41.36/10.83 YES 41.36/10.84 41.36/10.84 Problem: 41.36/10.84 a(a(x1)) -> a(b(a(x1))) 41.36/10.84 b(b(x1)) -> a(a(x1)) 41.36/10.84 a(b(b(a(x1)))) -> x1 41.36/10.84 41.36/10.84 Proof: 41.36/10.84 DP Processor: 41.36/10.84 DPs: 41.36/10.84 a#(a(x1)) -> b#(a(x1)) 41.36/10.84 a#(a(x1)) -> a#(b(a(x1))) 41.36/10.84 b#(b(x1)) -> a#(x1) 41.36/10.84 b#(b(x1)) -> a#(a(x1)) 41.36/10.84 TRS: 41.36/10.84 a(a(x1)) -> a(b(a(x1))) 41.36/10.84 b(b(x1)) -> a(a(x1)) 41.36/10.84 a(b(b(a(x1)))) -> x1 41.36/10.84 TDG Processor: 41.36/10.84 DPs: 41.36/10.84 a#(a(x1)) -> b#(a(x1)) 41.36/10.84 a#(a(x1)) -> a#(b(a(x1))) 41.36/10.84 b#(b(x1)) -> a#(x1) 41.36/10.84 b#(b(x1)) -> a#(a(x1)) 41.36/10.84 TRS: 41.36/10.84 a(a(x1)) -> a(b(a(x1))) 41.36/10.84 b(b(x1)) -> a(a(x1)) 41.36/10.84 a(b(b(a(x1)))) -> x1 41.36/10.84 graph: 41.36/10.84 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 41.36/10.84 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1)) 41.36/10.84 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 41.36/10.84 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 41.36/10.84 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(a(x1)) 41.36/10.84 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1) 41.36/10.84 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 41.36/10.84 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 41.36/10.84 Root-Labeling Processor: 41.36/10.84 DPs: 41.36/10.84 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.36/10.84 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.36/10.84 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.36/10.84 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.36/10.84 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.36/10.84 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.36/10.84 TRS: 41.36/10.84 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.36/10.84 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.36/10.84 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.36/10.84 f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1))) 41.36/10.84 f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1))) 41.36/10.84 f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1))) 41.36/10.84 a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1))) 41.36/10.84 a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1))) 41.36/10.84 a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1))) 41.36/10.84 b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1))) 41.36/10.84 b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1))) 41.36/10.84 b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1))) 41.36/10.84 f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(f4)(x1) 41.36/10.84 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1) 41.36/10.84 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1) 41.36/10.84 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1) 41.36/10.84 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1) 41.36/10.84 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1) 41.36/10.84 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1) 41.36/10.84 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1) 41.36/10.84 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.36/10.84 TDG Processor: 41.36/10.84 DPs: 41.36/10.84 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.36/10.84 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.36/10.84 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.36/10.84 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.36/10.84 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.36/10.84 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.36/10.84 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.36/10.84 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.36/10.84 TRS: 41.36/10.84 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.36/10.84 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.36/10.84 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.36/10.84 f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1))) 41.36/10.84 f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1))) 41.36/10.84 f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1))) 41.36/10.84 a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1))) 41.36/10.84 a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1))) 41.36/10.84 a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1))) 41.36/10.84 b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1))) 41.63/10.85 b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1))) 41.63/10.85 b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1))) 41.63/10.85 f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(f4)(x1) 41.63/10.85 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1) 41.63/10.85 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1) 41.63/10.85 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1) 41.63/10.85 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1) 41.63/10.85 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1) 41.63/10.85 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1) 41.63/10.85 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1) 41.63/10.85 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.63/10.85 graph: 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.85 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.85 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.85 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) -> 41.63/10.86 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.63/10.86 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.63/10.86 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) -> 41.66/10.88 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) -> 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.66/10.88 Polynomial Interpretation Processor: 41.66/10.88 dimension: 1 41.66/10.88 interpretation: 41.66/10.88 [b(b)](x0) = x0, 41.66/10.88 41.66/10.88 [f4(f4)](x0) = x0, 41.66/10.88 41.66/10.88 [b(f4)](x0) = x0 + 1, 41.66/10.88 41.66/10.88 [b(a)](x0) = x0, 41.66/10.88 41.66/10.88 [f4(b)](x0) = x0, 41.66/10.88 41.66/10.88 [a(b)](x0) = x0, 41.66/10.88 41.66/10.88 [a(a)](x0) = x0, 41.66/10.88 41.66/10.88 [b{#,(f4)}](x0) = x0 + 1, 41.66/10.88 41.66/10.88 [a(f4)](x0) = x0 + 1, 41.66/10.88 41.66/10.88 [f4(a)](x0) = x0, 41.66/10.88 41.66/10.88 [a{#,(f4)}](x0) = x0 + 1 41.66/10.88 orientation: 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(a)(a(f4)(x1))) 41.66/10.88 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(a)(x1))) 41.66/10.88 41.66/10.88 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(x1))) 41.66/10.88 41.66/10.88 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.66/10.88 41.66/10.88 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.66/10.88 41.66/10.88 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(f4)(x1)) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(x1)) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(x1)) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(a)(a(f4)(x1))) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(a(a)(x1))) 41.66/10.88 41.66/10.88 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(a(b)(x1))) 41.66/10.88 41.66/10.88 a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1))) 41.66/10.88 41.66/10.88 a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) 41.66/10.88 41.66/10.88 a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) 41.66/10.88 41.66/10.88 f4(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = f4(a)(a(a)(a(f4)(x1))) 41.66/10.88 41.66/10.88 f4(b)(b(b)(b(a)(x1))) = x1 >= x1 = f4(a)(a(a)(a(a)(x1))) 41.66/10.88 41.66/10.88 f4(b)(b(b)(b(b)(x1))) = x1 >= x1 = f4(a)(a(a)(a(b)(x1))) 41.66/10.88 41.66/10.88 a(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(a)(a(f4)(x1))) 41.66/10.88 41.66/10.88 a(b)(b(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(a)(a(a)(x1))) 41.66/10.88 41.66/10.88 a(b)(b(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(a)(a(b)(x1))) 41.73/11.01 41.73/11.01 b(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = b(a)(a(a)(a(f4)(x1))) 41.73/11.01 41.73/11.01 b(b)(b(b)(b(a)(x1))) = x1 >= x1 = b(a)(a(a)(a(a)(x1))) 41.73/11.01 41.73/11.01 b(b)(b(b)(b(b)(x1))) = x1 >= x1 = b(a)(a(a)(a(b)(x1))) 41.73/11.01 41.73/11.01 f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = f4(f4)(x1) 41.73/11.01 41.73/11.01 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f4(a)(x1) 41.73/11.01 41.73/11.01 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f4(b)(x1) 41.73/11.01 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 + 1 = a(f4)(x1) 41.73/11.01 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(a)(x1) 41.73/11.01 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(x1) 41.73/11.01 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 + 1 = b(f4)(x1) 41.73/11.01 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(a)(x1) 41.73/11.01 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(x1) 41.73/11.01 problem: 41.73/11.01 DPs: 41.73/11.01 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.73/11.01 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.73/11.01 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.73/11.01 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.73/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.73/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) 41.73/11.01 b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) 41.73/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.73/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) 41.73/11.01 TRS: 41.73/11.01 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.73/11.01 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.73/11.01 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.73/11.01 f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1))) 41.73/11.01 f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1))) 41.73/11.01 f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1))) 41.73/11.01 a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1))) 41.73/11.01 a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1))) 41.73/11.01 a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1))) 41.73/11.01 b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1))) 41.73/11.01 b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1))) 41.73/11.01 b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1))) 41.73/11.01 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1) 41.73/11.01 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1) 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1) 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1) 41.73/11.01 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1) 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1) 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1) 41.73/11.01 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.73/11.01 Polynomial Interpretation Processor: 41.73/11.01 dimension: 1 41.73/11.01 interpretation: 41.73/11.01 [b(b)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [b(f4)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [b(a)](x0) = x0, 41.73/11.01 41.73/11.01 [f4(b)](x0) = x0, 41.73/11.01 41.73/11.01 [a(b)](x0) = x0, 41.73/11.01 41.73/11.01 [a(a)](x0) = x0, 41.73/11.01 41.73/11.01 [b{#,(f4)}](x0) = x0, 41.73/11.01 41.73/11.01 [a(f4)](x0) = x0, 41.73/11.01 41.73/11.01 [f4(a)](x0) = x0, 41.73/11.01 41.73/11.01 [a{#,(f4)}](x0) = x0 41.73/11.01 orientation: 41.73/11.01 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(f4)(x1))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.73/11.01 41.73/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1)) 41.73/11.01 41.73/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(x1)) 41.73/11.01 41.73/11.01 b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(a(f4)(x1))) 41.73/11.01 41.73/11.01 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(x1))) 41.73/11.01 41.73/11.01 b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(f4)(x1)) = x1 >= x1 = a(b)(b(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 f4(b)(b(b)(b(f4)(x1))) = x1 + 2 >= x1 = f4(a)(a(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 f4(b)(b(b)(b(a)(x1))) = x1 + 1 >= x1 = f4(a)(a(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 f4(b)(b(b)(b(b)(x1))) = x1 + 2 >= x1 = f4(a)(a(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 a(b)(b(b)(b(f4)(x1))) = x1 + 2 >= x1 = a(a)(a(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 a(b)(b(b)(b(a)(x1))) = x1 + 1 >= x1 = a(a)(a(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 a(b)(b(b)(b(b)(x1))) = x1 + 2 >= x1 = a(a)(a(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 b(b)(b(b)(b(f4)(x1))) = x1 + 3 >= x1 = b(a)(a(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 b(b)(b(b)(b(a)(x1))) = x1 + 2 >= x1 = b(a)(a(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 b(b)(b(b)(b(b)(x1))) = x1 + 3 >= x1 = b(a)(a(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = f4(a)(x1) 41.93/11.16 41.93/11.16 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 = f4(b)(x1) 41.93/11.16 41.93/11.16 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = a(f4)(x1) 41.93/11.16 41.93/11.16 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = a(a)(x1) 41.93/11.16 41.93/11.16 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 = a(b)(x1) 41.93/11.16 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 + 1 = b(f4)(x1) 41.93/11.16 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = b(a)(x1) 41.93/11.16 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 + 1 = b(b)(x1) 41.93/11.16 problem: 41.93/11.16 DPs: 41.93/11.16 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.93/11.16 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.93/11.16 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.93/11.16 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.93/11.16 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.93/11.16 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.93/11.16 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.93/11.16 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.93/11.16 TRS: 41.93/11.16 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.93/11.16 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.93/11.16 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1) 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.93/11.16 Polynomial Interpretation Processor: 41.93/11.16 dimension: 1 41.93/11.16 interpretation: 41.93/11.16 [b(b)](x0) = x0 + 1, 41.93/11.16 41.93/11.16 [b(f4)](x0) = x0, 41.93/11.16 41.93/11.16 [b(a)](x0) = x0, 41.93/11.16 41.93/11.16 [f4(b)](x0) = x0, 41.93/11.16 41.93/11.16 [a(b)](x0) = x0, 41.93/11.16 41.93/11.16 [a(a)](x0) = x0, 41.93/11.16 41.93/11.16 [b{#,(f4)}](x0) = x0, 41.93/11.16 41.93/11.16 [a(f4)](x0) = x0, 41.93/11.16 41.93/11.16 [f4(a)](x0) = x0, 41.93/11.16 41.93/11.16 [a{#,(f4)}](x0) = x0 41.93/11.16 orientation: 41.93/11.16 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.93/11.16 41.93/11.16 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.93/11.16 41.93/11.16 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.93/11.16 41.93/11.16 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1)) 41.93/11.16 41.93/11.16 b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(f4)(x1)) = x1 >= x1 = a(b)(b(a)(a(f4)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) 41.93/11.16 41.93/11.16 a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) 41.93/11.16 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = b(f4)(x1) 41.93/11.16 41.93/11.16 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 + 1 = b(b)(x1) 41.93/11.16 problem: 41.93/11.16 DPs: 41.93/11.16 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.93/11.16 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.95/11.19 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) 41.95/11.19 b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) 41.95/11.19 TRS: 41.95/11.19 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.95/11.19 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.95/11.19 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.95/11.19 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.95/11.19 Polynomial Interpretation Processor: 41.95/11.19 dimension: 1 41.95/11.19 usable rules: 41.95/11.19 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.95/11.19 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.95/11.19 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.95/11.19 interpretation: 41.95/11.19 [b(b)](x0) = 0, 41.95/11.19 41.95/11.19 [b(a)](x0) = 0, 41.95/11.19 41.95/11.19 [f4(b)](x0) = 1, 41.95/11.19 41.95/11.19 [a(b)](x0) = 0, 41.95/11.19 41.95/11.19 [a(a)](x0) = 0, 41.95/11.19 41.95/11.19 [b{#,(f4)}](x0) = x0, 41.95/11.19 41.95/11.19 [a(f4)](x0) = 0, 41.95/11.19 41.95/11.19 [f4(a)](x0) = 0, 41.95/11.19 41.95/11.19 [a{#,(f4)}](x0) = 0 41.95/11.19 orientation: 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(f4)(x1))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(a)(x1))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(b)(x1))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.95/11.19 41.95/11.19 b{#,(f4)}(f4(b)(b(a)(x1))) = 1 >= 0 = a{#,(f4)}(f4(a)(x1)) 41.95/11.19 41.95/11.19 b{#,(f4)}(f4(b)(b(a)(x1))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(x1))) 41.95/11.19 41.95/11.19 a(a)(a(f4)(x1)) = 0 >= 0 = a(b)(b(a)(a(f4)(x1))) 41.95/11.19 41.95/11.19 a(a)(a(a)(x1)) = 0 >= 0 = a(b)(b(a)(a(a)(x1))) 41.95/11.19 41.95/11.19 a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(x1))) 41.95/11.19 41.95/11.19 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(x1) 41.95/11.19 problem: 41.95/11.19 DPs: 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.95/11.19 TRS: 41.95/11.19 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.95/11.19 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.95/11.19 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.95/11.19 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.95/11.19 SCC Processor: 41.95/11.19 #sccs: 1 41.95/11.19 #rules: 3 41.95/11.19 #arcs: 72/36 41.95/11.19 DPs: 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 41.95/11.19 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 41.95/11.19 TRS: 41.95/11.19 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 41.95/11.19 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 41.95/11.19 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 41.95/11.19 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1) 41.95/11.19 Polynomial Interpretation Processor: 41.95/11.19 dimension: 1 41.95/11.19 interpretation: 41.95/11.19 [b(b)](x0) = x0, 41.95/11.19 41.95/11.19 [b(a)](x0) = x0, 41.95/11.19 41.95/11.19 [f4(b)](x0) = x0, 41.95/11.19 41.95/11.19 [a(b)](x0) = x0 + 1, 41.95/11.19 41.95/11.19 [a(a)](x0) = x0 + 1, 41.95/11.19 41.95/11.19 [a(f4)](x0) = x0, 41.95/11.19 41.95/11.19 [f4(a)](x0) = x0, 41.95/11.19 41.95/11.19 [a{#,(f4)}](x0) = x0 41.95/11.19 orientation: 41.95/11.19 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 41.95/11.19 41.95/11.19 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 42.00/11.22 42.00/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 42.00/11.22 42.00/11.22 a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1))) 42.00/11.22 42.00/11.22 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(a)(x1))) 42.00/11.22 42.00/11.22 a(a)(a(b)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(b)(x1))) 42.00/11.22 42.00/11.22 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 2 >= x1 = b(b)(x1) 42.00/11.22 problem: 42.00/11.22 DPs: 42.00/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 42.00/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 42.00/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 42.00/11.22 TRS: 42.00/11.22 a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1))) 42.00/11.22 a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) 42.00/11.22 a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) 42.00/11.22 Polynomial Interpretation Processor: 42.00/11.22 dimension: 1 42.00/11.22 interpretation: 42.00/11.22 [b(a)](x0) = x0, 42.00/11.22 42.00/11.22 [f4(b)](x0) = x0, 42.00/11.22 42.00/11.22 [a(b)](x0) = x0, 42.00/11.22 42.00/11.22 [a(a)](x0) = x0 + 1, 42.00/11.22 42.00/11.22 [a(f4)](x0) = x0, 42.00/11.22 42.00/11.22 [f4(a)](x0) = x0, 42.00/11.22 42.00/11.22 [a{#,(f4)}](x0) = x0 42.00/11.22 orientation: 42.00/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 42.00/11.22 42.00/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 42.00/11.22 42.00/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 42.00/11.22 42.00/11.22 a(a)(a(f4)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(f4)(x1))) 42.00/11.22 42.00/11.22 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(a(a)(x1))) 42.00/11.22 42.00/11.22 a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(b)(x1))) 42.00/11.22 problem: 42.00/11.22 DPs: 42.00/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 42.00/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 42.00/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 42.00/11.22 TRS: 42.00/11.22 42.00/11.22 Polynomial Interpretation Processor: 42.00/11.22 dimension: 1 42.00/11.22 interpretation: 42.00/11.22 [b(a)](x0) = x0, 42.00/11.22 42.00/11.22 [f4(b)](x0) = x0, 42.00/11.22 42.00/11.22 [a(b)](x0) = x0, 42.00/11.22 42.00/11.22 [a(a)](x0) = x0 + 1, 42.00/11.22 42.00/11.22 [a(f4)](x0) = x0 + 1, 42.00/11.22 42.00/11.22 [f4(a)](x0) = x0 + 1, 42.00/11.22 42.00/11.22 [a{#,(f4)}](x0) = x0 42.00/11.22 orientation: 42.00/11.22 a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) 42.00/11.22 42.00/11.22 a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) 42.00/11.22 42.00/11.22 a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) 42.00/11.22 problem: 42.00/11.22 DPs: 42.00/11.22 42.00/11.22 TRS: 42.00/11.22 42.00/11.22 Qed 42.00/11.23 EOF