59.80/15.56 YES 60.11/15.58 60.11/15.58 Problem: 60.11/15.58 strict: 60.11/15.58 b(a(b(x1))) -> a(b(a(x1))) 60.11/15.58 c(c(a(x1))) -> b(a(c(x1))) 60.11/15.58 c(a(c(x1))) -> b(b(c(x1))) 60.11/15.58 b(a(c(x1))) -> a(c(c(x1))) 60.11/15.58 weak: 60.11/15.58 c(a(b(x1))) -> a(b(c(x1))) 60.11/15.58 b(a(a(x1))) -> a(c(c(x1))) 60.11/15.58 b(c(b(x1))) -> a(b(a(x1))) 60.11/15.58 60.11/15.58 Proof: 60.11/15.58 Root-Labeling Processor: 60.11/15.58 strict: 60.11/15.58 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 b(b)(b(a)(a(b)(b(c)(x1)))) -> b(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(c)(x1)))) -> a(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(b)(x1)))) -> c(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(a)(x1)))) -> c(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(c)(x1)))) -> c(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.58 b(c)(c(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.58 b(c)(c(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.58 b(c)(c(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.58 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.58 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.58 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.58 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.58 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.58 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.58 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 weak: 60.11/15.58 b(c)(c(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.58 b(c)(c(a)(a(b)(b(a)(x1)))) -> b(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.58 b(c)(c(a)(a(b)(b(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.58 a(c)(c(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.58 a(c)(c(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.58 a(c)(c(a)(a(b)(b(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.58 c(c)(c(a)(a(b)(b(b)(x1)))) -> c(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.58 c(c)(c(a)(a(b)(b(a)(x1)))) -> c(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.58 c(c)(c(a)(a(b)(b(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.58 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 a(b)(b(a)(a(a)(a(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 a(b)(b(a)(a(a)(a(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 c(b)(b(a)(a(a)(a(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.58 c(b)(b(a)(a(a)(a(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.58 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.58 b(b)(b(c)(c(b)(b(b)(x1)))) -> b(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 b(b)(b(c)(c(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 b(b)(b(c)(c(b)(b(c)(x1)))) -> b(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 a(b)(b(c)(c(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 a(b)(b(c)(c(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 a(b)(b(c)(c(b)(b(c)(x1)))) -> a(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 c(b)(b(c)(c(b)(b(b)(x1)))) -> c(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 c(b)(b(c)(c(b)(b(a)(x1)))) -> c(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 c(b)(b(c)(c(b)(b(c)(x1)))) -> c(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 RT Transformation Processor: 60.11/15.58 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 b(b)(b(a)(a(b)(b(c)(x1)))) -> b(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 a(b)(b(a)(a(b)(b(c)(x1)))) -> a(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(b)(x1)))) -> c(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(a)(x1)))) -> c(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.58 c(b)(b(a)(a(b)(b(c)(x1)))) -> c(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 b(c)(c(c)(c(a)(a(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 a(c)(c(c)(c(a)(a(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 60.11/15.58 c(c)(c(c)(c(a)(a(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 60.11/15.59 b(c)(c(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.59 b(c)(c(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.59 b(c)(c(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.59 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.59 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.59 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.59 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) 60.11/15.59 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) 60.11/15.59 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) 60.11/15.59 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 b(c)(c(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.59 b(c)(c(a)(a(b)(b(a)(x1)))) -> b(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.59 b(c)(c(a)(a(b)(b(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.59 a(c)(c(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.59 a(c)(c(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.59 a(c)(c(a)(a(b)(b(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.59 c(c)(c(a)(a(b)(b(b)(x1)))) -> c(a)(a(b)(b(c)(c(b)(x1)))) 60.11/15.59 c(c)(c(a)(a(b)(b(a)(x1)))) -> c(a)(a(b)(b(c)(c(a)(x1)))) 60.11/15.59 c(c)(c(a)(a(b)(b(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 60.11/15.59 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 a(b)(b(a)(a(a)(a(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 a(b)(b(a)(a(a)(a(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 c(b)(b(a)(a(a)(a(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 60.11/15.59 c(b)(b(a)(a(a)(a(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 60.11/15.59 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 60.11/15.59 b(b)(b(c)(c(b)(b(b)(x1)))) -> b(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.59 b(b)(b(c)(c(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.59 b(b)(b(c)(c(b)(b(c)(x1)))) -> b(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.59 a(b)(b(c)(c(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.59 a(b)(b(c)(c(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.59 a(b)(b(c)(c(b)(b(c)(x1)))) -> a(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.59 c(b)(b(c)(c(b)(b(b)(x1)))) -> c(a)(a(b)(b(a)(a(b)(x1)))) 60.11/15.59 c(b)(b(c)(c(b)(b(a)(x1)))) -> c(a)(a(b)(b(a)(a(a)(x1)))) 60.11/15.59 c(b)(b(c)(c(b)(b(c)(x1)))) -> c(a)(a(b)(b(a)(a(c)(x1)))) 60.11/15.59 KBO Processor: 60.11/15.59 weight function: 60.11/15.59 w0 = 1 60.11/15.59 w(c(c)) = w(c(a)) = w(c(b)) = w(a(c)) = w(b(c)) = w(a(a)) = w(a(b)) = w( 60.11/15.59 b(a)) = w(b(b)) = 1 60.11/15.59 precedence: 60.11/15.59 a(c) ~ b(c) > a(b) ~ b(b) > c(c) > c(b) > c(a) ~ a(a) ~ b(a) 60.11/15.59 problem: 60.11/15.59 60.11/15.59 Qed 60.11/15.59 EOF