43.51/11.38 YES 43.79/11.60 43.79/11.60 Problem: 43.79/11.60 a(a(a(b(x1)))) -> a(b(b(b(x1)))) 43.79/11.60 a(a(b(b(x1)))) -> a(b(b(a(x1)))) 43.79/11.60 a(b(a(b(x1)))) -> a(a(b(a(x1)))) 43.79/11.60 43.79/11.60 Proof: 43.79/11.60 DP Processor: 43.79/11.60 DPs: 43.79/11.60 a#(a(a(b(x1)))) -> a#(b(b(b(x1)))) 43.79/11.60 a#(a(b(b(x1)))) -> a#(x1) 43.79/11.60 a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) 43.79/11.60 a#(b(a(b(x1)))) -> a#(x1) 43.79/11.60 a#(b(a(b(x1)))) -> a#(b(a(x1))) 43.79/11.60 a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) 43.79/11.60 TRS: 43.79/11.60 a(a(a(b(x1)))) -> a(b(b(b(x1)))) 43.79/11.60 a(a(b(b(x1)))) -> a(b(b(a(x1)))) 43.79/11.60 a(b(a(b(x1)))) -> a(a(b(a(x1)))) 43.79/11.60 Polynomial Interpretation Processor: 43.79/11.60 dimension: 1 43.79/11.60 usable rules: 43.79/11.60 a(a(a(b(x1)))) -> a(b(b(b(x1)))) 43.79/11.60 a(a(b(b(x1)))) -> a(b(b(a(x1)))) 43.79/11.60 a(b(a(b(x1)))) -> a(a(b(a(x1)))) 43.79/11.60 interpretation: 43.79/11.60 [a#](x0) = x0, 43.79/11.60 43.79/11.60 [a](x0) = x0 + 1, 43.79/11.60 43.79/11.60 [b](x0) = x0 + 1 43.79/11.60 orientation: 43.79/11.60 a#(a(a(b(x1)))) = x1 + 3 >= x1 + 3 = a#(b(b(b(x1)))) 43.79/11.60 43.79/11.60 a#(a(b(b(x1)))) = x1 + 3 >= x1 = a#(x1) 43.79/11.60 43.79/11.60 a#(a(b(b(x1)))) = x1 + 3 >= x1 + 3 = a#(b(b(a(x1)))) 43.79/11.60 43.79/11.60 a#(b(a(b(x1)))) = x1 + 3 >= x1 = a#(x1) 43.79/11.60 43.79/11.60 a#(b(a(b(x1)))) = x1 + 3 >= x1 + 2 = a#(b(a(x1))) 43.79/11.60 43.79/11.60 a#(b(a(b(x1)))) = x1 + 3 >= x1 + 3 = a#(a(b(a(x1)))) 43.79/11.60 43.79/11.60 a(a(a(b(x1)))) = x1 + 4 >= x1 + 4 = a(b(b(b(x1)))) 43.79/11.60 43.79/11.60 a(a(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(b(b(a(x1)))) 43.79/11.60 43.79/11.60 a(b(a(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(b(a(x1)))) 43.79/11.60 problem: 43.79/11.60 DPs: 43.79/11.60 a#(a(a(b(x1)))) -> a#(b(b(b(x1)))) 43.79/11.60 a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) 43.79/11.60 a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) 43.79/11.60 TRS: 43.79/11.60 a(a(a(b(x1)))) -> a(b(b(b(x1)))) 43.79/11.60 a(a(b(b(x1)))) -> a(b(b(a(x1)))) 43.79/11.60 a(b(a(b(x1)))) -> a(a(b(a(x1)))) 43.79/11.60 Root-Labeling Processor: 43.79/11.60 DPs: 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(f3)(x1))))) 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 43.79/11.60 a{#,(f3)}(f3(b)(b(a)(a(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) 43.79/11.60 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 43.79/11.60 a{#,(f3)}(f3(b)(b(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 43.79/11.60 TRS: 43.79/11.60 a(a)(a(a)(a(b)(b(f3)(x1)))) -> a(b)(b(b)(b(b)(b(f3)(x1)))) 43.79/11.60 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 43.79/11.60 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 43.79/11.60 a(a)(a(b)(b(b)(b(f3)(x1)))) -> a(b)(b(b)(b(a)(a(f3)(x1)))) 43.79/11.60 a(a)(a(b)(b(b)(b(a)(x1)))) -> a(b)(b(b)(b(a)(a(a)(x1)))) 43.79/11.60 a(a)(a(b)(b(b)(b(b)(x1)))) -> a(b)(b(b)(b(a)(a(b)(x1)))) 43.79/11.60 a(b)(b(a)(a(b)(b(f3)(x1)))) -> a(a)(a(b)(b(a)(a(f3)(x1)))) 43.79/11.60 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 43.79/11.60 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 43.79/11.60 Polynomial Interpretation Processor: 43.79/11.60 dimension: 1 43.79/11.60 interpretation: 43.79/11.60 [a(f3)](x0) = x0, 43.79/11.60 43.79/11.60 [b(a)](x0) = x0, 43.79/11.60 43.79/11.60 [b(b)](x0) = x0, 43.79/11.60 43.79/11.60 [f3(b)](x0) = x0 + 1, 43.79/11.60 43.79/11.60 [b(f3)](x0) = x0 + 1, 43.79/11.60 43.79/11.60 [a(b)](x0) = x0, 43.79/11.60 43.79/11.60 [a(a)](x0) = x0, 43.79/11.60 43.79/11.60 [f3(a)](x0) = x0 + 1, 43.79/11.60 43.79/11.60 [a{#,(f3)}](x0) = x0 43.79/11.60 orientation: 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) = x1 + 2 >= x1 + 2 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(f3)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(f3)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 43.79/11.60 43.79/11.60 a{#,(f3)}(f3(b)(b(a)(a(b)(b(f3)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) 43.79/11.60 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(b)(x1))))) = x1 + 1 >= x1 + 1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(f3)(x1)))) = x1 + 1 >= x1 + 1 = a(b)(b(b)(b(b)(b(f3)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(a)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(b)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(b(b)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(b)(b(b)(b(f3)(x1)))) = x1 + 1 >= x1 = a(b)(b(b)(b(a)(a(f3)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(b)(b(b)(b(a)(a(a)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(b)(b(b)(b(a)(a(b)(x1)))) 44.05/11.87 44.05/11.87 a(b)(b(a)(a(b)(b(f3)(x1)))) = x1 + 1 >= x1 = a(a)(a(b)(b(a)(a(f3)(x1)))) 44.05/11.87 44.05/11.87 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(a)(x1)))) 44.05/11.87 44.05/11.87 a(b)(b(a)(a(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(x1)))) 44.05/11.87 problem: 44.05/11.87 DPs: 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 44.05/11.87 TRS: 44.05/11.87 a(a)(a(a)(a(b)(b(f3)(x1)))) -> a(b)(b(b)(b(b)(b(f3)(x1)))) 44.05/11.87 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 44.05/11.87 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 44.05/11.87 a(a)(a(b)(b(b)(b(a)(x1)))) -> a(b)(b(b)(b(a)(a(a)(x1)))) 44.05/11.87 a(a)(a(b)(b(b)(b(b)(x1)))) -> a(b)(b(b)(b(a)(a(b)(x1)))) 44.05/11.87 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.05/11.87 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.05/11.87 Polynomial Interpretation Processor: 44.05/11.87 dimension: 1 44.05/11.87 usable rules: 44.05/11.87 44.05/11.87 interpretation: 44.05/11.87 [b(a)](x0) = x0, 44.05/11.87 44.05/11.87 [b(b)](x0) = 1, 44.05/11.87 44.05/11.87 [f3(b)](x0) = x0, 44.05/11.87 44.05/11.87 [b(f3)](x0) = 0, 44.05/11.87 44.05/11.87 [a(b)](x0) = x0 + 1, 44.05/11.87 44.05/11.87 [a(a)](x0) = 1, 44.05/11.87 44.05/11.87 [f3(a)](x0) = 1, 44.05/11.87 44.05/11.87 [a{#,(f3)}](x0) = x0 + 1 44.05/11.87 orientation: 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) = 2 >= 2 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) = 2 >= 2 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) = 2 >= 2 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) = 2 >= 2 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) = 2 >= 2 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) = x1 + 2 >= 2 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.05/11.87 44.05/11.87 a{#,(f3)}(f3(b)(b(a)(a(b)(b(b)(x1))))) = 3 >= 2 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(f3)(x1)))) = 1 >= 2 = a(b)(b(b)(b(b)(b(f3)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(a)(x1)))) = 1 >= 2 = a(b)(b(b)(b(b)(b(a)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(a)(a(b)(b(b)(x1)))) = 1 >= 2 = a(b)(b(b)(b(b)(b(b)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(b)(b(b)(b(a)(x1)))) = 1 >= 2 = a(b)(b(b)(b(a)(a(a)(x1)))) 44.05/11.87 44.05/11.87 a(a)(a(b)(b(b)(b(b)(x1)))) = 1 >= 2 = a(b)(b(b)(b(a)(a(b)(x1)))) 44.05/11.87 44.05/11.87 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 + 2 >= 1 = a(a)(a(b)(b(a)(a(a)(x1)))) 44.05/11.87 44.05/11.87 a(b)(b(a)(a(b)(b(b)(x1)))) = 3 >= 1 = a(a)(a(b)(b(a)(a(b)(x1)))) 44.05/11.87 problem: 44.05/11.87 DPs: 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.05/11.87 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.35/12.14 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.35/12.14 TRS: 44.35/12.14 a(a)(a(a)(a(b)(b(f3)(x1)))) -> a(b)(b(b)(b(b)(b(f3)(x1)))) 44.35/12.14 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 44.35/12.14 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 44.35/12.14 a(a)(a(b)(b(b)(b(a)(x1)))) -> a(b)(b(b)(b(a)(a(a)(x1)))) 44.35/12.14 a(a)(a(b)(b(b)(b(b)(x1)))) -> a(b)(b(b)(b(a)(a(b)(x1)))) 44.35/12.14 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.35/12.14 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.35/12.14 Polynomial Interpretation Processor: 44.35/12.14 dimension: 1 44.35/12.14 usable rules: 44.35/12.14 44.35/12.14 interpretation: 44.35/12.14 [b(a)](x0) = 1, 44.35/12.14 44.35/12.14 [b(b)](x0) = 0, 44.35/12.14 44.35/12.14 [f3(b)](x0) = x0, 44.35/12.14 44.35/12.14 [b(f3)](x0) = 0, 44.35/12.14 44.35/12.14 [a(b)](x0) = 0, 44.35/12.14 44.35/12.14 [a(a)](x0) = 0, 44.35/12.14 44.35/12.14 [f3(a)](x0) = 0, 44.35/12.14 44.35/12.14 [a{#,(f3)}](x0) = x0 44.35/12.14 orientation: 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) = 0 >= 0 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) = 0 >= 0 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) = 0 >= 0 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) = 0 >= 0 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) = 0 >= 0 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(b)(b(a)(a(b)(b(a)(x1))))) = 1 >= 0 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.35/12.14 44.35/12.14 a(a)(a(a)(a(b)(b(f3)(x1)))) = 0 >= 0 = a(b)(b(b)(b(b)(b(f3)(x1)))) 44.35/12.14 44.35/12.14 a(a)(a(a)(a(b)(b(a)(x1)))) = 0 >= 0 = a(b)(b(b)(b(b)(b(a)(x1)))) 44.35/12.14 44.35/12.14 a(a)(a(a)(a(b)(b(b)(x1)))) = 0 >= 0 = a(b)(b(b)(b(b)(b(b)(x1)))) 44.35/12.14 44.35/12.14 a(a)(a(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(b)(b(b)(b(a)(a(a)(x1)))) 44.35/12.14 44.35/12.14 a(a)(a(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(b)(b(b)(b(a)(a(b)(x1)))) 44.35/12.14 44.35/12.14 a(b)(b(a)(a(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(b)(b(a)(a(a)(x1)))) 44.35/12.14 44.35/12.14 a(b)(b(a)(a(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(b)(b(a)(a(b)(x1)))) 44.35/12.14 problem: 44.35/12.14 DPs: 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.35/12.14 TRS: 44.35/12.14 a(a)(a(a)(a(b)(b(f3)(x1)))) -> a(b)(b(b)(b(b)(b(f3)(x1)))) 44.35/12.14 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 44.35/12.14 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 44.35/12.14 a(a)(a(b)(b(b)(b(a)(x1)))) -> a(b)(b(b)(b(a)(a(a)(x1)))) 44.35/12.14 a(a)(a(b)(b(b)(b(b)(x1)))) -> a(b)(b(b)(b(a)(a(b)(x1)))) 44.35/12.14 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.35/12.14 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.35/12.14 Polynomial Interpretation Processor: 44.35/12.14 dimension: 1 44.35/12.14 interpretation: 44.35/12.14 [b(a)](x0) = x0, 44.35/12.14 44.35/12.14 [b(b)](x0) = x0, 44.35/12.14 44.35/12.14 [f3(b)](x0) = x0, 44.35/12.14 44.35/12.14 [b(f3)](x0) = x0, 44.35/12.14 44.35/12.14 [a(b)](x0) = x0, 44.35/12.14 44.35/12.14 [a(a)](x0) = x0, 44.35/12.14 44.35/12.14 [f3(a)](x0) = x0 + 1, 44.35/12.14 44.35/12.14 [a{#,(f3)}](x0) = x0 + 1 44.35/12.14 orientation: 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(f3)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(a)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(a)(a(b)(b(b)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) 44.35/12.14 44.35/12.14 a{#,(f3)}(f3(a)(a(b)(b(b)(b(a)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(a)(x1))))) 44.39/12.18 44.39/12.18 a{#,(f3)}(f3(a)(a(b)(b(b)(b(b)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(b)(b(b)(b(a)(a(b)(x1))))) 44.39/12.18 44.39/12.18 a(a)(a(a)(a(b)(b(f3)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(b(f3)(x1)))) 44.39/12.18 44.39/12.18 a(a)(a(a)(a(b)(b(a)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(x1)))) 44.39/12.18 44.39/12.18 a(a)(a(a)(a(b)(b(b)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(b(b)(x1)))) 44.39/12.18 44.39/12.18 a(a)(a(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(b)(b(b)(b(a)(a(a)(x1)))) 44.39/12.18 44.39/12.18 a(a)(a(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(b)(b(b)(b(a)(a(b)(x1)))) 44.39/12.18 44.39/12.18 a(b)(b(a)(a(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(a)(x1)))) 44.39/12.18 44.39/12.18 a(b)(b(a)(a(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(x1)))) 44.39/12.18 problem: 44.39/12.18 DPs: 44.39/12.18 44.39/12.18 TRS: 44.39/12.18 a(a)(a(a)(a(b)(b(f3)(x1)))) -> a(b)(b(b)(b(b)(b(f3)(x1)))) 44.39/12.18 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 44.39/12.18 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 44.39/12.18 a(a)(a(b)(b(b)(b(a)(x1)))) -> a(b)(b(b)(b(a)(a(a)(x1)))) 44.39/12.18 a(a)(a(b)(b(b)(b(b)(x1)))) -> a(b)(b(b)(b(a)(a(b)(x1)))) 44.39/12.18 a(b)(b(a)(a(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.39/12.18 a(b)(b(a)(a(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.39/12.18 Qed 44.39/12.19 EOF