42.93/11.23 YES 43.18/11.41 43.18/11.41 Problem: 43.18/11.41 a(b(b(a(x1)))) -> b(a(b(a(x1)))) 43.18/11.41 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 43.18/11.41 a(a(a(a(x1)))) -> b(b(b(a(x1)))) 43.18/11.41 43.18/11.41 Proof: 43.18/11.41 DP Processor: 43.18/11.41 DPs: 43.18/11.41 a#(b(b(a(x1)))) -> a#(b(a(x1))) 43.18/11.41 a#(b(b(b(x1)))) -> a#(x1) 43.18/11.41 a#(b(b(b(x1)))) -> a#(b(a(x1))) 43.18/11.41 a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) 43.18/11.41 TRS: 43.18/11.41 a(b(b(a(x1)))) -> b(a(b(a(x1)))) 43.18/11.41 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 43.18/11.41 a(a(a(a(x1)))) -> b(b(b(a(x1)))) 43.18/11.41 Polynomial Interpretation Processor: 43.18/11.41 dimension: 1 43.18/11.41 usable rules: 43.18/11.41 a(b(b(a(x1)))) -> b(a(b(a(x1)))) 43.18/11.41 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 43.18/11.41 a(a(a(a(x1)))) -> b(b(b(a(x1)))) 43.18/11.41 interpretation: 43.18/11.41 [a#](x0) = x0, 43.18/11.41 43.18/11.41 [b](x0) = x0 + 1, 43.18/11.41 43.18/11.41 [a](x0) = x0 + 1 43.18/11.41 orientation: 43.18/11.41 a#(b(b(a(x1)))) = x1 + 3 >= x1 + 2 = a#(b(a(x1))) 43.18/11.41 43.18/11.41 a#(b(b(b(x1)))) = x1 + 3 >= x1 = a#(x1) 43.18/11.41 43.18/11.41 a#(b(b(b(x1)))) = x1 + 3 >= x1 + 2 = a#(b(a(x1))) 43.18/11.41 43.18/11.41 a#(b(b(b(x1)))) = x1 + 3 >= x1 + 3 = a#(a(b(a(x1)))) 43.18/11.41 43.18/11.41 a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(b(a(x1)))) 43.18/11.41 43.18/11.41 a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(b(a(x1)))) 43.18/11.41 43.18/11.41 a(a(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) 43.18/11.41 problem: 43.18/11.41 DPs: 43.18/11.41 a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) 43.18/11.41 TRS: 43.18/11.41 a(b(b(a(x1)))) -> b(a(b(a(x1)))) 43.18/11.41 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 43.18/11.41 a(a(a(a(x1)))) -> b(b(b(a(x1)))) 43.18/11.41 Root-Labeling Processor: 43.18/11.41 DPs: 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 TRS: 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 a(b)(b(b)(b(b)(b(f3)(x1)))) -> a(a)(a(b)(b(a)(a(f3)(x1)))) 43.18/11.41 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 43.18/11.41 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 43.18/11.41 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.18/11.41 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.18/11.41 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.18/11.41 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.18/11.41 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.18/11.41 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.18/11.41 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.18/11.41 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.18/11.41 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.18/11.41 Polynomial Interpretation Processor: 43.18/11.41 dimension: 1 43.18/11.41 interpretation: 43.18/11.41 [a(a)](x0) = x0, 43.18/11.41 43.18/11.41 [a(f3)](x0) = x0, 43.18/11.41 43.18/11.41 [b(a)](x0) = x0, 43.18/11.41 43.18/11.41 [a(b)](x0) = x0, 43.18/11.41 43.18/11.41 [f3(a)](x0) = x0, 43.18/11.41 43.18/11.41 [b(f3)](x0) = x0 + 1, 43.18/11.41 43.18/11.41 [b(b)](x0) = x0, 43.18/11.41 43.18/11.41 [f3(b)](x0) = x0, 43.18/11.41 43.18/11.41 [a{#,(f3)}](x0) = x0 43.18/11.41 orientation: 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) = x1 + 1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) = x1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 43.18/11.41 a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.18/11.41 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.18/11.41 43.18/11.41 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.18/11.41 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 43.63/11.80 a(b)(b(b)(b(b)(b(f3)(x1)))) = x1 + 1 >= x1 = a(a)(a(b)(b(a)(a(f3)(x1)))) 43.63/11.80 43.63/11.80 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(a)(x1)))) 43.63/11.80 43.63/11.80 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(x1)))) 43.63/11.80 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 problem: 43.63/11.80 DPs: 43.63/11.80 a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 TRS: 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 43.63/11.80 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 43.63/11.80 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 43.63/11.80 Polynomial Interpretation Processor: 43.63/11.80 dimension: 1 43.63/11.80 usable rules: 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 43.63/11.80 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.11/12.30 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 interpretation: 44.11/12.30 [a(a)](x0) = x0 + 1, 44.11/12.30 44.11/12.30 [a(f3)](x0) = 0, 44.11/12.30 44.11/12.30 [b(a)](x0) = x0, 44.11/12.30 44.11/12.30 [a(b)](x0) = x0, 44.11/12.30 44.11/12.30 [f3(a)](x0) = x0, 44.11/12.30 44.11/12.30 [b(b)](x0) = x0 + 1, 44.11/12.30 44.11/12.30 [f3(b)](x0) = x0, 44.11/12.30 44.11/12.30 [a{#,(f3)}](x0) = x0 44.11/12.30 orientation: 44.11/12.30 a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) = x1 + 2 >= x1 + 1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) = x1 + 3 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 1 >= 0 = f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 2 >= x1 + 1 = f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 2 >= 0 = a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 3 >= x1 + 1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 2 >= x1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 1 >= 1 = b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 + 1 = b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(a)(a(a)(x1)))) 44.11/12.30 44.11/12.30 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(x1)))) 44.11/12.30 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 3 >= 2 = f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 4 >= x1 + 3 = f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 3 >= x1 + 2 = f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 4 >= 2 = a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 5 >= x1 + 3 = a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 4 >= x1 + 2 = a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 3 >= 3 = b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 4 >= x1 + 4 = b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 problem: 44.11/12.30 DPs: 44.11/12.30 44.11/12.30 TRS: 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) 44.11/12.30 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) 44.11/12.30 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) 44.11/12.30 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) 44.11/12.30 b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) 44.11/12.30 Qed 44.11/12.30 EOF