43.02/11.20 YES 43.02/11.21 43.02/11.21 Problem: 43.02/11.21 b(b(b(x1))) -> a(x1) 43.02/11.21 a(a(x1)) -> a(b(a(x1))) 43.02/11.21 a(a(a(x1))) -> b(a(a(x1))) 43.02/11.21 43.02/11.21 Proof: 43.02/11.21 DP Processor: 43.02/11.21 DPs: 43.02/11.21 b#(b(b(x1))) -> a#(x1) 43.02/11.21 a#(a(x1)) -> b#(a(x1)) 43.02/11.21 a#(a(x1)) -> a#(b(a(x1))) 43.02/11.21 a#(a(a(x1))) -> b#(a(a(x1))) 43.02/11.21 TRS: 43.02/11.21 b(b(b(x1))) -> a(x1) 43.02/11.21 a(a(x1)) -> a(b(a(x1))) 43.02/11.21 a(a(a(x1))) -> b(a(a(x1))) 43.02/11.21 TDG Processor: 43.02/11.21 DPs: 43.02/11.21 b#(b(b(x1))) -> a#(x1) 43.02/11.21 a#(a(x1)) -> b#(a(x1)) 43.02/11.21 a#(a(x1)) -> a#(b(a(x1))) 43.02/11.21 a#(a(a(x1))) -> b#(a(a(x1))) 43.02/11.21 TRS: 43.02/11.21 b(b(b(x1))) -> a(x1) 43.02/11.21 a(a(x1)) -> a(b(a(x1))) 43.02/11.21 a(a(a(x1))) -> b(a(a(x1))) 43.02/11.21 graph: 43.02/11.21 a#(a(a(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) 43.02/11.21 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1))) 43.02/11.21 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 43.02/11.21 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 43.02/11.21 a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1) 43.02/11.21 b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1))) 43.02/11.21 b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 43.02/11.21 b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 43.02/11.21 Root-Labeling Processor: 43.02/11.21 DPs: 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.21 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.21 TRS: 43.02/11.21 f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 43.02/11.21 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.02/11.21 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.02/11.21 b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 43.02/11.21 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.02/11.21 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.02/11.21 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 43.02/11.21 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.02/11.21 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.02/11.21 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.02/11.21 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.02/11.21 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.02/11.21 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.21 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.21 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.21 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.21 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.21 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.21 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.21 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.21 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.21 TDG Processor: 43.02/11.21 DPs: 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.21 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.21 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.21 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.21 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.21 TRS: 43.02/11.21 f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 43.02/11.21 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.02/11.21 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.02/11.21 b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 43.02/11.22 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.02/11.22 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.02/11.22 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 43.02/11.22 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.02/11.22 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.02/11.22 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.02/11.22 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.02/11.22 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.02/11.22 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.22 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.22 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.22 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.22 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.22 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.22 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.02/11.22 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.02/11.22 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.02/11.22 graph: 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 43.02/11.22 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.22 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.23 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.23 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.25 Polynomial Interpretation Processor: 43.02/11.25 dimension: 1 43.02/11.25 interpretation: 43.02/11.25 [a(a)](x0) = x0, 43.02/11.25 43.02/11.25 [a(b)](x0) = x0, 43.02/11.25 43.02/11.25 [a(f4)](x0) = x0, 43.02/11.25 43.02/11.25 [f4(a)](x0) = x0, 43.02/11.25 43.02/11.25 [b(a)](x0) = x0, 43.02/11.25 43.02/11.25 [f4(f4)](x0) = x0, 43.02/11.25 43.02/11.25 [a{#,(f4)}](x0) = x0, 43.02/11.25 43.02/11.25 [b(f4)](x0) = x0 + 1, 43.02/11.25 43.02/11.25 [b(b)](x0) = x0, 43.02/11.25 43.02/11.25 [f4(b)](x0) = x0, 43.02/11.25 43.02/11.25 [b{#,(f4)}](x0) = x0 43.02/11.25 orientation: 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 = a{#,(f4)}(f4(f4)(x1)) 43.02/11.25 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a{#,(f4)}(f4(b)(x1)) 43.02/11.25 43.02/11.25 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1)) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(f4)(x1))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.02/11.25 43.02/11.25 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.09/11.30 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.09/11.30 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.09/11.30 43.09/11.30 f4(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 = f4(a)(a(f4)(x1)) 43.09/11.30 43.09/11.30 f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f4(a)(a(b)(x1)) 43.09/11.30 43.09/11.30 f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f4(a)(a(a)(x1)) 43.09/11.30 43.09/11.30 b(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 = b(a)(a(f4)(x1)) 43.09/11.30 43.09/11.30 b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1)) 43.09/11.30 43.09/11.30 b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1)) 43.09/11.30 43.09/11.30 a(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 = a(a)(a(f4)(x1)) 43.09/11.30 43.09/11.30 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1)) 43.09/11.30 43.09/11.30 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) 43.09/11.30 43.09/11.30 a(a)(a(f4)(x1)) = x1 >= x1 = a(b)(b(a)(a(f4)(x1))) 43.09/11.30 43.09/11.30 a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) 43.09/11.30 43.09/11.30 a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) 43.09/11.30 43.09/11.30 f4(a)(a(a)(a(a)(a(f4)(x1)))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 43.09/11.30 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 43.09/11.30 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 43.09/11.30 b(a)(a(a)(a(a)(a(f4)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 43.09/11.30 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 43.09/11.30 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 43.09/11.30 a(a)(a(a)(a(a)(a(f4)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 43.09/11.30 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 43.09/11.30 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 problem: 43.09/11.30 DPs: 43.09/11.30 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.09/11.30 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.09/11.30 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 43.09/11.30 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.09/11.30 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.09/11.30 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.09/11.30 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.09/11.30 TRS: 43.09/11.30 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.09/11.30 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.09/11.30 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.09/11.30 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.09/11.30 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.09/11.30 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.09/11.30 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.09/11.30 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.09/11.30 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.09/11.30 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.09/11.30 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.09/11.30 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.09/11.30 Polynomial Interpretation Processor: 43.09/11.30 dimension: 1 43.09/11.30 usable rules: 43.09/11.30 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.09/11.30 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.09/11.30 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.09/11.30 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.09/11.30 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.09/11.30 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.09/11.30 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.19/11.36 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.19/11.36 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.19/11.36 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 interpretation: 43.19/11.36 [a(a)](x0) = 1, 43.19/11.36 43.19/11.36 [a(b)](x0) = 1, 43.19/11.36 43.19/11.36 [a(f4)](x0) = 0, 43.19/11.36 43.19/11.36 [f4(a)](x0) = x0, 43.19/11.36 43.19/11.36 [b(a)](x0) = x0, 43.19/11.36 43.19/11.36 [a{#,(f4)}](x0) = 1, 43.19/11.36 43.19/11.36 [b(b)](x0) = 1, 43.19/11.36 43.19/11.36 [f4(b)](x0) = x0, 43.19/11.36 43.19/11.36 [b{#,(f4)}](x0) = x0 43.19/11.36 orientation: 43.19/11.36 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a{#,(f4)}(f4(b)(x1)) 43.19/11.36 43.19/11.36 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a{#,(f4)}(f4(a)(x1)) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(f4)(x1))) = 1 >= 0 = b{#,(f4)}(f4(a)(a(f4)(x1))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(b)(x1))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(b)(x1))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(x1))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(a)(x1))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(f4)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(b)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.19/11.36 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.19/11.36 43.19/11.36 f4(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = f4(a)(a(b)(x1)) 43.19/11.36 43.19/11.36 f4(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = f4(a)(a(a)(x1)) 43.19/11.36 43.19/11.36 b(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = b(a)(a(b)(x1)) 43.19/11.36 43.19/11.36 b(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = b(a)(a(a)(x1)) 43.19/11.36 43.19/11.36 a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(b)(x1)) 43.19/11.36 43.19/11.36 a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(a)(x1)) 43.19/11.36 43.19/11.36 a(a)(a(f4)(x1)) = 1 >= 1 = a(b)(b(a)(a(f4)(x1))) 43.19/11.36 43.19/11.36 a(a)(a(b)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(x1))) 43.19/11.36 43.19/11.36 a(a)(a(a)(x1)) = 1 >= 1 = a(b)(b(a)(a(a)(x1))) 43.19/11.36 43.19/11.36 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 43.19/11.36 f4(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = f4(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 43.19/11.36 f4(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = f4(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 43.19/11.36 b(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 43.19/11.36 b(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 43.19/11.36 b(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 43.19/11.36 a(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.36 43.19/11.36 a(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.36 43.19/11.36 a(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.36 problem: 43.19/11.36 DPs: 43.19/11.36 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 43.19/11.36 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 43.19/11.36 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.19/11.36 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.19/11.36 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.19/11.36 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.19/11.39 TRS: 43.19/11.39 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.19/11.39 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.19/11.39 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.19/11.39 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.19/11.39 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.19/11.39 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.19/11.39 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.19/11.39 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.19/11.39 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.19/11.39 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 Polynomial Interpretation Processor: 43.19/11.39 dimension: 1 43.19/11.39 usable rules: 43.19/11.39 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.19/11.39 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.19/11.39 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.19/11.39 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.19/11.39 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.19/11.39 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.19/11.39 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.19/11.39 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.19/11.39 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.19/11.39 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.19/11.39 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.19/11.39 interpretation: 43.19/11.39 [a(a)](x0) = x0 + 1, 43.19/11.39 43.19/11.39 [a(b)](x0) = x0, 43.19/11.39 43.19/11.39 [a(f4)](x0) = 0, 43.19/11.39 43.19/11.39 [f4(a)](x0) = x0, 43.19/11.39 43.19/11.39 [b(a)](x0) = x0, 43.19/11.39 43.19/11.39 [a{#,(f4)}](x0) = x0, 43.19/11.39 43.19/11.39 [b(b)](x0) = x0 + 1, 43.19/11.39 43.19/11.39 [f4(b)](x0) = x0, 43.19/11.39 43.19/11.39 [b{#,(f4)}](x0) = x0 43.19/11.39 orientation: 43.19/11.39 b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) = x1 + 2 >= x1 = a{#,(f4)}(f4(b)(x1)) 43.19/11.39 43.19/11.39 b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(x1)) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(a)(x1))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.19/11.39 43.19/11.39 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.19/11.39 43.19/11.39 f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 = f4(a)(a(b)(x1)) 43.19/11.39 43.19/11.39 f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 1 = f4(a)(a(a)(x1)) 43.19/11.39 43.19/11.39 b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 = b(a)(a(b)(x1)) 43.19/11.39 43.19/11.39 b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1)) 43.19/11.39 43.19/11.39 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(b)(x1)) 43.19/11.39 43.19/11.39 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) 43.23/11.43 43.23/11.43 a(a)(a(f4)(x1)) = 1 >= 0 = a(b)(b(a)(a(f4)(x1))) 43.23/11.43 43.23/11.43 a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(b)(x1))) 43.23/11.43 43.23/11.43 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(a(a)(x1))) 43.23/11.43 43.23/11.43 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 1 = f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 43.23/11.43 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 1 = f4(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 43.23/11.43 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = f4(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 43.23/11.43 b(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 2 = b(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 43.23/11.43 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 43.23/11.43 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 43.23/11.43 a(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 1 = a(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 43.23/11.43 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = a(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 43.23/11.43 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 problem: 43.23/11.43 DPs: 43.23/11.43 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 43.23/11.43 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 43.23/11.43 TRS: 43.23/11.43 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.23/11.43 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.23/11.43 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.23/11.43 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.23/11.43 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.23/11.43 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.23/11.43 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.23/11.43 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.23/11.43 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.23/11.43 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 SCC Processor: 43.23/11.43 #sccs: 1 43.23/11.43 #rules: 3 43.23/11.43 #arcs: 72/64 43.23/11.43 DPs: 43.23/11.43 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.23/11.43 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.23/11.43 TRS: 43.23/11.43 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.23/11.43 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.23/11.43 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.23/11.43 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.23/11.43 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.23/11.43 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.23/11.43 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.23/11.43 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.23/11.43 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.23/11.43 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.23/11.43 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.23/11.43 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.23/11.43 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 Polynomial Interpretation Processor: 43.26/11.47 dimension: 1 43.26/11.47 usable rules: 43.26/11.47 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.26/11.47 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.26/11.47 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.26/11.47 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.26/11.47 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.26/11.47 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.26/11.47 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.26/11.47 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 interpretation: 43.26/11.47 [a(a)](x0) = 0, 43.26/11.47 43.26/11.47 [a(b)](x0) = 0, 43.26/11.47 43.26/11.47 [a(f4)](x0) = 1, 43.26/11.47 43.26/11.47 [f4(a)](x0) = x0, 43.26/11.47 43.26/11.47 [b(a)](x0) = 0, 43.26/11.47 43.26/11.47 [a{#,(f4)}](x0) = x0, 43.26/11.47 43.26/11.47 [b(b)](x0) = 0, 43.26/11.47 43.26/11.47 [f4(b)](x0) = 0 43.26/11.47 orientation: 43.26/11.47 a{#,(f4)}(f4(a)(a(a)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.26/11.47 43.26/11.47 a{#,(f4)}(f4(a)(a(f4)(x1))) = 1 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 43.26/11.47 43.26/11.47 a{#,(f4)}(f4(a)(a(b)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.26/11.47 43.26/11.47 f4(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = f4(a)(a(b)(x1)) 43.26/11.47 43.26/11.47 f4(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = f4(a)(a(a)(x1)) 43.26/11.47 43.26/11.47 b(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = b(a)(a(b)(x1)) 43.26/11.47 43.26/11.47 b(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = b(a)(a(a)(x1)) 43.26/11.47 43.26/11.47 a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(b)(x1)) 43.26/11.47 43.26/11.47 a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(a)(x1)) 43.26/11.47 43.26/11.47 a(a)(a(f4)(x1)) = 0 >= 0 = a(b)(b(a)(a(f4)(x1))) 43.26/11.47 43.26/11.47 a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(x1))) 43.26/11.47 43.26/11.47 a(a)(a(a)(x1)) = 0 >= 0 = a(b)(b(a)(a(a)(x1))) 43.26/11.47 43.26/11.47 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 43.26/11.47 f4(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 43.26/11.47 f4(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 43.26/11.47 b(a)(a(a)(a(a)(a(f4)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 43.26/11.47 b(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 43.26/11.47 b(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 43.26/11.47 a(a)(a(a)(a(a)(a(f4)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 43.26/11.47 a(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 43.26/11.47 a(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 problem: 43.26/11.47 DPs: 43.26/11.47 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.26/11.47 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.26/11.47 TRS: 43.26/11.47 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.26/11.47 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.26/11.47 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.26/11.47 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.26/11.47 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.26/11.47 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.26/11.47 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.26/11.47 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.26/11.47 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.26/11.47 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.47 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.47 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.47 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 Polynomial Interpretation Processor: 43.26/11.52 dimension: 1 43.26/11.52 usable rules: 43.26/11.52 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.26/11.52 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.26/11.52 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.26/11.52 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.26/11.52 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.26/11.52 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.26/11.52 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.26/11.52 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.26/11.52 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.26/11.52 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 interpretation: 43.26/11.52 [a(a)](x0) = x0 + 1, 43.26/11.52 43.26/11.52 [a(b)](x0) = x0, 43.26/11.52 43.26/11.52 [a(f4)](x0) = 1, 43.26/11.52 43.26/11.52 [f4(a)](x0) = x0 + 1, 43.26/11.52 43.26/11.52 [b(a)](x0) = x0, 43.26/11.52 43.26/11.52 [a{#,(f4)}](x0) = x0, 43.26/11.52 43.26/11.52 [b(b)](x0) = x0 + 1, 43.26/11.52 43.26/11.52 [f4(b)](x0) = x0 43.26/11.52 orientation: 43.26/11.52 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 43.26/11.52 43.26/11.52 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 43.26/11.52 43.26/11.52 f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = f4(a)(a(b)(x1)) 43.26/11.52 43.26/11.52 f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = f4(a)(a(a)(x1)) 43.26/11.52 43.26/11.52 b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 = b(a)(a(b)(x1)) 43.26/11.52 43.26/11.52 b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1)) 43.26/11.52 43.26/11.52 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(b)(x1)) 43.26/11.52 43.26/11.52 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) 43.26/11.52 43.26/11.52 a(a)(a(f4)(x1)) = 2 >= 1 = a(b)(b(a)(a(f4)(x1))) 43.26/11.52 43.26/11.52 a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(b)(x1))) 43.26/11.52 43.26/11.52 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(a(a)(x1))) 43.26/11.52 43.26/11.52 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 4 >= 2 = f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 43.26/11.52 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 43.26/11.52 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 43.26/11.52 b(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 3 = b(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 43.26/11.52 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 43.26/11.52 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 43.26/11.52 a(a)(a(a)(a(a)(a(f4)(x1)))) = 4 >= 2 = a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 43.26/11.52 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 43.26/11.52 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 problem: 43.26/11.52 DPs: 43.26/11.52 43.26/11.52 TRS: 43.26/11.52 f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 43.26/11.52 f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 43.26/11.52 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 43.26/11.52 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 43.26/11.52 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 43.26/11.52 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 43.26/11.52 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 43.26/11.52 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 43.26/11.52 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 43.26/11.52 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(a)(a(a)(a(f4)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) 43.26/11.52 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) 43.26/11.52 Qed 43.26/11.52 EOF