41.30/10.92 YES 41.30/10.93 41.30/10.93 Problem: 41.30/10.93 b(a(b(x1))) -> a(x1) 41.30/10.93 a(a(a(x1))) -> b(x1) 41.30/10.93 b(b(x1)) -> b(a(b(x1))) 41.30/10.93 41.30/10.93 Proof: 41.30/10.93 DP Processor: 41.30/10.93 DPs: 41.30/10.93 b#(a(b(x1))) -> a#(x1) 41.30/10.93 a#(a(a(x1))) -> b#(x1) 41.30/10.93 b#(b(x1)) -> a#(b(x1)) 41.30/10.93 b#(b(x1)) -> b#(a(b(x1))) 41.30/10.93 TRS: 41.30/10.93 b(a(b(x1))) -> a(x1) 41.30/10.93 a(a(a(x1))) -> b(x1) 41.30/10.93 b(b(x1)) -> b(a(b(x1))) 41.30/10.93 TDG Processor: 41.30/10.93 DPs: 41.30/10.93 b#(a(b(x1))) -> a#(x1) 41.30/10.93 a#(a(a(x1))) -> b#(x1) 41.30/10.93 b#(b(x1)) -> a#(b(x1)) 41.30/10.93 b#(b(x1)) -> b#(a(b(x1))) 41.30/10.93 TRS: 41.30/10.93 b(a(b(x1))) -> a(x1) 41.30/10.93 a(a(a(x1))) -> b(x1) 41.30/10.93 b(b(x1)) -> b(a(b(x1))) 41.30/10.93 graph: 41.30/10.93 a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> b#(a(b(x1))) 41.30/10.93 a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(b(x1)) 41.30/10.93 a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1) 41.30/10.93 b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1) 41.30/10.93 b#(b(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1) 41.30/10.93 b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) 41.30/10.93 b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(x1)) 41.30/10.93 b#(b(x1)) -> b#(a(b(x1))) -> b#(a(b(x1))) -> a#(x1) 41.30/10.93 Root-Labeling Processor: 41.30/10.93 DPs: 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.30/10.93 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.30/10.93 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.30/10.93 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.30/10.93 TRS: 41.30/10.93 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.30/10.93 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.30/10.93 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.30/10.93 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.30/10.93 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.30/10.93 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.30/10.93 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.30/10.93 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.30/10.93 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.30/10.93 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.30/10.93 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.30/10.93 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.30/10.93 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.30/10.93 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.30/10.93 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.30/10.93 TDG Processor: 41.30/10.93 DPs: 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.30/10.93 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.30/10.93 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.30/10.93 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.30/10.93 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.30/10.93 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.30/10.93 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.30/10.93 TRS: 41.30/10.93 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.30/10.93 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.30/10.93 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.30/10.93 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.30/10.93 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.30/10.94 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.30/10.94 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.30/10.94 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.30/10.94 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.30/10.94 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.30/10.94 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.30/10.94 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.30/10.94 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.30/10.94 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.30/10.94 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.30/10.94 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.30/10.94 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.30/10.94 graph: 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.30/10.94 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.30/10.94 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) -> 41.57/10.95 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.95 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.57/10.95 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) 41.57/10.98 Polynomial Interpretation Processor: 41.57/10.98 dimension: 1 41.57/10.98 interpretation: 41.57/10.98 [a(f4)](x0) = x0 + 1, 41.57/10.98 41.57/10.98 [a(a)](x0) = x0, 41.57/10.98 41.57/10.98 [b(a)](x0) = x0, 41.57/10.98 41.57/10.98 [f4(b)](x0) = x0, 41.57/10.98 41.57/10.98 [b(b)](x0) = x0, 41.57/10.98 41.57/10.98 [f4(f4)](x0) = x0, 41.57/10.98 41.57/10.98 [a{#,(f4)}](x0) = x0 + 1, 41.57/10.98 41.57/10.98 [b(f4)](x0) = x0 + 1, 41.57/10.98 41.57/10.98 [a(b)](x0) = x0, 41.57/10.98 41.57/10.98 [f4(a)](x0) = x0, 41.57/10.98 41.57/10.98 [b{#,(f4)}](x0) = x0 + 1 41.57/10.98 orientation: 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(f4)(x1)) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(x1)) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(x1)) 41.57/10.98 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(f4)(x1)) 41.57/10.98 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(b)(x1)) 41.57/10.98 41.57/10.98 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(x1)) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(b)(b(f4)(x1))) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(b)(x1))) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(x1))) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.57/10.98 41.57/10.98 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.57/10.98 41.57/10.98 f4(b)(b(a)(a(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = f4(a)(a(f4)(x1)) 41.57/10.98 41.57/10.98 f4(b)(b(a)(a(b)(b(b)(x1)))) = x1 >= x1 = f4(a)(a(b)(x1)) 41.57/10.98 41.57/10.98 f4(b)(b(a)(a(b)(b(a)(x1)))) = x1 >= x1 = f4(a)(a(a)(x1)) 41.57/10.98 41.57/10.98 b(b)(b(a)(a(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(a)(a(f4)(x1)) 41.57/10.98 41.57/10.98 b(b)(b(a)(a(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1)) 41.57/10.98 41.57/10.98 b(b)(b(a)(a(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1)) 41.63/11.01 41.63/11.01 a(b)(b(a)(a(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = a(a)(a(f4)(x1)) 41.63/11.01 41.63/11.01 a(b)(b(a)(a(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1)) 41.63/11.01 41.63/11.01 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) 41.63/11.01 41.63/11.01 f4(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = f4(b)(b(f4)(x1)) 41.63/11.01 41.63/11.01 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = f4(b)(b(b)(x1)) 41.63/11.01 41.63/11.01 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = f4(b)(b(a)(x1)) 41.63/11.01 41.63/11.01 b(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(f4)(x1)) 41.63/11.01 41.63/11.01 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(x1)) 41.63/11.01 41.63/11.01 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(a)(x1)) 41.63/11.01 41.63/11.01 a(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = a(b)(b(f4)(x1)) 41.63/11.01 41.63/11.01 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(b)(x1)) 41.63/11.01 41.63/11.01 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(a)(x1)) 41.63/11.01 41.63/11.01 b(b)(b(f4)(x1)) = x1 + 1 >= x1 + 1 = b(a)(a(b)(b(f4)(x1))) 41.63/11.01 41.63/11.01 b(b)(b(b)(x1)) = x1 >= x1 = b(a)(a(b)(b(b)(x1))) 41.63/11.01 41.63/11.01 b(b)(b(a)(x1)) = x1 >= x1 = b(a)(a(b)(b(a)(x1))) 41.63/11.01 problem: 41.63/11.01 DPs: 41.63/11.01 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.63/11.01 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.63/11.01 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.63/11.01 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) 41.63/11.01 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.63/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.63/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.63/11.01 b{#,(f4)}(f4(b)(b(f4)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.63/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.63/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) -> b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.63/11.01 TRS: 41.63/11.01 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.63/11.01 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.63/11.01 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.63/11.01 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.63/11.01 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.63/11.01 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.63/11.01 Polynomial Interpretation Processor: 41.63/11.01 dimension: 1 41.63/11.01 usable rules: 41.63/11.01 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.63/11.01 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.63/11.01 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.63/11.01 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.63/11.01 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.63/11.01 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.63/11.01 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.63/11.01 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.63/11.01 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.63/11.01 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.63/11.05 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.63/11.05 interpretation: 41.63/11.05 [a(f4)](x0) = 0, 41.63/11.05 41.63/11.05 [a(a)](x0) = x0 + 1, 41.63/11.05 41.63/11.05 [b(a)](x0) = x0 + 1, 41.63/11.05 41.63/11.05 [f4(b)](x0) = x0 + 1, 41.63/11.05 41.63/11.05 [b(b)](x0) = x0 + 1, 41.63/11.05 41.63/11.05 [a{#,(f4)}](x0) = x0, 41.63/11.05 41.63/11.05 [b(f4)](x0) = 0, 41.63/11.05 41.63/11.05 [a(b)](x0) = x0, 41.63/11.05 41.63/11.05 [f4(a)](x0) = x0, 41.63/11.05 41.63/11.05 [b{#,(f4)}](x0) = x0 41.63/11.05 orientation: 41.63/11.05 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(x1)) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(x1)) 41.63/11.05 41.63/11.05 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(b)(x1)) 41.63/11.05 41.63/11.05 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 = b{#,(f4)}(f4(a)(x1)) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(f4)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(f4)(x1))) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(b)(b(b)(x1))) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(b)(b(a)(x1))) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(f4)(x1))) = 1 >= 0 = b{#,(f4)}(f4(a)(a(b)(b(f4)(x1)))) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) 41.63/11.05 41.63/11.05 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(b(a)(x1)))) 41.63/11.05 41.63/11.05 f4(b)(b(a)(a(b)(b(f4)(x1)))) = 2 >= 0 = f4(a)(a(f4)(x1)) 41.63/11.05 41.63/11.05 f4(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 3 >= x1 = f4(a)(a(b)(x1)) 41.63/11.05 41.63/11.05 f4(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = f4(a)(a(a)(x1)) 41.63/11.05 41.63/11.05 b(b)(b(a)(a(b)(b(f4)(x1)))) = 2 >= 1 = b(a)(a(f4)(x1)) 41.63/11.05 41.63/11.05 b(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(b)(x1)) 41.63/11.05 41.63/11.05 b(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 3 >= x1 + 2 = b(a)(a(a)(x1)) 41.63/11.05 41.63/11.05 a(b)(b(a)(a(b)(b(f4)(x1)))) = 1 >= 1 = a(a)(a(f4)(x1)) 41.63/11.05 41.63/11.05 a(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 2 >= x1 + 1 = a(a)(a(b)(x1)) 41.63/11.05 41.63/11.05 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) 41.63/11.05 41.63/11.05 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 1 = f4(b)(b(f4)(x1)) 41.63/11.05 41.63/11.05 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = f4(b)(b(b)(x1)) 41.63/11.05 41.63/11.05 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = f4(b)(b(a)(x1)) 41.63/11.05 41.63/11.05 b(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 1 = b(b)(b(f4)(x1)) 41.63/11.05 41.63/11.05 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 2 = b(b)(b(b)(x1)) 41.63/11.05 41.63/11.05 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = b(b)(b(a)(x1)) 41.63/11.05 41.63/11.05 a(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 0 = a(b)(b(f4)(x1)) 41.63/11.05 41.63/11.05 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = a(b)(b(b)(x1)) 41.63/11.05 41.63/11.05 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 1 = a(b)(b(a)(x1)) 41.63/11.05 41.63/11.05 b(b)(b(f4)(x1)) = 1 >= 1 = b(a)(a(b)(b(f4)(x1))) 41.63/11.05 41.63/11.05 b(b)(b(b)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(b)(x1))) 41.63/11.05 41.63/11.05 b(b)(b(a)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(a)(x1))) 41.63/11.05 problem: 41.63/11.05 DPs: 41.63/11.05 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) 41.63/11.05 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) 41.63/11.05 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.63/11.05 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.63/11.05 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.63/11.05 TRS: 41.63/11.05 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.63/11.05 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.63/11.05 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.63/11.05 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.63/11.05 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.63/11.05 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.63/11.05 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.63/11.05 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.63/11.05 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.63/11.05 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.63/11.05 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.63/11.05 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.63/11.05 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.63/11.05 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.68/11.09 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.68/11.09 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.68/11.09 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.68/11.09 Polynomial Interpretation Processor: 41.68/11.09 dimension: 1 41.68/11.09 usable rules: 41.68/11.09 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.68/11.09 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.68/11.09 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.68/11.09 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.68/11.09 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.68/11.09 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.68/11.09 interpretation: 41.68/11.09 [a(f4)](x0) = 0, 41.68/11.09 41.68/11.09 [a(a)](x0) = x0 + 1, 41.68/11.09 41.68/11.09 [b(a)](x0) = x0, 41.68/11.09 41.68/11.09 [f4(b)](x0) = x0, 41.68/11.09 41.68/11.09 [b(b)](x0) = x0 + 1, 41.68/11.09 41.68/11.09 [a{#,(f4)}](x0) = x0, 41.68/11.09 41.68/11.09 [b(f4)](x0) = 0, 41.68/11.09 41.68/11.09 [a(b)](x0) = x0 + 1, 41.68/11.09 41.68/11.09 [f4(a)](x0) = x0, 41.68/11.09 41.68/11.09 [b{#,(f4)}](x0) = x0 41.68/11.09 orientation: 41.68/11.09 b{#,(f4)}(f4(a)(a(b)(b(b)(x1)))) = x1 + 2 >= x1 = a{#,(f4)}(f4(b)(x1)) 41.68/11.09 41.68/11.09 a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 = b{#,(f4)}(f4(b)(x1)) 41.68/11.09 41.68/11.09 b{#,(f4)}(f4(b)(b(f4)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(f4)(x1))) 41.68/11.09 41.68/11.09 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(b)(x1))) 41.68/11.09 41.68/11.09 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(x1))) 41.68/11.09 41.68/11.09 f4(b)(b(a)(a(b)(b(f4)(x1)))) = 1 >= 0 = f4(a)(a(f4)(x1)) 41.68/11.09 41.68/11.09 f4(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 2 >= x1 + 1 = f4(a)(a(b)(x1)) 41.68/11.09 41.68/11.09 f4(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = f4(a)(a(a)(x1)) 41.68/11.09 41.68/11.09 b(b)(b(a)(a(b)(b(f4)(x1)))) = 2 >= 0 = b(a)(a(f4)(x1)) 41.68/11.09 41.68/11.09 b(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(b)(x1)) 41.68/11.09 41.68/11.09 b(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 2 >= x1 + 1 = b(a)(a(a)(x1)) 41.68/11.09 41.68/11.09 a(b)(b(a)(a(b)(b(f4)(x1)))) = 2 >= 1 = a(a)(a(f4)(x1)) 41.68/11.09 41.68/11.09 a(b)(b(a)(a(b)(b(b)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(b)(x1)) 41.68/11.09 41.68/11.09 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) 41.68/11.09 41.68/11.09 f4(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 0 = f4(b)(b(f4)(x1)) 41.68/11.09 41.68/11.09 f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = f4(b)(b(b)(x1)) 41.68/11.09 41.68/11.09 f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 = f4(b)(b(a)(x1)) 41.68/11.09 41.68/11.09 b(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 1 = b(b)(b(f4)(x1)) 41.68/11.09 41.68/11.09 b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 2 = b(b)(b(b)(x1)) 41.68/11.09 41.68/11.09 b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 1 = b(b)(b(a)(x1)) 41.68/11.09 41.68/11.09 a(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 1 = a(b)(b(f4)(x1)) 41.68/11.09 41.68/11.09 a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(b)(x1)) 41.68/11.09 41.68/11.09 a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 1 = a(b)(b(a)(x1)) 41.68/11.09 41.68/11.09 b(b)(b(f4)(x1)) = 1 >= 1 = b(a)(a(b)(b(f4)(x1))) 41.68/11.09 41.68/11.09 b(b)(b(b)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(b)(x1))) 41.68/11.09 41.68/11.09 b(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = b(a)(a(b)(b(a)(x1))) 41.68/11.09 problem: 41.68/11.09 DPs: 41.68/11.09 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(b)(b(f4)(x1))) 41.68/11.09 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(b(b)(x1))) 41.68/11.09 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(x1))) 41.68/11.09 TRS: 41.68/11.09 f4(b)(b(a)(a(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.68/11.09 f4(b)(b(a)(a(b)(b(b)(x1)))) -> f4(a)(a(b)(x1)) 41.68/11.09 f4(b)(b(a)(a(b)(b(a)(x1)))) -> f4(a)(a(a)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) 41.68/11.09 b(b)(b(a)(a(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) 41.68/11.09 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(f4)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(x1)) 41.68/11.09 f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(a)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(f4)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(x1)) 41.68/11.09 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(f4)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(x1)) 41.68/11.09 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(x1)) 41.68/11.09 b(b)(b(f4)(x1)) -> b(a)(a(b)(b(f4)(x1))) 41.68/11.09 b(b)(b(b)(x1)) -> b(a)(a(b)(b(b)(x1))) 41.68/11.09 b(b)(b(a)(x1)) -> b(a)(a(b)(b(a)(x1))) 41.68/11.09 SCC Processor: 41.68/11.09 #sccs: 0 41.68/11.09 #rules: 0 41.68/11.09 #arcs: 72/9 41.68/11.09 41.68/11.10 EOF