (^x.x)) b)) REDUCED to normal form. ------ 126291/12716580. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 126292/12716670. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.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)) REDUCED to normal form. ------ 126293/12716724. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 126294/12716760. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))((a a) a))) 5. ==[ beta ]==> (b ((^y.(a a))((a a) a))) 6. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126295/12716787. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.b)(a b))) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 126296/12716805. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 126297/12716841. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^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. ------ 126298/12716868. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))(b a))) 5. ==[ beta ]==> ((a (^x.(x x)))((b a)(b a))) REDUCED to normal form. ------ 126299/12716886. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 10. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 126300/12716895. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 126301/12716922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126302/12716949. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 126303/12716967. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a)) a)) REDUCED to normal form. ------ 126304/12717138. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)((^y.b)(^z.b))) 3. ==[ beta ]==> (b ((^y.b)(^z.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126305/12717300. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.(a a))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(a a))) REDUCED to normal form. ------ 126306/12717318. ------ 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)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126307/12717345. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.b) b)) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y) b)) 3. ==[ beta ]==> ((a b)((^y.y) b)) 4. ==[ alpha ]==> ((a b)((^x.x) b)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 126308/12717552. ------ 1. ==[ start ]==> (((a a)(a b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 126309/12717579. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (b a))) REDUCED to normal form. ------ 126310/12717606. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 126311/12717633. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)((^x.x) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a) b)) REDUCED to normal form. ------ 126312/12717705. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 126313/12717750. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126314/12717777. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 126315/12717831. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)(^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.b))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^y1.b))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 7. ==[ beta ]==> (((a a) a)(^y.b)) 8. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 126316/12717921. ------ 1. ==[ start ]==> (((a b) b)((^b.a)(b a))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(b a))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 126317/12717948. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 126318/12717966. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a)(^b.b))) 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. ------ 126319/12717975. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 126320/12717993. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z) b) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z) b) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) a)) 5. ==[ beta ]==> (((^y.y) b) a) 6. ==[ alpha ]==> (((^x.x) b) a) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 126321/12718002. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 126322/12718047. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b a) c)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b a) c)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a) c)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a) c)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a) c)) 7. ==[ beta ]==> (((^y.y)(^z.z))((b a) c)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b a) c)) 9. ==[ beta ]==> ((^y.y)((b a) c)) 10. ==[ alpha ]==> ((^x.x)((b a) c)) 11. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 126323/12718110. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 126324/12718137. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 126325/12718281. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^y.y))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 126326/12718308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(a ((^z.z) b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a (a a))(a ((^y.y) b))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.x) b))) 7. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 126327/12718335. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> ((((a a) a) a)((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 126328/12718362. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 126329/12718389. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 126330/12718416. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 126331/12718596. ------ 1. ==[ start ]==> (((a b) c)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 126332/12718623. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(a (^y.y))) 3. ==[ beta ]==> (((a a) b)(a (^y.y))) 4. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 126333/12718650. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 126334/12718668. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 126335/12718695. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 126336/12718704. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 126337/12718731. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 126338/12718749. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 126339/12718785. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126340/12718812. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 126341/12718830. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 126342/12718839. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.a))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 126343/12718866. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 126344/12718893. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 126345/12719172. ------ 1. ==[ start ]==> ((a (b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 126346/12719514. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126347/12719532. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)(^y.y))) 3. ==[ beta ]==> (((a b)(a b))((b a)(^y.y))) 4. ==[ alpha ]==> (((a b)(a b))((b a)(^x.x))) REDUCED to normal form. ------ 126348/12719595. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 126349/12719613. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a b)(^y.(y y)))) 3. ==[ beta ]==> (b ((a b)(^y.(y y)))) 4. ==[ alpha ]==> (b ((a b)(^x.(x x)))) REDUCED to normal form. ------ 126350/12719622. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 126351/12719649. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 126352/12719676. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 126353/12719721. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(a a)))) REDUCED to normal form. ------ 126354/12720000. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126355/12720099. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1)) 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. ------ 126356/12720297. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 126357/12720342. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 126358/12720396. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a b)(^z.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a b)(^z.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))((a b)(^y.a))) 8. ==[ alpha ]==> (((a a)(a a))((a b)(^x.a))) REDUCED to normal form. ------ 126359/12720405. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 126360/12720432. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((^y.b)((^z.a)(a (a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(a (a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 126361/12720477. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (a a))(^x1.a))) 3. ==[ beta ]==> (b ((a (a a))(^x1.a))) 4. ==[ alpha ]==> (b ((a (a a))(^x.a))) REDUCED to normal form. ------ 126362/12720486. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 126363/12720513. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)(a b))) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 126364/12720540. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 126365/12720585. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126366/12720612. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 126367/12720792. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(b ((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(b (a a))) REDUCED to normal form. ------ 126368/12720819. ------ 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 a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a)))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 126369/12720846. ------ 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)(a a))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a a))) REDUCED to normal form. ------ 126370/12720900. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(((a a) a) a)) REDUCED to normal form. ------ 126371/12720927. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a (a a)))) 6. ==[ alpha ]==> ((a b)((^x.x)(a (a a)))) 7. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 126372/12721098. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 126373/12721215. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 126374/12721242. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 126375/12721260. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(a a)))) 5. ==[ beta ]==> (b ((a a)(^y.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 126376/12721269. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 126377/12721287. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 126378/12721296. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 126379/12721377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126380/12721404. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 126381/12721431. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 126382/12721458. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 126383/12721485. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(a a))) REDUCED to normal form. ------ 126384/12721530. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.b) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126385/12721602. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a a) b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 126386/12721629. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 126387/12721656. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (^y.y))((a a) a))) 3. ==[ beta ]==> ((a (b a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> ((a (b a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 126388/12721683. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(a b))) REDUCED to normal form. ------ 126389/12721962. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> (((^y.y)(^z.z)) c) 6. ==[ alpha ]==> (((^x.x)(^y.y)) c) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 126390/12722097. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b) a)) 3. ==[ beta ]==> (b ((^z.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126391/12722241. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b (^y.a))) 3. ==[ beta ]==> ((b b)(b (^y.a))) 4. ==[ alpha ]==> ((b b)(b (^x.a))) REDUCED to normal form. ------ 126392/12722268. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.b))) REDUCED to normal form. ------ 126393/12722286. ------ 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. ------ 126394/12722313. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126395/12722322. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 126396/12722349. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((^y1.y1) a)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)((^y1.y1) a))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a ((^y1.y1) a))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1) a))) 9. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 126397/12722367. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> (((b a)(b a))(a (^y.(y y)))) 6. ==[ alpha ]==> (((b a)(b a))(a (^x.(x x)))) REDUCED to normal form. ------ 126398/12722430. ------ 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))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 126399/12722448. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a) a)) 3. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 126400/12722457. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 126401/12722511. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 126402/12722565. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 126403/12722592. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 126404/12722655. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 126405/12722682. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a ((^z.z) a))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a ((^y.y) a))) 7. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 126406/12722709. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 126407/12722736. ------ 1. ==[ start ]==> (((a (a a))(b a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(b a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(b a))((a a)(^x.x))) REDUCED to normal form. ------ 126408/12723006. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 126409/12723096. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a) c)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a) c)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126410/12723177. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((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. ------ 126411/12723285. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126412/12723321. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 126413/12723348. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 126414/12723393. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z)) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y)) a)) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 126415/12723420. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.a) b)) 3. ==[ beta ]==> ((^y.y)((^z.a) b)) 4. ==[ alpha ]==> ((^x.x)((^y.a) b)) 5. ==[ beta ]==> ((^y.a) b) 6. ==[ alpha ]==> ((^x.a) b) 7. ==[ beta ]==> a REDUCED to normal form. ------ 126416/12723456. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.a))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 126417/12723483. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 126418/12723555. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.a))) 3. ==[ beta ]==> (b ((a a)(^z.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 126419/12723564. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y) a)) 5. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 126420/12723591. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 126421/12723663. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126422/12723699. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 126423/12723726. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 126424/12723789. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a c)) REDUCED to normal form. ------ 126425/12723816. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 126426/12723843. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a (a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a (a (^y.y)))) 5. ==[ beta ]==> ((a b)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a b)(a (a (^x.x)))) REDUCED to normal form. ------ 126427/12723870. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 126428/12723897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b a)) 3. ==[ beta ]==> (((^y.y)(b a))(b a)) 4. ==[ alpha ]==> (((^x.x)(b a))(b a)) 5. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 126429/12723924. ------ 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. ------ 126430/12723951. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a (a a))) 3. ==[ beta ]==> (((a b)(a a))(a (a a))) REDUCED to normal form. ------ 126431/12723978. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a a)) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 126432/12724584. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^y.(y (^z.z)))(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z (^x1.x1)))(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> (((^z.(z (^x1.x1)))(^y1.(y1 (^z1.z1))))(^y.y)) 6. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(z (^x1.x1))))(^y1.y1)) 7. ==[ beta ]==> (((^z.(z (^x1.x1)))(^y.y))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.x1)) 9. ==[ beta ]==> (((^z.z)(^y.y))(^x1.x1)) 10. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 11. ==[ beta ]==> ((^y.y)(^z.z)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126433/12732714. ------ 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. ------ 126434/12732738. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126435/12732819. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126436/12733053. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126437/12733323. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((^y.y)(b (^z.z)))(((^y.y)(b (^z.z)))((^y.y)(b (^z.z))))) 4. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(b (^x1.x1)))((^y1.y1)(b (^z1.z1))))) 5. ==[ beta ]==> ((b (^y.y))(((^z.z)(b (^x1.x1)))((^y1.y1)(b (^z1.z1))))) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y)(b (^z.z)))((^x1.x1)(b (^y1.y1))))) 7. ==[ beta ]==> ((b (^x.x))((b (^z.z))((^x1.x1)(b (^y1.y1))))) 8. ==[ alpha ]==> ((b (^x.x))((b (^y.y))((^z.z)(b (^x1.x1))))) 9. ==[ beta ]==> ((b (^x.x))((b (^y.y))(b (^x1.x1)))) 10. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 126438/12733326. ------ 1. ==[ start ]==> ((a (a (a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 126439/12733713. ------ 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))) REDUCED to normal form. ------ 126440/12734619. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)(^z.b))) 3. ==[ beta ]==> (((^y.b)(^z.b)) b) 4. ==[ alpha ]==> (((^x.b)(^y.b)) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 126441/12734793. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((z z)(z z)))) 3. ==[ beta ]==> (b (^z.((z z)(z z)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 126442/12735006. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.((((^z.z)(^x1.x1))((^y1.y1)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a))))) 4. ==[ alpha ]==> (^x.((((^y.y)(^z.z))((^x1.x1)(a a)))(((^y1.y1)(^z1.z1))((^x2.x2)(a a))))) 5. ==[ beta ]==> (^x.(((^z.z)((^x1.x1)(a a)))(((^y1.y1)(^z1.z1))((^x2.x2)(a a))))) 6. ==[ alpha ]==> (^x.(((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a))))) 7. ==[ beta ]==> (^x.(((^z.z)(a a))(((^x1.x1)(^y1.y1))((^z1.z1)(a a))))) 8. ==[ alpha ]==> (^x.(((^y.y)(a a))(((^z.z)(^x1.x1))((^y1.y1)(a a))))) 9. ==[ beta ]==> (^x.((a a)(((^z.z)(^x1.x1))((^y1.y1)(a a))))) 10. ==[ alpha ]==> (^x.((a a)(((^y.y)(^z.z))((^x1.x1)(a a))))) 11. ==[ beta ]==> (^x.((a a)((^z.z)((^x1.x1)(a a))))) 12. ==[ alpha ]==> (^x.((a a)((^y.y)((^z.z)(a a))))) 13. ==[ beta ]==> (^x.((a a)((^z.z)(a a)))) 14. ==[ alpha ]==> (^x.((a a)((^y.y)(a a)))) 15. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 126443/12735450. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 126444/12735783. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^b.(^b.b))) 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. ------ 126445/12736404. ------ 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))))) REDUCED to normal form. ------ 126446/12736644. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.(^x1.x1)))) 3. ==[ eta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 126447/12737268. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(z a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(z a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(y a))) 5. ==[ beta ]==> ((a (a a))(^y.(y a))) 6. ==[ alpha ]==> ((a (a a))(^x.(x a))) REDUCED to normal form. ------ 126448/12737481. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^x1.a)(^y1.(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.a)(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> (a (^z.(^x1.x1))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 126449/12738294. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 126450/12738744. ------ 1. ==[ start ]==> (((a a)(^b.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 126451/12739185. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(z z)))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(y y)))) 7. ==[ beta ]==> ((a a)(^y.(^z.(y y)))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 126452/12739374. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(a y))) 3. ==[ eta ]==> ((((^x.x) b)(a a)) a) 4. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 126453/12739398. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(^z.z))) 3. ==[ beta ]==> ((((^y.b)(^z.z))((^y.b)(^z.z)))(((^y.b)(^z.z))((^y.b)(^z.z)))) 4. ==[ alpha ]==> ((((^x.b)(^y.y))((^z.b)(^x1.x1)))(((^y1.b)(^z1.z1))((^x2.b)(^y2.y2)))) 5. ==[ beta ]==> ((b ((^z.b)(^x1.x1)))(((^y1.b)(^z1.z1))((^x2.b)(^y2.y2)))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.y)))(((^z.b)(^x1.x1))((^y1.b)(^z1.z1)))) 7. ==[ beta ]==> ((b b)(((^z.b)(^x1.x1))((^y1.b)(^z1.z1)))) 8. ==[ alpha ]==> ((b b)(((^x.b)(^y.y))((^z.b)(^x1.x1)))) 9. ==[ beta ]==> ((b b)(b ((^z.b)(^x1.x1)))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(^y.y)))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 126454/12739572. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^a.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(z b))) 3. ==[ beta ]==> (b (^z.(z b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 126455/12739905. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 126456/12740478. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126457/12740868. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(z (z z)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(z (z z)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 126458/12741039. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 126459/12741138. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(a (a a)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126460/12741201. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 126461/12741264. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 126462/12741318. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 126463/12741372. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 126464/12741399. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 126465/12741426. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 126466/12741453. ------ 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. ------ 126467/12741483. ------ 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 (^x.x))((a a)(a b))) REDUCED to normal form. ------ 126468/12741510. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 126469/12741537. ------ 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. ------ 126470/12741564. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 126471/12741618. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126472/12741645. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^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. ------ 126473/12741672. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 126474/12741708. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 126475/12741762. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^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. ------ 126476/12741771. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) a)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) a)) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 126477/12741798. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 126478/12741843. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 126479/12741870. ------ 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))) 5. ==[ beta ]==> ((a a)((a a)(^y.b))) 6. ==[ alpha ]==> ((a a)((a a)(^x.b))) REDUCED to normal form. ------ 126480/12741897. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.(a a)))) REDUCED to normal form. ------ 126481/12741987. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 126482/12742014. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 126483/12742041. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 126484/12742068. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(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. ------ 126485/12742140. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) b) c)) 3. ==[ beta ]==> ((a b)(((^y.y) b) c)) 4. ==[ alpha ]==> ((a b)(((^x.x) b) c)) 5. ==[ beta ]==> ((a b)(b c)) REDUCED to normal form. ------ 126486/12742365. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 126487/12742392. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 126488/12742428. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126489/12742455. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(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. ------ 126490/12742509. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 8. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 9. ==[ beta ]==> (b (a (^y.y))) 10. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 126491/12742518. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.b) c)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x) c)) 3. ==[ beta ]==> (((a (a a)) b) c) REDUCED to normal form. ------ 126492/12742563. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 7. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 126493/12742590. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 126494/12742644. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a b)(a b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a b)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(a b))) REDUCED to normal form. ------ 126495/12742797. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 126496/12742977. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.a))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 7. ==[ beta ]==> (b ((a a)(^y.a))) 8. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 126497/12743004. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.b))) REDUCED to normal form. ------ 126498/12743058. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 126499/12743112. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126500/12743139. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126501/12743229. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 126502/12743256. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 126503/12743337. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 126504/12743364. ------ 1. ==[ start ]==> ((a (a b))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((a (a b))((^x.b)(^y.b))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 126505/12743535. ------ 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. ------ 126506/12743544. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b) a)((^x.(a a)) a)) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 126507/12743562. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) b)(a a))) 3. ==[ beta ]==> ((a b)(((^y.y) b)(a a))) 4. ==[ alpha ]==> ((a b)(((^x.x) b)(a a))) 5. ==[ beta ]==> ((a b)(b (a a))) REDUCED to normal form. ------ 126508/12743571. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.b) b)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y) b)) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 126509/12743589. ------ 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.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 126510/12743643. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((a a)(^y.y))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a a)(^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 126511/12743724. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a) a)(a b))) 3. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 126512/12743751. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 126513/12743850. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 126514/12743904. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 126515/12743922. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 126516/12743931. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 126517/12744165. ------ 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.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126518/12744192. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 126519/12744219. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b a)) REDUCED to normal form. ------ 126520/12744273. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a) c)) REDUCED to normal form. ------ 126521/12744417. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 126522/12744444. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 126523/12744498. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 126524/12744525. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.a)(^b.b))) 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. ------ 126525/12744570. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 126526/12744669. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 126527/12744804. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.z))(b a))) 3. ==[ beta ]==> (b ((a (^z.z))(b a))) 4. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 126528/12744867. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 126529/12744921. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 126530/12744948. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.b))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.b))((a a)(^y.(y y)))) REDUCED to normal form. ------ 126531/12745002. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126532/12745029. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(^z.b))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.b)) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 126533/12745056. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 126534/12745146. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 126535/12745173. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 126536/12745254. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 9. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 10. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126537/12745281. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 126538/12745308. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b) a)((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(^y.a))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 126539/12745335. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 126540/12745362. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 126541/12745389. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 126542/12745479. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a)(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a)(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(a a))) 5. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 126543/12745560. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a b)(a (a a)))) 3. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 126544/12745668. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 126545/12745695. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 126546/12745758. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a)(^y.y))) REDUCED to normal form. ------ 126547/12745812. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 126548/12745839. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)(^y.(y y)))) REDUCED to normal form. ------ 126549/12745866. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 126550/12745956. ------ 1. ==[ start ]==> (((a a)(b a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 126551/12745983. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 126552/12746010. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)(b a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(b a))) 5. ==[ beta ]==> ((a (a a))((^y.y)(b a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(b a))) 7. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 126553/12746091. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 126554/12746118. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 126555/12746172. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 126556/12746226. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 126557/12746316. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a)(^z.z))(a a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(^z.z))(a a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> ((a a)(((a a)(^z.z))(a a))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 126558/12746397. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (((a a) a)(a (a a)))) REDUCED to normal form. ------ 126559/12746505. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126560/12746532. ------ 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 a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 126561/12746622. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)(^y.a))) REDUCED to normal form. ------ 126562/12746649. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.b)(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.(y y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 126563/12746703. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.a))) REDUCED to normal form. ------ 126564/12746730. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a (^z.b))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.b))) REDUCED to normal form. ------ 126565/12746757. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 126566/12746811. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 126567/12746847. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 126568/12746874. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 126569/12746928. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 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. ------ 126570/12746955. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.a))) 7. ==[ beta ]==> ((a b)((^y.a)(^y.a))) 8. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 9. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 126571/12746982. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 126572/12747009. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 126573/12747108. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126574/12747153. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^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. ------ 126575/12747180. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z1.z1)(^x2.x2)))) 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. ------ 126576/12747432. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.a))) REDUCED to normal form. ------ 126577/12747459. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.y))(^z.b))) 3. ==[ beta ]==> ((b a)((a (^y.y))(^z.b))) 4. ==[ alpha ]==> ((b a)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 126578/12747486. ------ 1. ==[ start ]==> (((a a)(^b.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 126579/12747513. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a) a)) REDUCED to normal form. ------ 126580/12747747. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126581/12747756. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 126582/12747783. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) c)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 126583/12747873. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c (^y.a))) 3. ==[ beta ]==> ((a (b a))(c (^y.a))) 4. ==[ alpha ]==> ((a (b a))(c (^x.a))) REDUCED to normal form. ------ 126584/12747900. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(b (^y.b))) REDUCED to normal form. ------ 126585/12747927. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(a (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(a (^z.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(a (^z.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(a a)))) 7. ==[ beta ]==> ((a a)(a (^y.(a a)))) 8. ==[ alpha ]==> ((a a)(a (^x.(a a)))) REDUCED to normal form. ------ 126586/12747954. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)(a a))) 3. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 126587/12747981. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 126588/12748008. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 126589/12748035. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 126590/12748089. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.x1)) REDUCED to normal form. ------ 126591/12748116. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.y)(a b))) 3. ==[ beta ]==> ((b (a a))((^y.y)(a b))) 4. ==[ alpha ]==> ((b (a a))((^x.x)(a b))) 5. ==[ beta ]==> ((b (a a))(a b)) REDUCED to normal form. ------ 126592/12748143. ------ 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. ------ 126593/12748314. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(a (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 126594/12748422. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126595/12748539. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 126596/12748566. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (a a))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (a a))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(^x1.a))) REDUCED to normal form. ------ 126597/12748647. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 126598/12748674. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a) a)) REDUCED to normal form. ------ 126599/12748728. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a)) c)) REDUCED to normal form. ------ 126600/12748953. ------ 1. ==[ start ]==> (((a (a a))(b a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 126601/12749007. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 126602/12749034. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 126603/12749061. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 126604/12749088. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 126605/12749142. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 126606/12749169. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 126607/12749196. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 126608/12749223. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 126609/12749313. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2) a)(a (^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2) a)(a (^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126610/12749538. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a) b)) 3. ==[ beta ]==> ((b c)(((^y.y) a) b)) 4. ==[ alpha ]==> ((b c)(((^x.x) a) b)) 5. ==[ beta ]==> ((b c)(a b)) REDUCED to normal form. ------ 126611/12749565. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x)) c)) REDUCED to normal form. ------ 126612/12749610. ------ 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)))) REDUCED to normal form. ------ 126613/12749637. ------ 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) 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. ------ 126614/12749673. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 126615/12749691. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a) a)) REDUCED to normal form. ------ 126616/12749772. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 126617/12749781. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 126618/12749808. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a) a)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a) a)) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 126619/12749880. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126620/12749889. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 126621/12749916. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 126622/12750006. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 126623/12750033. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 126624/12750060. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 126625/12750087. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 126626/12750114. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 126627/12750141. ------ 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)(^x.x)))(a a)) REDUCED to normal form. ------ 126628/12750168. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 126629/12750195. ------ 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. ------ 126630/12751926. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126631/12758940. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b)) c) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b)) c) 3. ==[ beta ]==> (((a a)(a b)) c) REDUCED to normal form. ------ 126632/12759288. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ eta ]==> ((^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))) REDUCED to normal form. ------ 126633/12759459. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 126634/12759570. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(y (^z.z)))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> ((^z.(z (^x1.x1)))(^y.y)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 9. ==[ beta ]==> ((^z.z)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126635/12759783. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126636/12760341. ------ 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. ------ 126637/12760674. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126638/12760677. ------ 1. ==[ start ]==> ((a (^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 126639/12761028. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 126640/12761037. ------ 1. ==[ start ]==> (((a b) a)(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 126641/12761448. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.y)(((b a)(^z.a))((b a)(^z.a)))) 4. ==[ alpha ]==> ((^x.x)(((b a)(^y.a))((b a)(^z.a)))) 5. ==[ beta ]==> (((b a)(^y.a))((b a)(^z.a))) 6. ==[ alpha ]==> (((b a)(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 126642/12761703. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^b.((^a.a) b))) 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. ------ 126643/12762333. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 126644/12763224. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(b a))) REDUCED to normal form. ------ 126645/12763242. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126646/12763428. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 126647/12764295. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126648/12764319. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126649/12764634. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a) d)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a) d)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 126650/12764997. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 126651/12765609. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.b))) 3. ==[ beta ]==> ((b (a a))(^y.(^z.b))) 4. ==[ alpha ]==> ((b (a a))(^x.(^y.b))) REDUCED to normal form. ------ 126652/12765633. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b) a)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b) a)) 3. ==[ beta ]==> ((((a b) a)((a b) a))(((a b) a)((a b) a))) REDUCED to normal form. ------ 126653/12765807. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.z))) 3. ==[ beta ]==> (b (^z.(^x1.z))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 126654/12765996. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(^z.b))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.b))) REDUCED to normal form. ------ 126655/12766158. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.((a a) a))) 3. ==[ beta ]==> (b (^y.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 126656/12766329. ------ 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. ------ 126657/12766887. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 126658/12766995. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126659/12767103. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 126660/12767373. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126661/12767382. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 126662/12767499. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 126663/12767553. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.b)) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.b)) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.b)) 5. ==[ beta ]==> ((a b)(^y.b)) 6. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 126664/12767607. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.z)) 3. ==[ beta ]==> (((^y.y)(b a))(^z.z)) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.y)) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 126665/12767661. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.a)) 3. ==[ beta ]==> (((a b)(a a))(^y.a)) 4. ==[ alpha ]==> (((a b)(a a))(^x.a)) REDUCED to normal form. ------ 126666/12767688. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(a 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. ------ 126667/12767736. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (a (((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (a (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (a ((a a)(a b))) REDUCED to normal form. ------ 126668/12767763. ------ 1. ==[ start ]==> (((a a) a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) a)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a) a)((a b)(a a))) REDUCED to normal form. ------ 126669/12767790. ------ 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)))) REDUCED to normal form. ------ 126670/12767817. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 126671/12767844. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((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. ------ 126672/12767871. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a a) b)(a ((^y.y) b))) 4. ==[ alpha ]==> (((a a) b)(a ((^x.x) b))) 5. ==[ beta ]==> (((a a) b)(a b)) REDUCED to normal form. ------ 126673/12767898. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 126674/12767925. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(b (^z.z)))) REDUCED to normal form. ------ 126675/12767988. ------ 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)))) REDUCED to normal form. ------ 126676/12768015. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.a))) REDUCED to normal form. ------ 126677/12768042. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 126678/12768051. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 126679/12768132. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))(a b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(a b))) 5. ==[ beta ]==> (a ((^y.(a a))(a b))) 6. ==[ alpha ]==> (a ((^x.(a a))(a b))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 126680/12768159. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 126681/12768213. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 126682/12768231. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a a))(^y.(^z.(^x1.x1))))) 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. ------ 126683/12768258. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 126684/12768321. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y)(b (^z.z)))((^y.y)(b (^z.z)))) 6. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.z)(b (^x1.x1)))) 7. ==[ beta ]==> ((b (^y.y))((^z.z)(b (^x1.x1)))) 8. ==[ alpha ]==> ((b (^x.x))((^y.y)(b (^z.z)))) 9. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 10. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 126685/12768402. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.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. ------ 126686/12768429. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 126687/12768510. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 126688/12768537. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 126689/12768672. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126690/12768762. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a)) b)(b (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) b)(b (a (^x.x)))) REDUCED to normal form. ------ 126691/12768789. ------ 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.y1) a))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (a ((a (^y.(^z.z)))((^x1.x1) a))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))((^z.z) a))) 7. ==[ beta ]==> (a ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 126692/12768816. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(a (a a)))) REDUCED to normal form. ------ 126693/12768843. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 126694/12768870. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.a))((a a)((a a) a))) REDUCED to normal form. ------ 126695/12768897. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 126696/12768924. ------ 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) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 8. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 9. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 126697/12769095. ------ 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. ------ 126698/12769131. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 126699/12769266. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)(a b))) 3. ==[ beta ]==> (((a a) a)((^y.b)(a b))) 4. ==[ alpha ]==> (((a a) a)((^x.b)(a b))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 126700/12769347. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))(b a))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))(b a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))(b a))) 7. ==[ beta ]==> ((a a)((^y.(y y))(b a))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(b a))) 9. ==[ beta ]==> ((a a)((b a)(b a))) REDUCED to normal form. ------ 126701/12769428. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.b))((a a)(a a))) REDUCED to normal form. ------ 126702/12769446. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a)(a a)) a)) REDUCED to normal form. ------ 126703/12769473. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) b) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) b) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b b)) REDUCED to normal form. ------ 126704/12769617. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((^y.b)((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((^x.b)((^y.b)(^z.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 126705/12769761. ------ 1. ==[ start ]==> ((((a a) a) b)(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)(b ((^x.x) b))) 3. ==[ beta ]==> ((((a a) a) b)(b b)) REDUCED to normal form. ------ 126706/12769779. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 126707/12769788. ------ 1. ==[ start ]==> (((a b) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 126708/12769815. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a a)(^x.b))(b (a a))) REDUCED to normal form. ------ 126709/12769869. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 126710/12769896. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 126711/12769923. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 126712/12769950. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 126713/12769977. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)(a b))) REDUCED to normal form. ------ 126714/12770148. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 126715/12770175. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 126716/12770202. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a)(^y.a))) 3. ==[ beta ]==> ((a (a a))((b a)(^y.a))) 4. ==[ alpha ]==> ((a (a a))((b a)(^x.a))) REDUCED to normal form. ------ 126717/12770238. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^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. ------ 126718/12770292. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)((a a) a))) 5. ==[ beta ]==> ((^y.y)((^y1.b)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 7. ==[ beta ]==> ((^y.b)((a a) a)) 8. ==[ alpha ]==> ((^x.b)((a a) a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 126719/12770373. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 126720/12770427. ------ 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))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 126721/12770454. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^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) 9. ==[ beta ]==> b REDUCED to normal form. ------ 126722/12770508. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 11. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 12. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126723/12770589. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126724/12770796. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b) 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. ------ 126725/12770814. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 126726/12770823. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 126727/12771048. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c (^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 126728/12771057. ------ 1. ==[ start ]==> (((a b) c)((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a b) c)((a (^x.x))(b a))) REDUCED to normal form. ------ 126729/12771084. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b)((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) b)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 126730/12771129. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 126731/12771210. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 126732/12771291. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126733/12771390. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126734/12771417. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 126735/12771444. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a) b)) 3. ==[ beta ]==> ((a (a b))((b a) b)) REDUCED to normal form. ------ 126736/12771867. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)((a a) a)) REDUCED to normal form. ------ 126737/12771975. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a a)(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a a)(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)(b a))) REDUCED to normal form. ------ 126738/12771993. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 126739/12772074. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126740/12772182. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a b)(a b))) REDUCED to normal form. ------ 126741/12772200. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(b a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(b a))(a (^x.(a a)))) REDUCED to normal form. ------ 126742/12772281. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a) a)) REDUCED to normal form. ------ 126743/12772308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y)) b)) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y)) b)) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 126744/12772479. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126745/12772758. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^z.z))(a a))) REDUCED to normal form. ------ 126746/12772776. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 126747/12772785. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 126748/12772857. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a (^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a (^y.y)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 126749/12772938. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126750/12773046. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^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. ------ 126751/12773073. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 126752/12773091. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a) b)) REDUCED to normal form. ------ 126753/12773118. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a b) c)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a b) c)) REDUCED to normal form. ------ 126754/12773352. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126755/12773361. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 126756/12773388. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a) d)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a) d)) 3. ==[ beta ]==> ((a b)((^y.a) d)) 4. ==[ alpha ]==> ((a b)((^x.a) d)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 126757/12773559. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(a a))) 3. ==[ beta ]==> (b ((^z.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126758/12773667. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126759/12773721. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126760/12773748. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.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. ------ 126761/12773802. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 126762/12773883. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 126763/12773892. ------ 1. ==[ start ]==> (((a b)(^c.a))(d ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))(d (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))(d (^y.y))) REDUCED to normal form. ------ 126764/12773919. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((a a) a))) REDUCED to normal form. ------ 126765/12773946. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (a b))) REDUCED to normal form. ------ 126766/12774000. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(a a))) REDUCED to normal form. ------ 126767/12774027. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 126768/12774198. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a b)(^x.x))) REDUCED to normal form. ------ 126769/12774225. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 126770/12774252. ------ 1. ==[ start ]==> ((((^a.a)(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.y1))(^z1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.a))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 126771/12774279. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 126772/12774360. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a a)(^y.b))) 3. ==[ beta ]==> ((b (a a))((a a)(^y.b))) 4. ==[ alpha ]==> ((b (a a))((a a)(^x.b))) REDUCED to normal form. ------ 126773/12774387. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b) a)) REDUCED to normal form. ------ 126774/12774423. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 126775/12774558. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.b))) 3. ==[ beta ]==> (b ((^z.z)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.x)(^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 126776/12774702. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b b)((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b b)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((b b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 126777/12774729. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a a)((a a) a))) REDUCED to normal form. ------ 126778/12774747. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(a (^y.b))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.b))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.b))) REDUCED to normal form. ------ 126779/12774774. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 126780/12774828. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (((b a)(b a))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (((b a)(b a))(a ((^y.y) a))) 8. ==[ alpha ]==> (((b a)(b a))(a ((^x.x) a))) 9. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 126781/12774909. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 126782/12775017. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126783/12775026. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (a (a a)))) REDUCED to normal form. ------ 126784/12775053. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 126785/12775080. ------ 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. ------ 126786/12775116. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 126787/12775143. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z)) c)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z)) c)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y)) c)) 5. ==[ beta ]==> (((a (^x.x)) b)(c c)) REDUCED to normal form. ------ 126788/12775251. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 8. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 126789/12775278. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 126790/12775305. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a a)((a a) a))(a (^y.a))) 6. ==[ alpha ]==> (((a a)((a a) a))(a (^x.a))) REDUCED to normal form. ------ 126791/12775332. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 126792/12775386. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) 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)((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z) a)) 7. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 126793/12775413. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (a a)) b)) 3. ==[ beta ]==> ((b (a (^y.y)))((a (a a)) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 126794/12775638. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 126795/12775746. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126796/12775782. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d (a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d (a a))) 3. ==[ beta ]==> ((b c)(d (a a))) REDUCED to normal form. ------ 126797/12775809. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c (a (^x.x)))) REDUCED to normal form. ------ 126798/12775854. ------ 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 (^x.x))(^z.(z z))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 126799/12775917. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 126800/12775935. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (^x1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (^y1.a))) REDUCED to normal form. ------ 126801/12775944. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 126802/12776016. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126803/12776025. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b c)) REDUCED to normal form. ------ 126804/12776124. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126805/12776133. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 126806/12776160. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(a a))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(a a))) REDUCED to normal form. ------ 126807/12776187. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 126808/12776250. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 126809/12776277. ------ 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)) a)) REDUCED to normal form. ------ 126810/12776304. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((a a) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a) b)) 5. ==[ beta ]==> ((a b)((a a) b)) REDUCED to normal form. ------ 126811/12776331. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 126812/12776358. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z) b)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y) b)) 5. ==[ beta ]==> ((b a)((^y.y) b)) 6. ==[ alpha ]==> ((b a)((^x.x) b)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 126813/12776385. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 126814/12776412. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a) a)) 3. ==[ beta ]==> (((a b)(a a))((a a) a)) REDUCED to normal form. ------ 126815/12776439. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.y) a)) 3. ==[ beta ]==> (((a a)(a b))((^y.y) a)) 4. ==[ alpha ]==> (((a a)(a b))((^x.x) a)) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 126816/12776465. ------ 1. ==[ start ]==> (^a.(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (^x.(((x x)(^y.y))((x x) x))) REDUCED to normal form. ------ 126817/12776466. ------ 1. ==[ start ]==> (a (((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (a (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 126818/12778179. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126819/12785220. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a)) a) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 126820/12785226. ------ 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. ------ 126821/12785253. ------ 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)(a a))(a b))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a))(a b))) 6. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a b))) 7. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 126822/12785280. ------ 1. ==[ start ]==> ((^a.b)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.b)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 126823/12785361. ------ 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 ]==> (((a (a a))(a (^z.(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 126824/12785478. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (^y.((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (^x.((b (^y.y))(^z.z))) REDUCED to normal form. ------ 126825/12786936. ------ 1. ==[ start ]==> ((^a.(^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 126826/12786939. ------ 1. ==[ start ]==> ((a (^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 126827/12787299. ------ 1. ==[ start ]==> (((a b) a)(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 126828/12787965. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 126829/12787974. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^b.((^a.a) b))) 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. ------ 126830/12788307. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.((^z.z) b))) 3. ==[ beta ]==> ((((a a) a) a)(^y.((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.((^y.y) b))) 5. ==[ beta ]==> ((((a a) a) a)(^x.b)) REDUCED to normal form. ------ 126831/12788385. ------ 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))((^x1.x1) a))) 3. ==[ beta ]==> (((((a a)(^z.z))((^x1.x1) a))(((a a)(^z.z))((^x1.x1) a)))(^y.y)) 4. ==[ alpha ]==> (((((a a)(^x.x))((^y.y) a))(((a a)(^z.z))((^x1.x1) a)))(^y1.y1)) 5. ==[ beta ]==> (((((a a)(^x.x)) a)(((a a)(^z.z))((^x1.x1) a)))(^y1.y1)) 6. ==[ alpha ]==> (((((a a)(^x.x)) a)(((a a)(^y.y))((^z.z) a)))(^x1.x1)) 7. ==[ beta ]==> (((((a a)(^x.x)) a)(((a a)(^y.y)) a))(^x1.x1)) 8. ==[ alpha ]==> (((((a a)(^x.x)) a)(((a a)(^y.y)) a))(^z.z)) REDUCED to normal form. ------ 126832/12788622. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 126833/12789513. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 126834/12789690. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))(^y1.b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 126835/12790566. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 126836/12790581. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126837/12790818. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 126838/12790896. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 126839/12791268. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(a a))) REDUCED to normal form. ------ 126840/12792420. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 126841/12792429. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.((a a) a))) REDUCED to normal form. ------ 126842/12792591. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 126843/12792975. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c ((^z.z) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 126844/12793365. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.d)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.d)) 3. ==[ beta ]==> ((b (^y.y))(^z.d)) 4. ==[ alpha ]==> ((b (^x.x))(^y.d)) REDUCED to normal form. ------ 126845/12793563. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.b))(^y.a)) REDUCED to normal form. ------ 126846/12793644. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.a))) REDUCED to normal form. ------ 126847/12793842. ------ 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)))) REDUCED to normal form. ------ 126848/12793869. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(a a))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(a a))) 5. ==[ beta ]==> ((b a)(^y.(a a))) 6. ==[ alpha ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 126849/12793923. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.b)) 3. ==[ beta ]==> (((a b)(a a))(^y.b)) 4. ==[ alpha ]==> (((a b)(a a))(^x.b)) REDUCED to normal form. ------ 126850/12793950. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^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. ------ 126851/12793977. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 126852/12793989. ------ 1. ==[ start ]==> ((a a)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 126853/12794016. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 126854/12794043. ------ 1. ==[ start ]==> ((a b)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> ((a b)((a b)(a a))) REDUCED to normal form. ------ 126855/12794097. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(b a))) 5. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 126856/12794124. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 126857/12794241. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 126858/12794277. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126859/12794322. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 126860/12794349. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 126861/12794403. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (a (((^y.y)(a a))(^z.b))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.b))) 7. ==[ beta ]==> (a ((a a)(^y.b))) 8. ==[ alpha ]==> (a ((a a)(^x.b))) REDUCED to normal form. ------ 126862/12794412. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 126863/12794430. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 126864/12794439. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 126865/12794574. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 126866/12794619. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 5. ==[ beta ]==> ((b (^y.y)) a) 6. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 126867/12794655. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 126868/12794673. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) b) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) b) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) c)) 5. ==[ beta ]==> ((^y.y)(((^z.z) b) c)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 7. ==[ beta ]==> (((^y.y) b) c) 8. ==[ alpha ]==> (((^x.x) b) c) 9. ==[ beta ]==> (b c) REDUCED to normal form. ------ 126869/12794682. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.a)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.a)) REDUCED to normal form. ------ 126870/12794709. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 126871/12794790. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 126872/12794898. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((b b)(^y.(^z.z))) 8. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 126873/12795231. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^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. ------ 126874/12795258. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (a a))(b a))) REDUCED to normal form. ------ 126875/12795285. ------ 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) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 126876/12795312. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 126877/12795339. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a a)((a a)(a a)))) 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. ------ 126878/12795402. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 126879/12795456. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)(^z.(z z)))) 5. ==[ beta ]==> (a ((b a)(^z.(z z)))) 6. ==[ alpha ]==> (a ((b a)(^x.(x x)))) REDUCED to normal form. ------ 126880/12795492. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^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. ------ 126881/12795519. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 126882/12795537. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a) 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. ------ 126883/12795564. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(a a))) 6. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 126884/12795573. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 126885/12795600. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 126886/12795627. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((b a)(b a))) REDUCED to normal form. ------ 126887/12795654. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126888/12795681. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 126889/12795699. ------ 1. ==[ start ]==> ((a (^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 126890/12795870. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126891/12796032. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 126892/12796059. ------ 1. ==[ start ]==> (((a b) a)((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(^y.(a a))) 4. ==[ alpha ]==> (((a b) a)(^x.(a a))) REDUCED to normal form. ------ 126893/12796077. ------ 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)) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 126894/12796104. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.b) 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) 7. ==[ beta ]==> b REDUCED to normal form. ------ 126895/12796284. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)(a a))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)(a a))) 7. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 126896/12796311. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 126897/12796338. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) a)(b a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(b a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(b a))) 7. ==[ beta ]==> ((a (^x.x))(a (b a))) REDUCED to normal form. ------ 126898/12796365. ------ 1. ==[ start ]==> (((a (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.(^z.z))))) REDUCED to normal form. ------ 126899/12796392. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((a a)((^z.z) b))) 6. ==[ alpha ]==> (((^x.x) a)((a a)((^y.y) b))) 7. ==[ beta ]==> (a ((a a)((^y.y) b))) 8. ==[ alpha ]==> (a ((a a)((^x.x) b))) 9. ==[ beta ]==> (a ((a a) b)) REDUCED to normal form. ------ 126900/12796437. ------ 1. ==[ start ]==> (((^a.b) b)((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.y)(a a))) 3. ==[ beta ]==> (b ((^y.y)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 126901/12796482. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.(a a))((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.(a a))((b a)(^y.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126902/12796509. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 126903/12796563. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(^y1.a))) 5. ==[ beta ]==> ((^y.y)((a b)(^y1.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. ------ 126904/12796644. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 126905/12796653. ------ 1. ==[ start ]==> (((a b) b)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> (((a b) b)(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 126906/12796680. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)(b a))) 3. ==[ beta ]==> (((a a) a)((^y.a)(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(b a))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 126907/12796698. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126908/12796707. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(a (^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. ------ 126909/12796725. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a)(^b.b))) 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. ------ 126910/12796734. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 126911/12796779. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1))) b)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1))) b)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1))) b)) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1))) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1))) b)) 9. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1))) b)) 10. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) b)) 11. ==[ beta ]==> ((a (^y.(^z.z))) b) 12. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 126912/12796788. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 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. ------ 126913/12796842. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 126914/12796869. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 126915/12796896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 126916/12797040. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(b (a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))(b (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 126917/12797067. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(a ((^y.y) b))) 3. ==[ beta ]==> ((((a a) a) a)(a ((^y.y) b))) 4. ==[ alpha ]==> ((((a a) a) a)(a ((^x.x) b))) 5. ==[ beta ]==> ((((a a) a) a)(a b)) REDUCED to normal form. ------ 126918/12797094. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 126919/12797121. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b a)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(a (^x.x)))) REDUCED to normal form. ------ 126920/12797148. ------ 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) a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 126921/12797328. ------ 1. ==[ start ]==> (((a b) c)(c (^d.a))) 2. ==[ alpha ]==> (((a b) c)(c (^x.a))) REDUCED to normal form. ------ 126922/12797355. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 126923/12797382. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 126924/12797400. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 126925/12797427. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 126926/12797463. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 126927/12797481. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(^y.(y y)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 126928/12797517. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126929/12797562. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (b ((^y.y)(^z.b))) 6. ==[ alpha ]==> (b ((^x.x)(^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 126930/12797571. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 126931/12797598. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z)(a a)))) 9. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 126932/12797625. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 126933/12797994. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) a)) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 126934/12798273. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 126935/12798327. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(a (^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. ------ 126936/12798345. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 126937/12798354. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 126938/12798381. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.b)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 126939/12798453. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(^x1.b))) REDUCED to normal form. ------ 126940/12798732. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126941/12799056. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 126942/12799128. ------ 1. ==[ start ]==> (((^a.(a 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))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))((a a)(^y.(^z.z)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 126943/12799137. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 126944/12799164. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.b)((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.b)((^y.b)((^z.z) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 126945/12799209. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 126946/12799218. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 126947/12799245. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 126948/12799272. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 126949/12799326. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.x1))) REDUCED to normal form. ------ 126950/12799344. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 126951/12799524. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c (a b))) 3. ==[ beta ]==> (((a b)(^y.y))(c (a b))) 4. ==[ alpha ]==> (((a b)(^x.x))(c (a b))) REDUCED to normal form. ------ 126952/12799551. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(b ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(b (a a))) REDUCED to normal form. ------ 126953/12799578. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a ((a a)(^y.y)))) REDUCED to normal form. ------ 126954/12799632. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)(a (^z.z)))) REDUCED to normal form. ------ 126955/12799659. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((a b)(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> ((a b)(((a a) a)((^x.x) a))) 5. ==[ beta ]==> ((a b)(((a a) a) a)) REDUCED to normal form. ------ 126956/12799668. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a) d)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) d)) 3. ==[ beta ]==> ((^y.y)((^z.a) d)) 4. ==[ alpha ]==> ((^x.x)((^y.a) d)) 5. ==[ beta ]==> ((^y.a) d) 6. ==[ alpha ]==> ((^x.a) d) 7. ==[ beta ]==> a REDUCED to normal form. ------ 126957/12799830. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^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. ------ 126958/12799938. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126959/12799947. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 10. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 126960/12799974. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)((a a) a))) 3. ==[ beta ]==> ((b a)((^y.a)((a a) a))) 4. ==[ alpha ]==> ((b a)((^x.a)((a a) a))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 126961/12799992. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.b))) 5. ==[ beta ]==> (b ((a (^y.y))(^z.b))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 126962/12800001. ------ 1. ==[ start ]==> (((a a)(^b.b))((^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. ------ 126963/12800019. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 126964/12800028. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.z1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 126965/12800073. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b) b)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b) b)) REDUCED to normal form. ------ 126966/12800109. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 126967/12800136. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 126968/12800163. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 126969/12800190. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 126970/12800217. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 126971/12800262. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126972/12800334. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a) b)((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y) a))) 7. ==[ beta ]==> (((a a) b)((^y.y) a)) 8. ==[ alpha ]==> (((a a) b)((^x.x) a)) 9. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 126973/12800361. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))(a (a a)))) REDUCED to normal form. ------ 126974/12800388. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (b a))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (b a))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (b a))(a (^y.y))) 8. ==[ alpha ]==> ((a (b a))(a (^x.x))) REDUCED to normal form. ------ 126975/12800415. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 126976/12800442. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(a b))) 7. ==[ beta ]==> ((a a)((a a)(a b))) REDUCED to normal form. ------ 126977/12800694. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 126978/12800973. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b b)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 126979/12801000. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(b (^x.a))) REDUCED to normal form. ------ 126980/12801045. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.y))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 126981/12801054. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 126982/12801081. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 126983/12801099. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (a a))(^y.a))) 3. ==[ beta ]==> (((b a)(b a))((a (a a))(^y.a))) 4. ==[ alpha ]==> (((b a)(b a))((a (a a))(^x.a))) REDUCED to normal form. ------ 126984/12801162. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 126985/12801180. ------ 1. ==[ start ]==> (((^a.b)(a b))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a a)(^y.a))) 3. ==[ beta ]==> (b ((a a)(^y.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 126986/12801189. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b))((a a) a)) REDUCED to normal form. ------ 126987/12801243. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 126988/12801297. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 126989/12801324. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 126990/12801387. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(^y.y))(a a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 126991/12801414. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 126992/12801441. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a ((^z.z) a))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 126993/12801468. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 126994/12801495. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(^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. ------ 126995/12801738. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c ((^y.y) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(c a)) REDUCED to normal form. ------ 126996/12801828. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126997/12802017. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 126998/12802053. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((b c)((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((b c)((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((b c)((^y.y)(^y.y))) 6. ==[ alpha ]==> ((b c)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b c)(^y.y)) 8. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 126999/12802080. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 127000/12802152. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(z z)) a)) 3. ==[ beta ]==> ((^y.y)((^z.(z z)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y y)) a)) 5. ==[ beta ]==> ((^y.(y y)) a) 6. ==[ alpha ]==> ((^x.(x x)) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127001/12802188. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 127002/12802215. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (^x1.a))) REDUCED to normal form. ------ 127003/12802287. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 127004/12802296. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 127005/12802323. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 127006/12802404. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.a)) REDUCED to normal form. ------ 127007/12802431. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c (^z.z))) 3. ==[ beta ]==> ((b (^y.a))(c (^z.z))) 4. ==[ alpha ]==> ((b (^x.a))(c (^y.y))) REDUCED to normal form. ------ 127008/12802458. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 127009/12802521. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b b)) REDUCED to normal form. ------ 127010/12802575. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (a a))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (a a))) 5. ==[ beta ]==> ((a b)(b (a a))) REDUCED to normal form. ------ 127011/12802602. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 127012/12802629. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(a a))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(a a))) 5. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 127013/12802656. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 127014/12802683. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a b)) 3. ==[ beta ]==> (((a b)(a a))(a b)) REDUCED to normal form. ------ 127015/12802710. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a (a a))) 3. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 127016/12802737. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 127017/12809418. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(a y))) 3. ==[ eta ]==> ((^x.((x x)(x x))) a) 4. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 127018/12811500. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a)) b) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 127019/12811524. ------ 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) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127020/12811605. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127021/12811839. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)((^x1.x1) a))) 3. ==[ eta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 127022/12812109. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))(((^y.(^z.z))((a a)(a a)))((^y.(^z.z))((a a)(a a))))) 4. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.(^x1.x1))((a a)(a a)))((^y1.(^z1.z1))((a a)(a a))))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((a a)(a a)))((^y1.(^z1.z1))((a a)(a a))))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a)(a a)))((^x1.(^y1.y1))((a a)(a a))))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))((^x1.(^y1.y1))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127023/12812460. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127024/12813246. ------ 1. ==[ start ]==> (((a a)((a a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 127025/12813405. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^z.a)) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.a)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 127026/12813606. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((y y)(y y)))) 3. ==[ beta ]==> ((a b)(^y.((y y)(y y)))) 4. ==[ alpha ]==> ((a b)(^x.((x x)(x x)))) REDUCED to normal form. ------ 127027/12813792. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a) a)(a b))) 3. ==[ beta ]==> (^y.((((a a) a)(a b))(((a a) a)(a b)))) 4. ==[ alpha ]==> (^x.((((a a) a)(a b))(((a a) a)(a b)))) REDUCED to normal form. ------ 127028/12813999. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.(^y1.y1)))(a (^z1.z1)))((^z.(^x1.(^y1.y1)))(a (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1)))(a (^y1.y1)))((^z1.(^x2.(^y2.y2)))(a (^z2.z2))))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(a (^y1.y1)))((^z1.(^x2.(^y2.y2)))(a (^z2.z2)))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 7. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127029/12814263. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 127030/12814596. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^b.(^b.b))) 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. ------ 127031/12815217. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 127032/12815430. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))(^z.(a a)))) 3. ==[ eta ]==> (b ((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 127033/12815523. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^z.(z (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 127034/12815793. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(b a))) 3. ==[ beta ]==> (((a b)(a b))(^y.(b a))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(b a))) REDUCED to normal form. ------ 127035/12816081. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(x a))) REDUCED to normal form. ------ 127036/12816267. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((^x1.(x1 x1))(^y1.b))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.x1))) 7. ==[ beta ]==> (b (^z.(^x1.x1))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 127037/12816360. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(b z))) 3. ==[ eta ]==> (((^x.(x x))(^y.(a a))) b) 4. ==[ beta ]==> (((^y.(a a))(^y.(a a))) b) 5. ==[ alpha ]==> (((^x.(a a))(^y.(a a))) b) 6. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 127038/12816603. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b 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))) REDUCED to normal form. ------ 127039/12817107. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 127040/12817791. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.((^z1.z1)(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1)(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127041/12817998. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 127042/12818184. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.y)(a b))) 3. ==[ beta ]==> ((((^y.y)(a b))((^y.y)(a b)))(((^y.y)(a b))((^y.y)(a b)))) 4. ==[ alpha ]==> ((((^x.x)(a b))((^y.y)(a b)))(((^z.z)(a b))((^x1.x1)(a b)))) 5. ==[ beta ]==> (((a b)((^y.y)(a b)))(((^z.z)(a b))((^x1.x1)(a b)))) 6. ==[ alpha ]==> (((a b)((^x.x)(a b)))(((^y.y)(a b))((^z.z)(a b)))) 7. ==[ beta ]==> (((a b)(a b))(((^y.y)(a b))((^z.z)(a b)))) 8. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a b))((^y.y)(a b)))) 9. ==[ beta ]==> (((a b)(a b))((a b)((^y.y)(a b)))) 10. ==[ alpha ]==> (((a b)(a b))((a b)((^x.x)(a b)))) 11. ==[ beta ]==> (((a b)(a b))((a b)(a b))) REDUCED to normal form. ------ 127043/12818187. ------ 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. ------ 127044/12818718. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 127045/12819186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^z.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 127046/12819264. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127047/12819438. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(a (a a)))) 3. ==[ beta ]==> (b (^z.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 127048/12819681. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(z (z z)))) 3. ==[ beta ]==> ((^y.y)(^z.(z (z z)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y y)))) 5. ==[ beta ]==> (^y.(y (y y))) 6. ==[ alpha ]==> (^x.(x (x x))) REDUCED to normal form. ------ 127049/12819852. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 127050/12820077. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 127051/12820131. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 127052/12820185. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 127053/12820212. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(a a))) 3. ==[ beta ]==> (((a b)(a a))(^y.(a a))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(a a))) REDUCED to normal form. ------ 127054/12820239. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(^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. ------ 127055/12820266. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 127056/12820296. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 127057/12820323. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(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. ------ 127058/12820350. ------ 1. ==[ start ]==> (((^a.a)(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a a)((a b)((^x.x)(a a)))) 5. ==[ beta ]==> ((a a)((a b)(a a))) REDUCED to normal form. ------ 127059/12820377. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 127060/12820431. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127061/12820458. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 127062/12820485. ------ 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)))) REDUCED to normal form. ------ 127063/12820512. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 127064/12820575. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((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. ------ 127065/12820611. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((a a)((^y.y) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 127066/12820656. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 127067/12820710. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.b))) REDUCED to normal form. ------ 127068/12820737. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.(a a)))) REDUCED to normal form. ------ 127069/12820800. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 127070/12820827. ------ 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 z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 127071/12820854. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (a a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 127072/12820881. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 127073/12820953. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a)(a a)) b)) 3. ==[ beta ]==> ((a b)(((a a)(a a)) b)) REDUCED to normal form. ------ 127074/12820980. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b) c)) 3. ==[ beta ]==> (((a (a a)) a)(b c)) REDUCED to normal form. ------ 127075/12821124. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 127076/12821205. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 127077/12821232. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 127078/12821241. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127079/12821268. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 127080/12821322. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((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. ------ 127081/12821331. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(a a)) b)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a)) b)) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 127082/12821358. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z) c)) 3. ==[ beta ]==> (((^y.y) a)((^z.z) c)) 4. ==[ alpha ]==> (((^x.x) a)((^y.y) c)) 5. ==[ beta ]==> (a ((^y.y) c)) 6. ==[ alpha ]==> (a ((^x.x) c)) 7. ==[ beta ]==> (a c) REDUCED to normal form. ------ 127083/12821376. ------ 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.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 127084/12821403. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((b a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 5. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 127085/12821457. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 127086/12821637. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(b (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(a a)))) 5. ==[ beta ]==> ((a a)(b (^y.(a a)))) 6. ==[ alpha ]==> ((a a)(b (^x.(a a)))) REDUCED to normal form. ------ 127087/12821790. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 127088/12821871. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(^x1.(a a)))) REDUCED to normal form. ------ 127089/12821952. ------ 1. ==[ start ]==> ((((^a.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.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127090/12821979. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 127091/12822015. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 127092/12822069. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(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)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 127093/12822096. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 127094/12822177. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 127095/12822348. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b ((^z.z) b))) 3. ==[ beta ]==> (b (b ((^z.z) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 127096/12822375. ------ 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. ------ 127097/12822384. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a)) a)) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 127098/12822402. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a a))) 5. ==[ beta ]==> (((^y.y) b)(a a)) 6. ==[ alpha ]==> (((^x.x) b)(a a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 127099/12822438. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1))) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1))) c)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 127100/12822456. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b a)((^y.y) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)((^x.x) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((b a) a)) REDUCED to normal form. ------ 127101/12822537. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 127102/12822564. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(a b))) REDUCED to normal form. ------ 127103/12822690. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(b (^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b (^x1.x1))) 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. ------ 127104/12822735. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.z))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 127105/12822744. ------ 1. ==[ start ]==> (((a b)(a a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)(a a))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 127106/12822771. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 127107/12822951. ------ 1. ==[ start ]==> (((a b) b)((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 127108/12823005. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 127109/12823032. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(^z.z))) REDUCED to normal form. ------ 127110/12823086. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 127111/12823113. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b a) c)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a) c)) 5. ==[ beta ]==> ((^y.(y y))((b a) c)) 6. ==[ alpha ]==> ((^x.(x x))((b a) c)) 7. ==[ beta ]==> (((b a) c)((b a) c)) REDUCED to normal form. ------ 127112/12823257. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 127113/12823338. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 127114/12823365. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) 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. ------ 127115/12823383. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b) a)) 2. ==[ alpha ]==> (((^x.b) c)((^y.y) a)) 3. ==[ beta ]==> (b ((^y.y) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127116/12823482. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (a a))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 127117/12823617. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (b (a ((a a)(^y.y)))) 6. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 127118/12823734. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 127119/12823761. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 127120/12823815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127121/12823869. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.b)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.b)) REDUCED to normal form. ------ 127122/12823896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 127123/12823959. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(b 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. ------ 127124/12823986. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^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. ------ 127125/12824013. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 127126/12824094. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a a)) REDUCED to normal form. ------ 127127/12824121. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 127128/12824175. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 127129/12824202. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 127130/12824292. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 127131/12824373. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (b ((a a)((^y.y) a))) 6. ==[ alpha ]==> (b ((a a)((^x.x) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 127132/12824481. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (a a))(a b))) 3. ==[ beta ]==> ((b a)((a (a a))(a b))) REDUCED to normal form. ------ 127133/12824508. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 127134/12824562. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)(b a))) 3. ==[ beta ]==> (((a b)(a b))((a a)(b a))) REDUCED to normal form. ------ 127135/12824625. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 127136/12824652. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.a))) REDUCED to normal form. ------ 127137/12824679. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.a))((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.(y y)))) REDUCED to normal form. ------ 127138/12824706. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 127139/12824769. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(x x))(a b))) 3. ==[ beta ]==> (((a a)(b a))((a b)(a b))) REDUCED to normal form. ------ 127140/12824796. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 127141/12824823. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 127142/12824850. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(b a))) 3. ==[ beta ]==> (((a (a a))(a b))(b a)) REDUCED to normal form. ------ 127143/12824931. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 127144/12824958. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.(z z)))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.(y y)))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 127145/12825039. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 127146/12825129. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(a (b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(a (b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(a (b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(a (b a))) 5. ==[ beta ]==> ((a a)(a (b a))) REDUCED to normal form. ------ 127147/12825210. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (b ((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((a b)((^x.x) a))) 5. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 127148/12825318. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127149/12825345. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 127150/12825372. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 127151/12825435. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 127152/12825462. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.a))) 5. ==[ beta ]==> ((^y.b)((a b)(^z.a))) 6. ==[ alpha ]==> ((^x.b)((a b)(^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127153/12825516. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 127154/12825570. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a (^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a (^z.b))) REDUCED to normal form. ------ 127155/12825687. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 127156/12825714. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 127157/12825768. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 127158/12825822. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 127159/12825849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 127160/12825921. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127161/12825966. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((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. ------ 127162/12825993. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(^x2.x2))(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. ------ 127163/12826245. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127164/12826272. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((b a)(a (^y.a))) 6. ==[ alpha ]==> ((b a)(a (^x.a))) REDUCED to normal form. ------ 127165/12826299. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 127166/12826326. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^y1.(a a)))) REDUCED to normal form. ------ 127167/12826407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a) a) c)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a) a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a) c)) 5. ==[ beta ]==> ((^y.(a a))(((a a) a) c)) 6. ==[ alpha ]==> ((^x.(a a))(((a a) a) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127168/12826560. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(a ((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127169/12826569. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 127170/12826596. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.b) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.b) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.b) b)) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 127171/12826740. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(b (^x1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(b (^x1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(b (^z.b))) 6. ==[ alpha ]==> (((^x.x)(a a))(b (^y.b))) 7. ==[ beta ]==> ((a a)(b (^y.b))) 8. ==[ alpha ]==> ((a a)(b (^x.b))) REDUCED to normal form. ------ 127172/12826767. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 127173/12826794. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(a a))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 127174/12826848. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 127175/12826902. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 127176/12826929. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 127177/12826956. ------ 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. ------ 127178/12827127. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 127179/12827235. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127180/12827316. ------ 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. ------ 127181/12827352. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.z))) REDUCED to normal form. ------ 127182/12827379. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 8. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 127183/12827460. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127184/12827487. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 127185/12827541. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 127186/12827766. ------ 1. ==[ start ]==> (((a (a a))(b a))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(c (^x.(x x)))) REDUCED to normal form. ------ 127187/12827793. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 127188/12827847. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 127189/12827874. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 127190/12827901. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 127191/12827955. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 127192/12827982. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 127193/12828009. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(x x))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((^y.(^z.z))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 127194/12828036. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 127195/12828126. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127196/12828207. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a a)(a (a a)))) 3. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 127197/12828351. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (a a)) a)) 3. ==[ beta ]==> ((b c)((a (a a)) a)) REDUCED to normal form. ------ 127198/12828378. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) a) b)) 3. ==[ beta ]==> ((((a a)(a a)) b)(a b)) REDUCED to normal form. ------ 127199/12828423. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))(b ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.x))(b ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.x))(b a)) REDUCED to normal form. ------ 127200/12828450. ------ 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)))) 4. ==[ alpha ]==> ((^x.x)(a (a (a a)))) 5. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 127201/12828486. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) b)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 127202/12828504. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(a (^z1.z1)))) REDUCED to normal form. ------ 127203/12828585. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c b)) 3. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 127204/12828594. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127205/12828621. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 127206/12828693. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127207/12828729. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a) a)) 3. ==[ beta ]==> ((b (^y.a))((^z.a) a)) 4. ==[ alpha ]==> ((b (^x.a))((^y.a) a)) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 127208/12828756. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127209/12828819. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 127210/12828846. ------ 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)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a (^y.y))) REDUCED to normal form. ------ 127211/12828873. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 127212/12828900. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 127213/12828927. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (^z.z))) 3. ==[ beta ]==> (((^y.y)(b a))(b (^z.z))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (^y.y))) 5. ==[ beta ]==> ((b a)(b (^y.y))) 6. ==[ alpha ]==> ((b a)(b (^x.x))) REDUCED to normal form. ------ 127214/12828954. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 127215/12828981. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)(a a))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(a a))) 5. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 127216/12829008. ------ 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. ------ 127217/12829035. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.y))) REDUCED to normal form. ------ 127218/12834411. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127219/12838155. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) b)(^x1.a))) 3. ==[ eta ]==> ((^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. ------ 127220/12838464. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 127221/12838650. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127222/12839541. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 127223/12839922. ------ 1. ==[ start ]==> (((^a.a)(a b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((a b)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 127224/12839931. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((y y)(y y)))) REDUCED to normal form. ------ 127225/12840315. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.(^x1.x1)))(^y1.(^z1.z1)))((a (^z.(^x1.x1)))(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2)))(^y2.(^z2.z2))))) 5. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2)))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) REDUCED to normal form. ------ 127226/12840930. ------ 1. ==[ start ]==> (((^a.b) c)(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)(^y.((^z.z) b))) 3. ==[ beta ]==> (b (^y.((^z.z) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 127227/12841245. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^a.(^b.b))) 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. ------ 127228/12841839. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b (^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127229/12842118. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(b a))) REDUCED to normal form. ------ 127230/12842295. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 127231/12842397. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.a))) REDUCED to normal form. ------ 127232/12843186. ------ 1. ==[ start ]==> ((^a.(^b.b))((^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. ------ 127233/12843189. ------ 1. ==[ start ]==> ((a (^b.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 127234/12843501. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.b) c)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.b) c)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127235/12843675. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 127236/12844107. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127237/12844116. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1)(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 y1))) REDUCED to normal form. ------ 127238/12844500. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a a)(^y.b))) 3. ==[ beta ]==> ((((a a)(^y.b))((a a)(^y.b)))(((a a)(^y.b))((a a)(^y.b)))) 4. ==[ alpha ]==> ((((a a)(^x.b))((a a)(^y.b)))(((a a)(^z.b))((a a)(^x1.b)))) REDUCED to normal form. ------ 127239/12844890. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 127240/12845580. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127241/12845997. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 127242/12846276. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) b)(^y.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)) REDUCED to normal form. ------ 127243/12846501. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 127244/12846528. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 127245/12846555. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.a)) 2. ==[ alpha ]==> ((((^x.x)(a 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. ------ 127246/12846582. ------ 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. ------ 127247/12846630. ------ 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))) REDUCED to normal form. ------ 127248/12846657. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a a) a)((a a)(a b))) REDUCED to normal form. ------ 127249/12846684. ------ 1. ==[ start ]==> (((a a)(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 127250/12846711. ------ 1. ==[ start ]==> (((^a.a) b)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (b (((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 127251/12846738. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 7. ==[ beta ]==> ((^y.y)(b a)) 8. ==[ alpha ]==> ((^x.x)(b a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127252/12846765. ------ 1. ==[ start ]==> (((a a) b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 127253/12846792. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x)) a)(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a ((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x)) a)(a b)) REDUCED to normal form. ------ 127254/12846819. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 127255/12846846. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(b (^z.z)))) REDUCED to normal form. ------ 127256/12846882. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 127257/12846909. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 127258/12846936. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.a))) 5. ==[ beta ]==> ((a a)(b (^y.a))) 6. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 127259/12846945. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.a)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.a)((^y.y)((^z.z) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 127260/12846972. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127261/12847053. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127262/12847152. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 127263/12847179. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) a)(^b.b))) 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. ------ 127264/12847215. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))((^y.(^z.z))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 9. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 10. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127265/12847242. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((^y.y)(b (^z.z))) 6. ==[ alpha ]==> ((^x.x)(b (^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127266/12847323. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.b)(^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. ------ 127267/12847350. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127268/12847431. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 127269/12847566. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127270/12847656. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(a a))(a a))) REDUCED to normal form. ------ 127271/12847683. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (a (((^y.y) b)(a (^z.z)))) 6. ==[ alpha ]==> (a (((^x.x) b)(a (^y.y)))) 7. ==[ beta ]==> (a (b (a (^y.y)))) 8. ==[ alpha ]==> (a (b (a (^x.x)))) REDUCED to normal form. ------ 127272/12847710. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 127273/12847737. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)(a (a a)))) REDUCED to normal form. ------ 127274/12847764. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 127275/12847791. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 127276/12847818. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(a b))) 5. ==[ beta ]==> ((^y.y)((a b)(a b))) 6. ==[ alpha ]==> ((^x.x)((a b)(a b))) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 127277/12848025. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(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 a) REDUCED to normal form. ------ 127278/12848079. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 127279/12848160. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))((a a) a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 127280/12848187. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.b)(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a b))) 5. ==[ beta ]==> ((^y.b)(a b)) 6. ==[ alpha ]==> ((^x.b)(a b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127281/12848241. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))((a a)(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 127282/12848322. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 127283/12848367. ------ 1. ==[ start ]==> (((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)) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a)) a)) REDUCED to normal form. ------ 127284/12848394. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) b) b)) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) b) b)) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b) b)) 5. ==[ beta ]==> ((a (a (a a)))(b b)) REDUCED to normal form. ------ 127285/12848511. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127286/12848592. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) IRREDUCIBLE: cycle. ------ 127287/12848655. ------ 1. ==[ start ]==> ((((a a) a) b)(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 127288/12848673. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.a))(^b.b))) 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 (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127289/12848682. ------ 1. ==[ start ]==> (((a b) a)(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b) a)(b ((^x.x) b))) 3. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 127290/12848700. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 127291/12848709. ------ 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. ------ 127292/12848763. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 127293/12848790. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((b a) a)) REDUCED to normal form. ------ 127294/12848817. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 127295/12848844. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 127296/12848871. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)((a a) a))) REDUCED to normal form. ------ 127297/12849069. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.y))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.x))) REDUCED to normal form. ------ 127298/12849096. ------ 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.(^y1.y1)))) 3. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127299/12849105. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127300/12849186. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127301/12849267. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127302/12849321. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(b a))) 5. ==[ beta ]==> ((a a)((^y.a)(b a))) 6. ==[ alpha ]==> ((a a)((^x.a)(b a))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 127303/12849348. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127304/12849402. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.b)(^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)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127305/12849483. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^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. ------ 127306/12849708. ------ 1. ==[ start ]==> (((^a.b) c)(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)(a ((^y.y) b))) 3. ==[ beta ]==> (b (a ((^y.y) b))) 4. ==[ alpha ]==> (b (a ((^x.x) b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 127307/12849717. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y) a)) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 127308/12849744. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 127309/12849951. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b) c)(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b) c)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 127310/12849978. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.y))(b a))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))(b a))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(b a))) REDUCED to normal form. ------ 127311/12850005. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 127312/12850023. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(a (^b.b))) 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. ------ 127313/12850050. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127314/12850185. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)((a a) a))) 3. ==[ beta ]==> (b ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127315/12850311. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127316/12850338. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 127317/12850365. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((b a) b)) REDUCED to normal form. ------ 127318/12850617. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 127319/12850761. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)(^y.y))) REDUCED to normal form. ------ 127320/12850869. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 127321/12850896. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(b a))) REDUCED to normal form. ------ 127322/12850968. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^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. ------ 127323/12851076. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 127324/12851094. ------ 1. ==[ start ]==> (((a a)(b a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(b a))((a (a a))(^x.b))) REDUCED to normal form. ------ 127325/12851121. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 127326/12851202. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((b a) a)) 3. ==[ beta ]==> (((^y.y)((a a) a))((b a) a)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((b a) a)) 5. ==[ beta ]==> (((a a) a)((b a) a)) REDUCED to normal form. ------ 127327/12851229. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 127328/12851256. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(a a)) c)) 3. ==[ beta ]==> (((a b)(a (a a)))((a a) c)) REDUCED to normal form. ------ 127329/12851373. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127330/12851652. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (a b))) REDUCED to normal form. ------ 127331/12851679. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 127332/12851697. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 127333/12851832. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (b ((^x1.a)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.a)(a (a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127334/12851940. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127335/12851967. ------ 1. ==[ start ]==> ((a (^b.b))((^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. ------ 127336/12851985. ------ 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)) a)) REDUCED to normal form. ------ 127337/12852012. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a) b)) REDUCED to normal form. ------ 127338/12852039. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b) c)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b) c)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b) c)) REDUCED to normal form. ------ 127339/12852246. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127340/12852255. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 127341/12852282. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.b) c)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.b) c)) 3. ==[ beta ]==> ((a b)((^y.b) c)) 4. ==[ alpha ]==> ((a b)((^x.b) c)) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 127342/12852453. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 127343/12852561. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(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. ------ 127344/12852615. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((a a) a))) 5. ==[ beta ]==> (b ((^y.a)((a a) a))) 6. ==[ alpha ]==> (b ((^x.a)((a a) a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127345/12852642. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 127346/12852696. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 127347/12852777. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) 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. ------ 127348/12852885. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127349/12852894. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a a))) REDUCED to normal form. ------ 127350/12852921. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)(a a))) 3. ==[ beta ]==> ((b (^y.y))((a b)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(a a))) REDUCED to normal form. ------ 127351/12852957. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.a) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a) c)) 3. ==[ beta ]==> (((a a) b)((^y.a) c)) 4. ==[ alpha ]==> (((a a) b)((^x.a) c)) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 127352/12853119. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((a b)(^x.x))) REDUCED to normal form. ------ 127353/12853146. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 127354/12853173. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.a)) REDUCED to normal form. ------ 127355/12853227. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 127356/12853254. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (^y.y))(^z.a))) 3. ==[ beta ]==> ((b (a a))((a (^y.y))(^z.a))) 4. ==[ alpha ]==> ((b (a a))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 127357/12853281. ------ 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. ------ 127358/12853317. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 127359/12853452. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127360/12853596. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) a)(a (a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)(a (a a)))) 5. ==[ beta ]==> ((b b)(a (a (a a)))) REDUCED to normal form. ------ 127361/12853623. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 127362/12853641. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(b (^y.a))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.a))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.a))) REDUCED to normal form. ------ 127363/12853668. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(a (^x1.b))) 3. ==[ beta ]==> ((^y.y)(a (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(a (^y.b))) 5. ==[ beta ]==> (a (^y.b)) 6. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 127364/12853722. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 127365/12853803. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127366/12853911. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127367/12853947. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (a (a a)))) REDUCED to normal form. ------ 127368/12853974. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b (^y.y))) REDUCED to normal form. ------ 127369/12854037. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 127370/12854172. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 127371/12854199. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 127372/12854226. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 127373/12854280. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 127374/12854307. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 127375/12854334. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a (a a)) b)) REDUCED to normal form. ------ 127376/12854361. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a) c)) 3. ==[ beta ]==> ((a (b (^x.x)))(a c)) REDUCED to normal form. ------ 127377/12854532. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b (^z.(z z)))) 3. ==[ beta ]==> (b (b (^z.(z z)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 127378/12854640. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127379/12854748. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 127380/12854775. ------ 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 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 127381/12854811. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^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. ------ 127382/12854838. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 127383/12854910. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(a a))) 3. ==[ beta ]==> (b ((^z.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127384/12854919. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c b)) REDUCED to normal form. ------ 127385/12854946. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b c)) 3. ==[ beta ]==> (((a a)(^y.b))(b c)) 4. ==[ alpha ]==> (((a a)(^x.b))(b c)) REDUCED to normal form. ------ 127386/12855018. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127387/12855027. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (a (^x1.x1)))) REDUCED to normal form. ------ 127388/12855054. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.a))(a ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.a))(a ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 127389/12855081. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 127390/12855144. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 127391/12855171. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 127392/12855198. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y)) a)) 5. ==[ beta ]==> ((a b)((a (^y.y)) a)) 6. ==[ alpha ]==> ((a b)((a (^x.x)) a)) REDUCED to normal form. ------ 127393/12855225. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a) b)) REDUCED to normal form. ------ 127394/12855252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((b a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 127395/12855279. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y) b)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 127396/12855306. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 127397/12855333. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a) a)) 3. ==[ beta ]==> (((a a)(a b))((a a) a)) REDUCED to normal form. ------ 127398/12855360. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y) a)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 127399/12855386. ------ 1. ==[ start ]==> (^a.((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (^x.((b x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (^x.((b x)(^z.z))) 4. ==[ alpha ]==> (^x.((b x)(^y.y))) REDUCED to normal form. ------ 127400/12855387. ------ 1. ==[ start ]==> (a ((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (a ((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (a ((b a)(^y.y))) 4. ==[ alpha ]==> (a ((b a)(^x.x))) REDUCED to normal form. ------ 127401/12860745. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127402/12864174. ------ 1. ==[ start ]==> ((^a.a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 127403/12864201. ------ 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)(^y.y))((a a) a))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 127404/12864228. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(a b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 127405/12864309. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))(b a))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.z)) 5. ==[ beta ]==> (((^y.y)(b a))(^z.z)) 6. ==[ alpha ]==> (((^x.x)(b a))(^y.y)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 127406/12864807. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 127407/12865551. ------ 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. ------ 127408/12865884. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 127409/12866274. ------ 1. ==[ start ]==> (((a a)(^a.b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 127410/12866625. ------ 1. ==[ start ]==> (((^a.b) b)(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(^z.(y y)))) 3. ==[ beta ]==> (b (^y.(^z.(y y)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 127411/12867273. ------ 1. ==[ start ]==> (((^a.b) c)(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 127412/12867282. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^y.b)) REDUCED to normal form. ------ 127413/12867333. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((((b a)(a (^z.z)))((b a)(a (^z.z))))(^y.y)) 4. ==[ alpha ]==> ((((b a)(a (^x.x)))((b a)(a (^y.y))))(^z.z)) REDUCED to normal form. ------ 127414/12869529. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127415/12869532. ------ 1. ==[ start ]==> ((a (^b.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 127416/12869844. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127417/12870459. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(a a)))) REDUCED to normal form. ------ 127418/12870657. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(a b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(a b))) REDUCED to normal form. ------ 127419/12871242. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.b))) REDUCED to normal form. ------ 127420/12871575. ------ 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. ------ 127421/12872241. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(a (a a)))) 3. ==[ beta ]==> ((b c)(^y.(a (a a)))) 4. ==[ alpha ]==> ((b c)(^x.(a (a a)))) REDUCED to normal form. ------ 127422/12872619. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 127423/12872763. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.c)) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.c)) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.c)) 5. ==[ beta ]==> ((a b)(^y.c)) 6. ==[ alpha ]==> ((a b)(^x.c)) REDUCED to normal form. ------ 127424/12872817. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(y (^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((b a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 127425/12872898. ------ 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. ------ 127426/12872925. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 127427/12872964. ------ 1. ==[ start ]==> ((a a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a a)((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a a)((b a)(^y.y))) 4. ==[ alpha ]==> ((a a)((b a)(^x.x))) REDUCED to normal form. ------ 127428/12872991. ------ 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. ------ 127429/12873018. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a b))) 3. ==[ beta ]==> ((a b)((a a)(a b))) REDUCED to normal form. ------ 127430/12873072. ------ 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. ------ 127431/12873099. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(b a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> ((a (a (^x.x)))(b a)) REDUCED to normal form. ------ 127432/12873297. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((^y.a)(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 127433/12873324. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 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))) REDUCED to normal form. ------ 127434/12873333. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 127435/12873387. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 127436/12873405. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 127437/12873414. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 127438/12873441. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 127439/12873549. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a a)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a a)((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 127440/12873648. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a)) b)) 5. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 127441/12873675. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b) c)) 3. ==[ beta ]==> ((a (a a))(((^y.y) b) c)) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b) c)) 5. ==[ beta ]==> ((a (a a))(b c)) REDUCED to normal form. ------ 127442/12873684. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 127443/12873711. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 127444/12874053. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) c)) 5. ==[ beta ]==> ((^y.y)((^z.z) c)) 6. ==[ alpha ]==> ((^x.x)((^y.y) c)) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 127445/12874206. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 127446/12874233. ------ 1. ==[ start ]==> (((a (^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))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)(^y.y))) REDUCED to normal form. ------ 127447/12874260. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(b a))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(b a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(b a))) 5. ==[ beta ]==> ((a a)((a (a a))(b a))) REDUCED to normal form. ------ 127448/12874287. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 127449/12874314. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z) b))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y) b))) 7. ==[ beta ]==> ((a a)((a (^x.x)) b)) REDUCED to normal form. ------ 127450/12874341. ------ 1. ==[ start ]==> ((a ((a a) a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 127451/12874377. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 127452/12874431. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (a ((a (^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 127453/12874539. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.b))) 5. ==[ beta ]==> ((a b)(^y.b)) 6. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 127454/12874548. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 127455/12874602. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 127456/12874629. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127457/12874656. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 127458/12874674. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 127459/12874845. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127460/12875007. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 127461/12875034. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 127462/12875061. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 127463/12875259. ------ 1. ==[ start ]==> (((a a)(a b))(((a a) a)(a b))) REDUCED to normal form. ------ 127464/12875286. ------ 1. ==[ start ]==> (((a (^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.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 127465/12875313. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 127466/12875340. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a (b a))) REDUCED to normal form. ------ 127467/12875367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a ((a (^y.y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (a ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 127468/12875394. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a a) b)) REDUCED to normal form. ------ 127469/12875412. ------ 1. ==[ start ]==> (((^a.b) b)(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(a (^y.(a a)))) 3. ==[ beta ]==> (b (a (^y.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 127470/12875457. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127471/12875484. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 127472/12875538. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 127473/12875619. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 127474/12875628. ------ 1. ==[ start ]==> (((a b) b)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 127475/12875655. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 127476/12875682. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(b a))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 127477/12875700. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 127478/12875709. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 127479/12875754. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b) a)) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b) a)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b) a)) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) a)) 9. ==[ beta ]==> ((^y.y)(((^z.z) b) a)) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b) a)) 11. ==[ beta ]==> (((^y.y) b) a) 12. ==[ alpha ]==> (((^x.x) b) a) 13. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127480/12875763. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127481/12875790. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 9. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127482/12875844. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127483/12875871. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 127484/12876042. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a) a)(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a) a)(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 127485/12876060. ------ 1. ==[ start ]==> (((^a.b) c)((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b) c)((^y.y)(^z.z))) 3. ==[ beta ]==> (b ((^y.y)(^z.z))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127486/12876069. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(a ((^y.y) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a b)) REDUCED to normal form. ------ 127487/12876096. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 127488/12876123. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 127489/12876159. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) d)) 5. ==[ beta ]==> ((^y.(^z.z)) d) 6. ==[ alpha ]==> ((^x.(^y.y)) d) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127490/12876303. ------ 1. ==[ start ]==> (((a b) c)(d (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(d (^x.(^y.y)))) REDUCED to normal form. ------ 127491/12876330. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c (^y.a))) 3. ==[ beta ]==> (((a a) b)(c (^y.a))) 4. ==[ alpha ]==> (((a a) b)(c (^x.a))) REDUCED to normal form. ------ 127492/12876357. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127493/12876402. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127494/12876411. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a a))) 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. ------ 127495/12876456. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 127496/12876492. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127497/12876519. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 127498/12876537. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a) a)(^z.a))) 3. ==[ beta ]==> (b (((a a) a)(^z.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 127499/12876546. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 127500/12876573. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127501/12876600. ------ 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 z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 127502/12877050. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127503/12877221. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 127504/12877320. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 127505/12877329. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 127506/12877356. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 127507/12877383. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 127508/12877707. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^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. ------ 127509/12877887. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (b ((^x1.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 127510/12878103. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 127511/12878112. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 127512/12878139. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127513/12878184. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 127514/12878193. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 127515/12878220. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 127516/12878247. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 127517/12878292. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127518/12878301. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 127519/12878319. ------ 1. ==[ start ]==> ((a (^b.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 127520/12878553. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(b (a a))) REDUCED to normal form. ------ 127521/12878607. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)(a a))) REDUCED to normal form. ------ 127522/12878634. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a b)(a (^y.y)))) 3. ==[ beta ]==> ((a b)((a b)(a (^y.y)))) 4. ==[ alpha ]==> ((a b)((a b)(a (^x.x)))) REDUCED to normal form. ------ 127523/12878643. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.b) c)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) c)) 3. ==[ beta ]==> ((^y.y)((^z.b) c)) 4. ==[ alpha ]==> ((^x.x)((^y.b) c)) 5. ==[ beta ]==> ((^y.b) c) 6. ==[ alpha ]==> ((^x.b) c) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127524/12878913. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.(y2 y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.(y2 y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127525/12878922. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 127526/12878949. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b a)((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 10. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 11. ==[ beta ]==> ((b a)(^y.y)) 12. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 127527/12878967. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 7. ==[ beta ]==> (b (a (^y.a))) 8. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 127528/12878976. ------ 1. ==[ start ]==> (((a a)(^b.b))((^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. ------ 127529/12878994. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 127530/12879003. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 127531/12879048. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a) a)) REDUCED to normal form. ------ 127532/12879084. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127533/12879111. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 127534/12879138. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 127535/12879165. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127536/12879192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 127537/12879246. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(a a))) REDUCED to normal form. ------ 127538/12879309. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)(a (^y.y)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 127539/12879336. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1) a)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1) a)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 127540/12879363. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a (b a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 127541/12879390. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 127542/12879417. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))((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))) REDUCED to normal form. ------ 127543/12879444. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a a)(a b))) REDUCED to normal form. ------ 127544/12879669. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 127545/12879912. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127546/12880029. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.b))) REDUCED to normal form. ------ 127547/12880074. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((b a)(b a))(^y.(^z.z))) 8. ==[ alpha ]==> (((b a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 127548/12880137. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 127549/12880155. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 127550/12880164. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 127551/12880218. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 127552/12880272. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 127553/12880299. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 127554/12880326. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z))(^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. ------ 127555/12880362. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(a ((a a) a))) REDUCED to normal form. ------ 127556/12880389. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 127557/12880416. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 127558/12880443. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(b a))(a ((^y.y) a))) 4. ==[ alpha ]==> (((a (a a))(b a))(a ((^x.x) a))) 5. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 127559/12880470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 127560/12880497. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 127561/12880803. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127562/12880992. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127563/12881028. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(a (a a)))) 3. ==[ beta ]==> ((b c)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((b c)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((b c)(a (a a))) REDUCED to normal form. ------ 127564/12881055. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 127565/12881100. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z)) c)) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z)) c)) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y)) c)) REDUCED to normal form. ------ 127566/12881181. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 127567/12881262. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^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. ------ 127568/12881271. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 127569/12881298. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 127570/12881370. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127571/12881379. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 127572/12881406. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b (^x.a))(^z.a)) 6. ==[ alpha ]==> ((b (^x.a))(^y.a)) REDUCED to normal form. ------ 127573/12881496. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c a)) REDUCED to normal form. ------ 127574/12881523. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b b)) REDUCED to normal form. ------ 127575/12881550. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a c)) 3. ==[ beta ]==> ((a ((^y.y) b))(a c)) 4. ==[ alpha ]==> ((a ((^x.x) b))(a c)) 5. ==[ beta ]==> ((a b)(a c)) REDUCED to normal form. ------ 127576/12881577. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (a a))) REDUCED to normal form. ------ 127577/12881604. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a (a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(b a))(a (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(b a))(a (a (^y.y)))) 5. ==[ beta ]==> ((b a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((b a)(a (a (^x.x)))) REDUCED to normal form. ------ 127578/12881631. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 127579/12881658. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b a)) 3. ==[ beta ]==> (((a b)(a a))(b a)) REDUCED to normal form. ------ 127580/12881685. ------ 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. ------ 127581/12881712. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 127582/12882003. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (^x.(^y.(b (^z.z)))) REDUCED to normal form. ------ 127583/12890553. ------ 1. ==[ start ]==> ((^a.(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127584/12890634. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127585/12890796. ------ 1. ==[ start ]==> ((^a.(^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a a)(b (^z.z)))) 3. ==[ beta ]==> (^y.((a a)(b (^z.z)))) 4. ==[ alpha ]==> (^x.((a a)(b (^y.y)))) REDUCED to normal form. ------ 127586/12890799. ------ 1. ==[ start ]==> ((a (^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 127587/12891138. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((^y.a)((^z.z) b))(((^y.a)((^z.z) b))((^y.a)((^z.z) b)))) 4. ==[ alpha ]==> (((^x.a)((^y.y) b))(((^z.a)((^x1.x1) b))((^y1.a)((^z1.z1) b)))) 5. ==[ beta ]==> (a (((^z.a)((^x1.x1) b))((^y1.a)((^z1.z1) b)))) 6. ==[ alpha ]==> (a (((^x.a)((^y.y) b))((^z.a)((^x1.x1) b)))) 7. ==[ beta ]==> (a (a ((^z.a)((^x1.x1) b)))) 8. ==[ alpha ]==> (a (a ((^x.a)((^y.y) b)))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 127588/12891489. ------ 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.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127589/12891582. ------ 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))) REDUCED to normal form. ------ 127590/12891921. ------ 1. ==[ start ]==> ((^a.((a a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(b (^y.(a a)))) 3. ==[ beta ]==> (((b (^y.(a a)))(b (^y.(a a))))(b (^y.(a a)))) 4. ==[ alpha ]==> (((b (^x.(a a)))(b (^y.(a a))))(b (^z.(a a)))) REDUCED to normal form. ------ 127591/12892302. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((a a)(a a)))) REDUCED to normal form. ------ 127592/12892434. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127593/12892662. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((^y.y)(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y)(y y)))) 5. ==[ beta ]==> (^y.((y y)(y y))) 6. ==[ alpha ]==> (^x.((x x)(x x))) REDUCED to normal form. ------ 127594/12892821. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)((a a) a))) 3. ==[ beta ]==> (^y.(((a b)((a a) a))((a b)((a a) a)))) 4. ==[ alpha ]==> (^x.(((a b)((a a) a))((a b)((a a) a)))) REDUCED to normal form. ------ 127595/12893004. ------ 1. ==[ start ]==> (((a b)(a a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 127596/12893028. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.b)(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. ------ 127597/12893652. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 127598/12894273. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 127599/12894459. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.b))) 3. ==[ eta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127600/12895137. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(b 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. ------ 127601/12895296. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(^z1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127602/12895920. ------ 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)))) REDUCED to normal form. ------ 127603/12896388. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 127604/12897054. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 127605/12897213. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))(((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a) a)))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a) a))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a)))) 11. ==[ beta ]==> (((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a))) 12. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a))) 13. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 15. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 16. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127606/12897603. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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)) REDUCED to normal form. ------ 127607/12897945. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(^y.a))) REDUCED to normal form. ------ 127608/12898107. ------ 1. ==[ start ]==> (((a b)(a b))(^a.(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.x))) REDUCED to normal form. ------ 127609/12898242. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 127610/12898293. ------ 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 (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127611/12898386. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((^y2.y2)(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((^y2.y2)(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127612/12898611. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(z z)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(y y)))) REDUCED to normal form. ------ 127613/12898989. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.z)) 3. ==[ beta ]==> ((b (^y.a))(^z.z)) 4. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 127614/12899079. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 127615/12899133. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(a (^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(a (^z.z)))) 6. ==[ alpha ]==> ((a b)(^x.(a (^y.y)))) REDUCED to normal form. ------ 127616/12899187. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 127617/12899241. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 127618/12899268. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(a a))) 3. ==[ beta ]==> (((a a)(a b))(^y.(a a))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(a a))) REDUCED to normal form. ------ 127619/12899295. ------ 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. ------ 127620/12899352. ------ 1. ==[ start ]==> ((a (^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))((b a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 127621/12899379. ------ 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)) REDUCED to normal form. ------ 127622/12899406. ------ 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))) 5. ==[ beta ]==> ((a a)((a a)(a b))) REDUCED to normal form. ------ 127623/12899433. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 127624/12899487. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127625/12899514. ------ 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))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 127626/12899541. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.x))(a ((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) b))) 7. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 127627/12899568. ------ 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)((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^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. ------ 127628/12899595. ------ 1. ==[ start ]==> ((a (^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((a a)(b (^y.y)))) REDUCED to normal form. ------ 127629/12899631. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 127630/12899712. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 127631/12899739. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a a)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 127632/12899766. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 127633/12899793. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.b))) REDUCED to normal form. ------ 127634/12899820. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 127635/12899883. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 127636/12899910. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 127637/12899928. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((a a)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 127638/12899937. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.a)((^y.y) b))) 3. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 127639/12900009. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a) b)((b (^y.y)) a)) 3. ==[ beta ]==> ((a b)((b (^y.y)) a)) 4. ==[ alpha ]==> ((a b)((b (^x.x)) a)) REDUCED to normal form. ------ 127640/12900036. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a)(a a)) b)) REDUCED to normal form. ------ 127641/12900063. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(^x.(x x)))(b c)) REDUCED to normal form. ------ 127642/12900180. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 127643/12900207. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 127644/12900288. ------ 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.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 127645/12900378. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (b (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(a (b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 127646/12900432. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 7. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 8. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 9. ==[ beta ]==> (b (a (^y.y))) 10. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 127647/12900441. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) c) REDUCED to normal form. ------ 127648/12900459. ------ 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.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 127649/12900513. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 127650/12900720. ------ 1. ==[ start ]==> ((a ((a a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(b (^x.(a a)))) REDUCED to normal form. ------ 127651/12900846. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)((b a)(^y.(y y)))) 5. ==[ beta ]==> (b ((b a)(^y.(y y)))) 6. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 127652/12900873. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 127653/12900927. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.b))) REDUCED to normal form. ------ 127654/12900954. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 127655/12900981. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 127656/12901035. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127657/12901071. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 127658/12901098. ------ 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 a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 127659/12901152. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) 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. ------ 127660/12901179. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.a))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 127661/12901233. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 127662/12901404. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 127663/12901431. ------ 1. ==[ start ]==> (((^a.a)(a b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a b))(b ((^y.y) b))) 3. ==[ beta ]==> ((a b)(b ((^y.y) b))) 4. ==[ alpha ]==> ((a b)(b ((^x.x) b))) 5. ==[ beta ]==> ((a b)(b b)) REDUCED to normal form. ------ 127664/12901458. ------ 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. ------ 127665/12901494. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 127666/12901512. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 127667/12901593. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y)(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 127668/12901620. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)((a a) a))) REDUCED to normal form. ------ 127669/12901773. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 127670/12901800. ------ 1. ==[ start ]==> (((a b)(a a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 127671/12901827. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.b)(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. ------ 127672/12902007. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b) b)((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b) b)((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b) b)(^y.(a a))) 6. ==[ alpha ]==> (((a b) b)(^x.(a a))) REDUCED to normal form. ------ 127673/12902088. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 127674/12902142. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) b) a)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 127675/12902169. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z))) b)) 7. ==[ beta ]==> (((a (^y.(^z.z))) b)((a (^y.(^z.z))) b)) 8. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 127676/12902196. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b a) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b a) c)) REDUCED to normal form. ------ 127677/12902286. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 127678/12902313. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 127679/12902340. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 127680/12902421. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 127681/12902448. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 127682/12902538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^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)(^x.x)) a) REDUCED to normal form. ------ 127683/12902673. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 127684/12902754. ------ 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.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 127685/12902790. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 127686/12902817. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 127687/12902871. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127688/12902898. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 127689/12902925. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 127690/12902952. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.b))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.b))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.b)) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 127691/12902979. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 127692/12903015. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 127693/12903042. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 127694/12903069. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a b))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 127695/12903096. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))(^x1.x1))) 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. ------ 127696/12903177. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 127697/12903204. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 127698/12903258. ------ 1. ==[ start ]==> ((a (b a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 127699/12903348. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b (b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b (b a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b (b a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b (b a))) 5. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 127700/12903429. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 127701/12903537. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((b a)((^y.y)((a a) a))) 6. ==[ alpha ]==> ((b a)((^x.x)((a a) a))) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 127702/12903564. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((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. ------ 127703/12903618. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 127704/12903681. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 127705/12903708. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127706/12903735. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 127707/12903762. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 127708/12903825. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 127709/12903852. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 127710/12903879. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 127711/12903906. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 127712/12903933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(b a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(b a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 127713/12903987. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 127714/12904014. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 127715/12904041. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 127716/12904095. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^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. ------ 127717/12904185. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(b ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(b ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(b ((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((a a)(^x.x)))) REDUCED to normal form. ------ 127718/12904266. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (b ((a a)(a (^y.y)))) 6. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 127719/12904374. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (a a))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127720/12904401. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 127721/12904428. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 127722/12904491. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 127723/12904518. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 127724/12904572. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 127725/12904599. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 127726/12904626. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (a a))(^z.a))) REDUCED to normal form. ------ 127727/12904680. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 127728/12904716. ------ 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)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 127729/12904743. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 127730/12904770. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 127731/12904797. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 127732/12904824. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.(y y)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 127733/12904851. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 127734/12904878. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 127735/12904905. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 127736/12904932. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 127737/12904977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127738/12905022. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a b)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 127739/12905049. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^z1.z1) 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. ------ 127740/12905184. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 127741/12905301. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(z z))) REDUCED to normal form. ------ 127742/12905328. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((b a)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((b a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 127743/12905355. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.x))(a (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.a))) REDUCED to normal form. ------ 127744/12905382. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) REDUCED to normal form. ------ 127745/12905463. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b) b)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b) b)) 5. ==[ beta ]==> ((^y.(a a))((a b) b)) 6. ==[ alpha ]==> ((^x.(a a))((a b) b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127746/12905490. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a) a) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a) a) c)) REDUCED to normal form. ------ 127747/12905517. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z)) d)) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z) d)) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y) d)) 5. ==[ beta ]==> (((a b)(^x.a)) d) REDUCED to normal form. ------ 127748/12905616. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(b (a b))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127749/12905652. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(a a)) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a)) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a)) a)) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 127750/12905823. ------ 1. ==[ start ]==> ((((a a) a)(a b))(b (^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(b (^x.b))) REDUCED to normal form. ------ 127751/12905850. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(a a)))) REDUCED to normal form. ------ 127752/12905877. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a a))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 127753/12905958. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 127754/12905985. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 127755/12906012. ------ 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. ------ 127756/12906183. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 127757/12906291. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127758/12906372. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 127759/12906399. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((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. ------ 127760/12906435. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 127761/12906516. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 127762/12906543. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127763/12906597. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a) a)) REDUCED to normal form. ------ 127764/12906651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a)) c)) REDUCED to normal form. ------ 127765/12906876. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 127766/12906903. ------ 1. ==[ start ]==> (((a b)(a b))(a (^c.a))) 2. ==[ alpha ]==> (((a b)(a b))(a (^x.a))) REDUCED to normal form. ------ 127767/12906930. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 127768/12906957. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^x1.x1))(a (^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 127769/12907011. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 127770/12907038. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 127771/12907065. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 127772/12907092. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 127773/12907182. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a ((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127774/12907263. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((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. ------ 127775/12907407. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)(^y.(y y)))) 3. ==[ beta ]==> ((b c)((a a)(^y.(y y)))) 4. ==[ alpha ]==> ((b c)((a a)(^x.(x x)))) REDUCED to normal form. ------ 127776/12907434. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a)) a)) REDUCED to normal form. ------ 127777/12907479. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(c (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(c (a (^y.y)))) REDUCED to normal form. ------ 127778/12907506. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b ((^z.z) a))) 3. ==[ beta ]==> ((^y.y)(b ((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127779/12907542. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) a)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 127780/12907560. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (a a))) REDUCED to normal form. ------ 127781/12907569. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 127782/12907650. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 127783/12907677. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127784/12907758. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1)) b)) REDUCED to normal form. ------ 127785/12907785. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a) c)) 3. ==[ beta ]==> ((b (^y.a))((a a) c)) 4. ==[ alpha ]==> ((b (^x.a))((a a) c)) REDUCED to normal form. ------ 127786/12907812. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 127787/12907875. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 127788/12907902. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 127789/12907929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a b)(a (^y.y))) 8. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 127790/12907956. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 127791/12907983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^a.(^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)))) 7. ==[ beta ]==> ((b a)(^y.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 127792/12908010. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 127793/12908037. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(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. ------ 127794/12908064. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.y)(a a))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 127795/12908091. ------ 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. ------ 127796/12917265. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ eta ]==> ((^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. ------ 127797/12917436. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 127798/12917535. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((^y.y) a)(^z.z))((((^y.y) a)(^z.z))(((^y.y) a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.y))((((^z.z) a)(^x1.x1))(((^y1.y1) a)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.y))((((^z.z) a)(^x1.x1))(((^y1.y1) a)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.x))((((^y.y) a)(^z.z))(((^x1.x1) a)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))((a (^z.z))(((^x1.x1) a)(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(((^z.z) a)(^x1.x1)))) 9. ==[ beta ]==> ((a (^x.x))((a (^y.y))(a (^x1.x1)))) 10. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 127799/12917760. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127800/12917988. ------ 1. ==[ start ]==> (((a (a a)) b)(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 127801/12918651. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 127802/12919059. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^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. ------ 127803/12919392. ------ 1. ==[ start ]==> (((^a.b) b)(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)(^y.((^z.z) b))) 3. ==[ beta ]==> (b (^y.((^z.z) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 127804/12919425. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((((^z.z) b)(^x1.x1))(((^z.z) b)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) b)(^z.z))(((^x1.x1) b)(^y1.y1)))) 5. ==[ beta ]==> ((((^y.y) b)(^z.z))(((^x1.x1) b)(^y1.y1))) 6. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z) b)(^x1.x1))) 7. ==[ beta ]==> ((b (^y.y))(((^z.z) b)(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.x))(((^y.y) b)(^z.z))) 9. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 10. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 127805/12919734. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(x x))((^y.y)(^z.z)))(^y1.y1)) 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. ------ 127806/12920040. ------ 1. ==[ start ]==> (((^a.b) c)(^d.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 127807/12920100. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((^z.(^x1.(^y1.y1))) b)((^z.(^x1.(^y1.y1))) b))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1))) b))(^x2.x2)) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.(^z1.z1))) b))(^x2.x2)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1))) b))(^z1.z1)) 7. ==[ beta ]==> ((^y.y)(^z1.z1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127808/12920382. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127809/12920670. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127810/12922296. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127811/12922578. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127812/12922611. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a)) b)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127813/12922785. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^d.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 127814/12923028. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 127815/12923253. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 127816/12923649. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^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) a) 5. ==[ alpha ]==> ((^x.x) a) 6. ==[ beta ]==> a REDUCED to normal form. ------ 127817/12924009. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((a a) a))) REDUCED to normal form. ------ 127818/12924639. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 127819/12924690. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (a a)) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127820/12924783. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127821/12925008. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.d)) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.y)) 3. ==[ beta ]==> ((b c)(^y.y)) 4. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 127822/12925143. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(z (z z)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(z (z z)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 127823/12925242. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 127824/12925413. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127825/12925476. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.c)) REDUCED to normal form. ------ 127826/12925530. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 127827/12925584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.b)) 3. ==[ beta ]==> (((^y.y)(b a))(^z.b)) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.b)) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 127828/12925638. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.b)) 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. ------ 127829/12925665. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(^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. ------ 127830/12925767. ------ 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. ------ 127831/12925794. ------ 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. ------ 127832/12925821. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(a b))) REDUCED to normal form. ------ 127833/12925848. ------ 1. ==[ start ]==> (((^a.a) b)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) b)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 127834/12925875. ------ 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)((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. ------ 127835/12925902. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a a) b)((^y.y)(b a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(b a))) 5. ==[ beta ]==> (((a a) b)(b a)) REDUCED to normal form. ------ 127836/12925929. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 127837/12925956. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 127838/12925983. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 127839/12926046. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 127840/12926073. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) 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. ------ 127841/12926082. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 127842/12926109. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 127843/12926244. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 127844/12926316. ------ 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.(^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. ------ 127845/12926343. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> ((a (a (a a)))(a (^y.y))) 4. ==[ alpha ]==> ((a (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 127846/12926352. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(y y))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(x x))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (((^y.a)((^z.z) b))((^y.a)((^z.z) b))) 6. ==[ alpha ]==> (((^x.a)((^y.y) b))((^z.a)((^x1.x1) b))) 7. ==[ beta ]==> (a ((^z.a)((^x1.x1) b))) 8. ==[ alpha ]==> (a ((^x.a)((^y.y) b))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127847/12926379. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((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. ------ 127848/12926487. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 127849/12926568. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127850/12926703. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127851/12926730. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 127852/12926793. ------ 1. ==[ start ]==> (((a (a a)) b)(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(a (b (^x.x)))) REDUCED to normal form. ------ 127853/12926820. ------ 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. ------ 127854/12926847. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 127855/12926874. ------ 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.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 127856/12926901. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))((b a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))((b a)(a (a a)))) REDUCED to normal form. ------ 127857/12926928. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 127858/12926955. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 7. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 8. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 9. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 127859/12927216. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (a ((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 127860/12927324. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((^y.(a a))((a a) a)) 6. ==[ alpha ]==> ((^x.(a a))((a a) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 127861/12927459. ------ 1. ==[ start ]==> ((a (^a.b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 127862/12927477. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 127863/12927531. ------ 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. ------ 127864/12927558. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y) b) b)) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y) b) b)) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b) b)) 5. ==[ beta ]==> (((a (a a)) a)(b b)) REDUCED to normal form. ------ 127865/12927648. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127866/12927810. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127867/12927819. ------ 1. ==[ start ]==> (((a b) a)(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 127868/12927837. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))(^b.b))) 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)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 127869/12927846. ------ 1. ==[ start ]==> (((a a)(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))(b ((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.b))(b b)) REDUCED to normal form. ------ 127870/12927900. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 127871/12927927. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 127872/12927954. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)((^z.z) a))) 5. ==[ beta ]==> ((^y.a)((b a)((^z.z) a))) 6. ==[ alpha ]==> ((^x.a)((b a)((^y.y) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 127873/12927981. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 127874/12928008. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 127875/12928197. ------ 1. ==[ start ]==> (((^a.b) b)((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)((a a)((^y.y) b))) 3. ==[ beta ]==> (b ((a a)((^y.y) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 127876/12928233. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)(^z.z))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)(^y.y))) 5. ==[ beta ]==> ((a (a a))(b (^y.y))) 6. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 127877/12928242. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.b)(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. ------ 127878/12928269. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127879/12928323. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127880/12928404. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (b ((^x1.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127881/12928458. ------ 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 z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.(y y))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 127882/12928485. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.a)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b a))) 5. ==[ beta ]==> ((^y.a)(b a)) 6. ==[ alpha ]==> ((^x.a)(b a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 127883/12928539. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) b))) 9. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) b))) 10. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) b))) 11. ==[ beta ]==> ((^y.y)((^z.z) b)) 12. ==[ alpha ]==> ((^x.x)((^y.y) b)) 13. ==[ beta ]==> ((^y.y) b) 14. ==[ alpha ]==> ((^x.x) b) 15. ==[ beta ]==> b REDUCED to normal form. ------ 127884/12928845. ------ 1. ==[ start ]==> (((^a.b) c)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)(b (a (^y.(^z.z))))) 3. ==[ beta ]==> (b (b (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (b (a (^x.(^y.y))))) REDUCED to normal form. ------ 127885/12928881. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b) 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. ------ 127886/12928908. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 127887/12929088. ------ 1. ==[ start ]==> (((a b) c)((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> (((a b) c)((a (a a))(a a))) REDUCED to normal form. ------ 127888/12929115. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) b)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 127889/12929142. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(b a))) REDUCED to normal form. ------ 127890/12929160. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 127891/12929187. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(a (^x1.x1))) 3. ==[ beta ]==> ((^y.y)(a (^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 127892/12929322. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 127893/12929475. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 127894/12929502. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 127895/12929529. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a) b)) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a) b)) 7. ==[ beta ]==> ((^y.y)((b a) b)) 8. ==[ alpha ]==> ((^x.x)((b a) b)) 9. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 127896/12929898. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a b)(a (a a)))) REDUCED to normal form. ------ 127897/12930006. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.(a a)))(a (a a))) REDUCED to normal form. ------ 127898/12930024. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))(c (^x.(^y.y)))) REDUCED to normal form. ------ 127899/12930033. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 127900/12930231. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(b a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a)(b a))(^y.a)) 6. ==[ alpha ]==> (((a a)(b a))(^x.a)) REDUCED to normal form. ------ 127901/12930258. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (a a))(^z.b))) REDUCED to normal form. ------ 127902/12930285. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.(a a)))) 7. ==[ beta ]==> ((a (a a))(a (^y.(a a)))) 8. ==[ alpha ]==> ((a (a a))(a (^x.(a a)))) REDUCED to normal form. ------ 127903/12930312. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 127904/12930366. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((b a) a)) 3. ==[ beta ]==> ((((a a) a)(^y.y))((b a) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((b a) a)) REDUCED to normal form. ------ 127905/12930393. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(a (a a)))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 127906/12930510. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 127907/12930591. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 127908/12930789. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (a a))((a a) a))) REDUCED to normal form. ------ 127909/12930816. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a (a b))) REDUCED to normal form. ------ 127910/12930834. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(c (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(c (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(a a)))) 5. ==[ beta ]==> (c (^y.(a a))) 6. ==[ alpha ]==> (c (^x.(a a))) REDUCED to normal form. ------ 127911/12930969. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (b ((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 127912/12931077. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127913/12931104. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 127914/12931149. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 127915/12931176. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a) b)) REDUCED to normal form. ------ 127916/12931203. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a b) c)) 3. ==[ beta ]==> (((a (a a))(a a))((a b) c)) REDUCED to normal form. ------ 127917/12931383. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(a ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127918/12931419. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a)) b)) 3. ==[ beta ]==> ((a b)((^y.(a a)) b)) 4. ==[ alpha ]==> ((a b)((^x.(a a)) b)) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 127919/12931590. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 127920/12931752. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(y y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (((^y.y)(^z.z))((^y.y)(^z.z)))) 8. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 11. ==[ beta ]==> (b ((^y.y)(^z.z))) 12. ==[ alpha ]==> (b ((^x.x)(^y.y))) 13. ==[ beta ]==> (b (^y.y)) 14. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 127921/12931779. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^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. ------ 127922/12931833. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 127923/12931914. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127924/12932022. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127925/12932031. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (a b))) REDUCED to normal form. ------ 127926/12932058. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.y))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 127927/12932094. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b) b)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b) b)) 3. ==[ beta ]==> (((a a) b)((^y.b) b)) 4. ==[ alpha ]==> (((a a) b)((^x.b) b)) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 127928/12932283. ------ 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 b)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 127929/12932310. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 127930/12932364. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (a a))(^x1.(x1 x1)))) REDUCED to normal form. ------ 127931/12932391. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 127932/12932454. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 127933/12932589. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 127934/12932733. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((b b)((a (a a))((^y.y) a))) 4. ==[ alpha ]==> ((b b)((a (a a))((^x.x) a))) 5. ==[ beta ]==> ((b b)((a (a a)) a)) REDUCED to normal form. ------ 127935/12932760. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (a (a a)))) REDUCED to normal form. ------ 127936/12932805. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.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. ------ 127937/12932814. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((a a) a))) REDUCED to normal form. ------ 127938/12932859. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(a a))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(a a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(a a))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 127939/12932940. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a 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. ------ 127940/12933048. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127941/12933174. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a) a)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a) a)) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 127942/12933201. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 127943/12933228. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x)) c)) 3. ==[ beta ]==> (((a (a a))(b a))(c c)) REDUCED to normal form. ------ 127944/12933336. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 8. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 127945/12933363. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 127946/12933417. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 127947/12933444. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 127948/12933471. ------ 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)) 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. ------ 127949/12933498. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 127950/12933588. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.x2)(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.x2)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127951/12933669. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c (^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 127952/12933777. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127953/12933813. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b d)) 2. ==[ alpha ]==> ((((^x.x) b) c)(b d)) 3. ==[ beta ]==> ((b c)(b d)) REDUCED to normal form. ------ 127954/12933885. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 127955/12933912. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127956/12933948. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(a (a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(a (a (a a)))) REDUCED to normal form. ------ 127957/12933975. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 127958/12934047. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> (b (a (^z.(z z)))) 4. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 127959/12934083. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c b)) 3. ==[ beta ]==> (((a a)(^y.b))(c b)) 4. ==[ alpha ]==> (((a a)(^x.b))(c b)) REDUCED to normal form. ------ 127960/12934155. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127961/12934191. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.a))(b (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.a))(b (a (^y.y)))) REDUCED to normal form. ------ 127962/12934218. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 127963/12934281. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y) c)) 3. ==[ beta ]==> (((a a)(b (^x.x))) c) REDUCED to normal form. ------ 127964/12934308. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 127965/12934335. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 127966/12934362. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z)) a)) REDUCED to normal form. ------ 127967/12934389. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a) b)) 3. ==[ beta ]==> (((^y.y)(b a))((a a) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((a a) b)) 5. ==[ beta ]==> ((b a)((a a) b)) REDUCED to normal form. ------ 127968/12934416. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 127969/12934443. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y) b)) 3. ==[ beta ]==> (((a b)(a a))((^y.y) b)) 4. ==[ alpha ]==> (((a b)(a a))((^x.x) b)) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 127970/12934470. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((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. ------ 127971/12934497. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a) a)) REDUCED to normal form. ------ 127972/12934550. ------ 1. ==[ start ]==> (^a.((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (^x.((x (^y.(^z.z)))(x (x x)))) REDUCED to normal form. ------ 127973/12934551. ------ 1. ==[ start ]==> (a ((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (a ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 127974/12943359. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a))) a) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 127975/12943365. ------ 1. ==[ start ]==> ((^a.a)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 127976/12943392. ------ 1. ==[ start ]==> ((^a.(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((b a)((^y.y)(^z.z)))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((b a)((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((b a)(^y.y))((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((b a)(^x.x))((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((b a)(^x.x))((b a)(^z.z))) 8. ==[ alpha ]==> (((b a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 127977/12943419. ------ 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 REDUCED to normal form. ------ 127978/12943500. ------ 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 ]==> ((((a a) a)((a a)(^z.z)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 127979/12943860. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 127980/12944034. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(y (^z.z)))) 3. ==[ beta ]==> ((a b)(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 127981/12944742. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a (^y.y))((^z.z) b))((a (^y.y))((^z.z) b)))((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> ((((a (^x.x))((^y.y) b))((a (^z.z))((^x1.x1) b)))((a (^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> ((((a (^x.x)) b)((a (^z.z))((^x1.x1) b)))((a (^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> ((((a (^x.x)) b)((a (^y.y))((^z.z) b)))((a (^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> ((((a (^x.x)) b)((a (^y.y)) b))((a (^x1.x1))((^y1.y1) b))) 8. ==[ alpha ]==> ((((a (^x.x)) b)((a (^y.y)) b))((a (^z.z))((^x1.x1) b))) 9. ==[ beta ]==> ((((a (^x.x)) b)((a (^y.y)) b))((a (^z.z)) b)) REDUCED to normal form. ------ 127982/12945075. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 127983/12945825. ------ 1. ==[ start ]==> (((a b)(a a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a))(^x.b)) REDUCED to normal form. ------ 127984/12946167. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 127985/12946500. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 127986/12946524. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a (^z.(^x1.x1)))(a a))((a (^z.(^x1.x1)))(a a)))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1)))(a a)))(^y1.y1)) REDUCED to normal form. ------ 127987/12946815. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 127988/12947706. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 127989/12947829. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 127990/12948720. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127991/12949002. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 127992/12949011. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 127993/12949035. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 127994/12949677. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 127995/12949875. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(a b))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(a b))) REDUCED to normal form. ------ 127996/12950073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 127997/12950460. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.b))) REDUCED to normal form. ------ 127998/12950622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((a a) a))) REDUCED to normal form. ------ 127999/12950793. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.((z z) z))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.((z z) z))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.((y y) y))) REDUCED to normal form. ------ 128000/12950928. ------ 1. ==[ start ]==> (((a b)(a b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(^x.(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 128001/12951459. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(a (a a)))) REDUCED to normal form. ------ 128002/12951567. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 128003/12951675. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 128004/12951837. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 128005/12951900. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 128006/12952035. ------ 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)))) REDUCED to normal form. ------ 128007/12952062. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(a a))) 3. ==[ beta ]==> (((a b)(a a))(^y.(a a))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(a a))) REDUCED to normal form. ------ 128008/12952116. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.b)) REDUCED to normal form. ------ 128009/12952170. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 128010/12952182. ------ 1. ==[ start ]==> ((a a)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 128011/12952209. ------ 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. ------ 128012/12952236. ------ 1. ==[ start ]==> ((a b)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a b)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 128013/12952290. ------ 1. ==[ start ]==> (((a a)(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(a a))) REDUCED to normal form. ------ 128014/12952317. ------ 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)))) REDUCED to normal form. ------ 128015/12952452. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 128016/12952515. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 128017/12952542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.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. ------ 128018/12952551. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z) a)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) a)) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 128019/12952578. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 128020/12952596. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> (a ((b a)(^y.(^z.z)))) 6. ==[ alpha ]==> (a ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 128021/12952659. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 128022/12952677. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 128023/12952767. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 128024/12952785. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((((^y.y) a)(^z.z))(((^y.y) a)(^z.z))) 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. ------ 128025/12952812. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(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))) REDUCED to normal form. ------ 128026/12952848. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a b)((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 128027/12952866. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b (^z.z)) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((b (^z.z)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) a)) 5. ==[ beta ]==> ((^y.y)((b (^z.z)) a)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 7. ==[ beta ]==> ((b (^y.y)) a) 8. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 128028/12952893. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a (a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 128029/12952920. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 5. ==[ beta ]==> (((^y.y) b) c) 6. ==[ alpha ]==> (((^x.x) b) c) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 128030/12952929. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.a)) REDUCED to normal form. ------ 128031/12952956. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 128032/12953091. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(^c.(^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. ------ 128033/12953298. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^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. ------ 128034/12953424. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(a b))) REDUCED to normal form. ------ 128035/12953451. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 128036/12953478. ------ 1. ==[ start ]==> ((((^a.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))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) 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)((^y.y)((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)((^x.x)((a a)(^y.y)))) 9. ==[ beta ]==> ((a a)((a a)(^y.y))) 10. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 128037/12953505. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (a a))(b a))) REDUCED to normal form. ------ 128038/12953532. ------ 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) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 128039/12953559. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> ((a ((a a) a))((a (^x.x)) b)) REDUCED to normal form. ------ 128040/12953649. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (((^z.z) b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> (a (b (^y.(^z.z)))) 8. ==[ alpha ]==> (a (b (^x.(^y.y)))) REDUCED to normal form. ------ 128041/12953685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 128042/12953730. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 128043/12953766. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 128044/12953793. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.b)(a b))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.b)(a b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)(a b))) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 128045/12953811. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)(^z.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)(^z.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(^y.(a a)))) 7. ==[ beta ]==> ((a a)(((a a) a)(^y.(a a)))) 8. ==[ alpha ]==> ((a a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 128046/12953820. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 128047/12953847. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128048/12953874. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((b a)(b a))) REDUCED to normal form. ------ 128049/12953892. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.b))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 128050/12954252. ------ 1. ==[ start ]==> (((a b) a)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 128051/12954279. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 128052/12954351. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y) b)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y) b)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x) b)) 5. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 128053/12954477. ------ 1. ==[ start ]==> (((a a)(a b))((a b)((a a) a))) REDUCED to normal form. ------ 128054/12954504. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a) a)(a b))) REDUCED to normal form. ------ 128055/12954531. ------ 1. ==[ start ]==> ((((^a.a) a)((^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))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(a a)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 11. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 128056/12954558. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 128057/12954585. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)(b a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(b a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(b a))) 7. ==[ beta ]==> (a (((^y.y) a)(b a))) 8. ==[ alpha ]==> (a (((^x.x) a)(b a))) 9. ==[ beta ]==> (a (a (b a))) REDUCED to normal form. ------ 128058/12954612. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 128059/12954630. ------ 1. ==[ start ]==> (((^a.b) b)(b (^b.b))) 2. ==[ alpha ]==> (((^x.b) b)(b (^y.y))) 3. ==[ beta ]==> (b (b (^y.y))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 128060/12954639. ------ 1. ==[ start ]==> (((a b)(a a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))((a a)((^x.x) b))) 3. ==[ beta ]==> (((a b)(a a))((a a) b)) REDUCED to normal form. ------ 128061/12954675. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 128062/12954702. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 128063/12954756. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 128064/12954837. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(^x1.b))) 3. ==[ beta ]==> (b (((a a) a)(^x1.b))) 4. ==[ alpha ]==> (b (((a a) a)(^x.b))) REDUCED to normal form. ------ 128065/12954846. ------ 1. ==[ start ]==> (((a b) b)((^c.a)(a b))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(a b))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 128066/12954873. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 128067/12954900. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 128068/12954927. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 128069/12954972. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a a)(^b.b))) 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. ------ 128070/12954981. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 128071/12955008. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((^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. ------ 128072/12955035. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 128073/12955053. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 128074/12955278. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 128075/12955287. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 128076/12955314. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(a ((^y.y) b))) 3. ==[ beta ]==> (((a a)(a a))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) b))) 5. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 128077/12955341. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 128078/12955629. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 128079/12955656. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 128080/12955674. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 128081/12955710. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128082/12955737. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 128083/12955755. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 128084/12955764. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 128085/12955818. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 128086/12956466. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 128087/12956520. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 128088/12956538. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a)(^y.y))) 3. ==[ beta ]==> (b ((b a)(^y.y))) 4. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 128089/12956574. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 128090/12956601. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 128091/12956646. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 128092/12957105. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^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. ------ 128093/12957357. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 128094/12957402. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (b ((a b)(^x1.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 128095/12957411. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 128096/12957465. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 128097/12957510. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128098/12957519. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 128099/12957537. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 128100/12957816. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128101/12957825. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 128102/12957852. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a a))) 5. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 128103/12957861. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^z.(a a)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) b)) 5. ==[ beta ]==> ((^y.(a a)) b) 6. ==[ alpha ]==> ((^x.(a a)) b) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 128104/12957888. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b) c)) 3. ==[ beta ]==> ((^y.y)((^z1.b) c)) 4. ==[ alpha ]==> ((^x.x)((^y.b) c)) 5. ==[ beta ]==> ((^y.b) c) 6. ==[ alpha ]==> ((^x.b) c) 7. ==[ beta ]==> b REDUCED to normal form. ------ 128105/12958131. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128106/12958140. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 128107/12958167. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 128108/12958185. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 128109/12958194. ------ 1. ==[ start ]==> (((a a)(^b.b))((^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. ------ 128110/12958221. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 128111/12958266. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 128112/12958302. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 128113/12958329. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 128114/12958347. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 128115/12958356. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 128116/12958383. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 128117/12958410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 128118/12958464. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 128119/12958491. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.x))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 128120/12958527. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(a a))) 3. ==[ beta ]==> (((a a) b)((a b)(a a))) REDUCED to normal form. ------ 128121/12958554. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)(a (^x1.x1)))) REDUCED to normal form. ------ 128122/12958581. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (b a))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((a (b a))((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((a (b a))((^y.y) a)) 8. ==[ alpha ]==> ((a (b a))((^x.x) a)) 9. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 128123/12958608. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 128124/12958635. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((a a)(a ((^y.y)(^z.z)))) 10. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.y)))) 11. ==[ beta ]==> ((a a)(a (^y.y))) 12. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 128125/12958662. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 128126/12958689. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(a b))) REDUCED to normal form. ------ 128127/12958887. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^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. ------ 128128/12959130. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128129/12959247. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.a))) REDUCED to normal form. ------ 128130/12959274. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(a (^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.b))) REDUCED to normal form. ------ 128131/12959292. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a) a)(^y.y))) 3. ==[ beta ]==> (((b a)(b a))(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 128132/12959355. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 128133/12959373. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> (b (a (^y.(y y)))) 6. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 128134/12959382. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 128135/12959436. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) a)) REDUCED to normal form. ------ 128136/12959481. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128137/12959490. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 128138/12959517. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.a)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.a))) 7. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 128139/12959544. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 128140/12959580. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(b ((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(b (^x.x))) REDUCED to normal form. ------ 128141/12959607. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a ((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(a ((a a) a))) REDUCED to normal form. ------ 128142/12959634. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a a))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 128143/12959661. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 128144/12959688. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1) 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. ------ 128145/12959715. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (^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)))) REDUCED to normal form. ------ 128146/12959742. ------ 1. ==[ start ]==> (((a b)(a b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.y))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.x))) REDUCED to normal form. ------ 128147/12960102. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 128148/12960210. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128149/12960246. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 128150/12960273. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a (a a))) REDUCED to normal form. ------ 128151/12960318. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z) a) b)) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a) b)) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a) b)) 5. ==[ beta ]==> ((b (^x.x))(a b)) REDUCED to normal form. ------ 128152/12960381. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 128153/12960399. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 128154/12960489. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 128155/12960516. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(a a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 128156/12960588. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128157/12960597. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 128158/12960624. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 128159/12960651. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 128160/12960714. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 128161/12960768. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b b)) 3. ==[ beta ]==> ((a ((^y.y) b))(b b)) 4. ==[ alpha ]==> ((a ((^x.x) b))(b b)) 5. ==[ beta ]==> ((a b)(b b)) REDUCED to normal form. ------ 128162/12960822. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (a a))) 3. ==[ beta ]==> (((^y.y)(b a))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (a a))) 5. ==[ beta ]==> ((b a)(b (a a))) REDUCED to normal form. ------ 128163/12960849. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 128164/12960876. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)(a a))) 3. ==[ beta ]==> (((a b)(a a))((a a)(a a))) REDUCED to normal form. ------ 128165/12960903. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b a)) 3. ==[ beta ]==> (((a a)(a b))(b a)) REDUCED to normal form. ------ 128166/12960930. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a b)) REDUCED to normal form. ------ 128167/12960984. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(a a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 128168/12969801. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a))) b) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 128169/12969825. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 128170/12969906. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 128171/12970068. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (^y.((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (^x.((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 128172/12970410. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(y y))(a (^z.(^x1.x1))))(((^y.(y y))(a (^z.(^x1.x1))))((^y.(y y))(a (^z.(^x1.x1)))))) 4. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.(x1 x1))(a (^y1.(^z1.z1))))((^x2.(x2 x2))(a (^y2.(^z2.z2)))))) 5. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.(x1 x1))(a (^y1.(^z1.z1))))((^x2.(x2 x2))(a (^y2.(^z2.z2)))))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.(y1 y1))(a (^z1.(^x2.x2))))((^y2.(y2 y2))(a (^z2.(^x3.x3)))))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a (^z1.(^x2.x2)))(a (^z1.(^x2.x2))))((^y2.(y2 y2))(a (^z2.(^x3.x3)))))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))((^z2.(z2 z2))(a (^x3.(^y3.y3)))))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))((a (^x3.(^y3.y3)))(a (^x3.(^y3.y3)))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))((a (^z2.(^x3.x3)))(a (^y3.(^z3.z3)))))) REDUCED to normal form. ------ 128173/12970485. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^c.(^d.(^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. ------ 128174/12971232. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^c.((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))) REDUCED to normal form. ------ 128175/12971601. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.((a a)(a a)))) REDUCED to normal form. ------ 128176/12972093. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))((^x1.x1)(^y1.y1)))(((^z.z)(a a))((^x1.x1)(^y1.y1))))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))((^z.z)(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(^x2.x2))))) 5. ==[ beta ]==> (^x.(((a a)((^z.z)(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(^x2.x2))))) 6. ==[ alpha ]==> (^x.(((a a)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1))))) 7. ==[ beta ]==> (^x.(((a a)(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1))))) 8. ==[ alpha ]==> (^x.(((a a)(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1))))) 9. ==[ beta ]==> (^x.(((a a)(^y.y))((a a)((^x1.x1)(^y1.y1))))) 10. ==[ alpha ]==> (^x.(((a a)(^y.y))((a a)((^z.z)(^x1.x1))))) 11. ==[ beta ]==> (^x.(((a a)(^y.y))((a a)(^x1.x1)))) 12. ==[ alpha ]==> (^x.(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 128177/12972618. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 128178/12972951. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^b.(^b.b))) 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. ------ 128179/12973572. ------ 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))))) REDUCED to normal form. ------ 128180/12973731. ------ 1. ==[ start ]==> ((^a.(b a))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.a))) 3. ==[ eta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 128181/12974436. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(b 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))) REDUCED to normal form. ------ 128182/12975219. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 128183/12975462. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 128184/12976353. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 128185/12976485. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.a)((^z.z)(^x1.x1)))((^y.a)((^z.z)(^x1.x1))))(((^y.a)((^z.z)(^x1.x1)))((^y.a)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.a)((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1))))(((^x2.a)((^y2.y2)(^z2.z2)))((^x3.a)((^y3.y3)(^z3.z3))))) 5. ==[ beta ]==> ((a ((^x1.a)((^y1.y1)(^z1.z1))))(((^x2.a)((^y2.y2)(^z2.z2)))((^x3.a)((^y3.y3)(^z3.z3))))) 6. ==[ alpha ]==> ((a ((^x.a)((^y.y)(^z.z))))(((^x1.a)((^y1.y1)(^z1.z1)))((^x2.a)((^y2.y2)(^z2.z2))))) 7. ==[ beta ]==> ((a a)(((^x1.a)((^y1.y1)(^z1.z1)))((^x2.a)((^y2.y2)(^z2.z2))))) 8. ==[ alpha ]==> ((a a)(((^x.a)((^y.y)(^z.z)))((^x1.a)((^y1.y1)(^z1.z1))))) 9. ==[ beta ]==> ((a a)(a ((^x1.a)((^y1.y1)(^z1.z1))))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)((^y.y)(^z.z))))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 128186/12977073. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.a))) REDUCED to normal form. ------ 128187/12977244. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.a))) REDUCED to normal form. ------ 128188/12977541. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 128189/12977565. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 128190/12977910. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(y y)))) REDUCED to normal form. ------ 128191/12978018. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.d)) 3. ==[ beta ]==> ((a (^y.y))(^z.d)) 4. ==[ alpha ]==> ((a (^x.x))(^y.d)) REDUCED to normal form. ------ 128192/12978036. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(y1 (y1 y1)))) REDUCED to normal form. ------ 128193/12978117. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (b (^z.((^x1.x1) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 128194/12978378. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.y))) REDUCED to normal form. ------ 128195/12978432. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 128196/12978486. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 128197/12978540. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 128198/12978567. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(a a))) REDUCED to normal form. ------ 128199/12978621. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 128200/12978651. ------ 1. ==[ start ]==> ((a (^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 128201/12978678. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 128202/12978705. ------ 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. ------ 128203/12978732. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 128204/12978786. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a)(^z.z))))