45.94/11.99 YES 45.94/12.00 45.94/12.00 Problem: 45.94/12.00 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 45.94/12.00 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 45.94/12.00 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 45.94/12.00 45.94/12.00 Proof: 45.94/12.00 DP Processor: 45.94/12.00 DPs: 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 TRS: 45.94/12.00 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 45.94/12.00 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 45.94/12.00 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 45.94/12.00 TDG Processor: 45.94/12.00 DPs: 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 TRS: 45.94/12.00 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 45.94/12.00 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 45.94/12.00 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 45.94/12.00 graph: 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(x1) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> 45.94/12.00 a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(x1) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> 45.94/12.00 b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(a(x1)) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(b(x1)) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) 45.94/12.00 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1)) 46.15/12.11 a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(x1) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> 46.15/12.11 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> 46.15/12.11 a#(b(b(b(x1)))) -> a#(a(b(x1))) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(x1)) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> 46.15/12.11 a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(b(x1)) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(x1) 46.15/12.11 SCC Processor: 46.15/12.11 #sccs: 2 46.15/12.11 #rules: 8 46.15/12.11 #arcs: 50/100 46.15/12.11 DPs: 46.15/12.11 a#(b(b(b(x1)))) -> a#(b(x1)) 46.15/12.11 a#(b(b(a(x1)))) -> a#(b(x1)) 46.15/12.11 a#(b(b(a(x1)))) -> a#(a(b(x1))) 46.15/12.11 a#(b(b(b(x1)))) -> a#(a(b(x1))) 46.15/12.11 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 46.15/12.11 TRS: 46.15/12.11 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.15/12.11 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.15/12.11 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.15/12.11 Polynomial Interpretation Processor: 46.15/12.11 dimension: 1 46.15/12.11 usable rules: 46.15/12.11 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.15/12.11 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.15/12.11 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.15/12.11 interpretation: 46.15/12.11 [a#](x0) = x0, 46.15/12.11 46.15/12.11 [b](x0) = x0 + 1, 46.15/12.11 46.15/12.11 [a](x0) = x0 + 1 46.15/12.11 orientation: 46.15/12.11 a#(b(b(b(x1)))) = x1 + 3 >= x1 + 1 = a#(b(x1)) 46.15/12.11 46.15/12.11 a#(b(b(a(x1)))) = x1 + 3 >= x1 + 1 = a#(b(x1)) 46.15/12.11 46.15/12.11 a#(b(b(a(x1)))) = x1 + 3 >= x1 + 2 = a#(a(b(x1))) 46.15/12.11 46.15/12.11 a#(b(b(b(x1)))) = x1 + 3 >= x1 + 2 = a#(a(b(x1))) 46.15/12.11 46.15/12.11 a#(b(b(b(x1)))) = x1 + 3 >= x1 + 3 = a#(a(a(b(x1)))) 46.15/12.11 46.15/12.11 a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(a(b(x1)))) 46.15/12.11 46.15/12.11 a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(a(b(x1)))) 46.15/12.11 46.15/12.11 b(b(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) 46.15/12.11 problem: 46.15/12.11 DPs: 46.15/12.11 a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 46.15/12.11 TRS: 46.15/12.11 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.15/12.11 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.15/12.11 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.15/12.11 Root-Labeling Processor: 46.15/12.11 DPs: 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.15/12.11 TRS: 46.15/12.11 f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.15/12.11 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.15/12.11 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.15/12.11 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.15/12.11 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.15/12.11 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.15/12.11 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.15/12.11 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.15/12.11 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.15/12.11 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) 46.15/12.11 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.15/12.11 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.15/12.11 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.15/12.11 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.15/12.11 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.15/12.11 Polynomial Interpretation Processor: 46.15/12.11 dimension: 1 46.15/12.11 interpretation: 46.15/12.11 [a(f4)](x0) = x0 + 1, 46.15/12.11 46.15/12.11 [b(a)](x0) = x0, 46.15/12.11 46.15/12.11 [a(b)](x0) = x0, 46.15/12.11 46.15/12.11 [a(a)](x0) = x0, 46.15/12.11 46.15/12.11 [f4(a)](x0) = x0, 46.15/12.11 46.15/12.11 [b(f4)](x0) = x0, 46.15/12.11 46.15/12.11 [b(b)](x0) = x0, 46.15/12.11 46.15/12.11 [f4(b)](x0) = x0, 46.15/12.11 46.15/12.11 [a{#,(f4)}](x0) = x0 46.15/12.11 orientation: 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) 46.15/12.11 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.15/12.11 46.15/12.11 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.59/12.49 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.59/12.49 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) 46.59/12.49 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 a(b)(b(b)(b(b)(b(f4)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(f4)(x1)))) 46.59/12.49 46.59/12.49 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(a)(x1)))) 46.59/12.49 46.59/12.49 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(b)(x1)))) 46.59/12.49 46.59/12.49 b(b)(b(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(a)(a(f4)(x1)))) 46.59/12.49 46.59/12.49 b(b)(b(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(a)(x1)))) 46.59/12.49 46.59/12.49 b(b)(b(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(b)(x1)))) 46.59/12.49 problem: 46.59/12.49 DPs: 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 TRS: 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) 46.59/12.49 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.59/12.49 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.59/12.49 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.59/12.49 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.59/12.49 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.59/12.49 Polynomial Interpretation Processor: 46.59/12.49 dimension: 1 46.59/12.49 usable rules: 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.59/12.49 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.59/12.49 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.59/12.49 interpretation: 46.59/12.49 [a(f4)](x0) = 0, 46.59/12.49 46.59/12.49 [b(a)](x0) = 0, 46.59/12.49 46.59/12.49 [a(b)](x0) = 0, 46.59/12.49 46.59/12.49 [a(a)](x0) = 0, 46.59/12.49 46.59/12.49 [f4(a)](x0) = 0, 46.59/12.49 46.59/12.49 [b(f4)](x0) = 1, 46.59/12.49 46.59/12.49 [b(b)](x0) = x0, 46.59/12.49 46.59/12.49 [f4(b)](x0) = x0, 46.59/12.49 46.59/12.49 [a{#,(f4)}](x0) = x0 46.59/12.49 orientation: 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) 46.59/12.49 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = 0 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 46.59/12.49 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.59/12.49 46.59/12.49 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.59/12.49 46.59/12.49 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 46.87/12.79 a(b)(b(b)(b(b)(b(f4)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(f4)(x1)))) 46.87/12.79 46.87/12.79 a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.79 46.87/12.79 a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.79 46.87/12.79 b(b)(b(a)(a(a)(a(f4)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f4)(x1)))) 46.87/12.79 46.87/12.79 b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.79 46.87/12.79 b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) 46.87/12.79 problem: 46.87/12.79 DPs: 46.87/12.79 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 TRS: 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) 46.87/12.79 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.79 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.87/12.79 Polynomial Interpretation Processor: 46.87/12.79 dimension: 1 46.87/12.79 usable rules: 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) 46.87/12.79 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.79 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.79 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.87/12.79 interpretation: 46.87/12.79 [a(f4)](x0) = 0, 46.87/12.79 46.87/12.79 [b(a)](x0) = x0, 46.87/12.79 46.87/12.79 [a(b)](x0) = x0, 46.87/12.79 46.87/12.79 [a(a)](x0) = 0, 46.87/12.79 46.87/12.79 [f4(a)](x0) = 0, 46.87/12.79 46.87/12.79 [b(f4)](x0) = 0, 46.87/12.79 46.87/12.79 [b(b)](x0) = 1, 46.87/12.79 46.87/12.79 [f4(b)](x0) = x0, 46.87/12.79 46.87/12.79 [a{#,(f4)}](x0) = x0 46.87/12.79 orientation: 46.87/12.79 a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.79 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.79 46.87/12.79 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 46.87/12.83 a(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(f4)(x1)))) 46.87/12.83 46.87/12.83 a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.83 46.87/12.83 a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.83 46.87/12.83 b(b)(b(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(f4)(x1)))) 46.87/12.83 46.87/12.83 b(b)(b(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.83 46.87/12.83 b(b)(b(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(b)(x1)))) 46.87/12.83 problem: 46.87/12.83 DPs: 46.87/12.83 46.87/12.83 TRS: 46.87/12.83 f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) 46.87/12.83 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.83 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 46.87/12.83 Qed 46.87/12.83 46.87/12.83 DPs: 46.87/12.83 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 46.87/12.83 b#(b(a(a(x1)))) -> b#(a(x1)) 46.87/12.83 b#(b(a(a(x1)))) -> b#(b(a(x1))) 46.87/12.83 TRS: 46.87/12.83 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.87/12.83 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.87/12.83 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.87/12.83 Polynomial Interpretation Processor: 46.87/12.83 dimension: 1 46.87/12.83 usable rules: 46.87/12.83 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.87/12.83 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.87/12.83 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.87/12.83 interpretation: 46.87/12.83 [b#](x0) = x0, 46.87/12.83 46.87/12.83 [b](x0) = x0 + 1, 46.87/12.83 46.87/12.83 [a](x0) = x0 + 1 46.87/12.83 orientation: 46.87/12.83 b#(b(a(a(x1)))) = x1 + 3 >= x1 + 3 = b#(b(b(a(x1)))) 46.87/12.83 46.87/12.83 b#(b(a(a(x1)))) = x1 + 3 >= x1 + 1 = b#(a(x1)) 46.87/12.83 46.87/12.83 b#(b(a(a(x1)))) = x1 + 3 >= x1 + 2 = b#(b(a(x1))) 46.87/12.83 46.87/12.83 a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(a(b(x1)))) 46.87/12.83 46.87/12.83 a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(a(b(x1)))) 46.87/12.83 46.87/12.83 b(b(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) 46.87/12.83 problem: 46.87/12.83 DPs: 46.87/12.83 b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) 46.87/12.83 TRS: 46.87/12.83 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 46.87/12.83 a(b(b(b(x1)))) -> a(a(a(b(x1)))) 46.87/12.83 b(b(a(a(x1)))) -> b(b(b(a(x1)))) 46.87/12.83 Root-Labeling Processor: 46.87/12.83 DPs: 46.87/12.83 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 46.87/12.83 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 46.87/12.83 b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) 46.87/12.83 TRS: 46.87/12.83 f14(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 46.87/12.83 f14(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 f14(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 46.87/12.83 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 46.87/12.83 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 46.87/12.83 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 46.87/12.83 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 46.87/12.83 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 46.87/12.83 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 46.87/12.83 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.14/13.08 Usable Rule Processor: 47.14/13.08 DPs: 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) 47.14/13.08 TRS: 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 47.14/13.08 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 47.14/13.08 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.14/13.08 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.14/13.08 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.14/13.08 Polynomial Interpretation Processor: 47.14/13.08 dimension: 1 47.14/13.08 interpretation: 47.14/13.08 [b(f14)](x0) = x0, 47.14/13.08 47.14/13.08 [a(f14)](x0) = x0 + 1, 47.14/13.08 47.14/13.08 [f14(b)](x0) = x0, 47.14/13.08 47.14/13.08 [b{#,(f14)}](x0) = x0, 47.14/13.08 47.14/13.08 [b(a)](x0) = x0, 47.14/13.08 47.14/13.08 [a(b)](x0) = x0, 47.14/13.08 47.14/13.08 [a(a)](x0) = x0, 47.14/13.08 47.14/13.08 [b(b)](x0) = x0 47.14/13.08 orientation: 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = x1 + 1 >= x1 + 1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.14/13.08 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 >= x1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.14/13.08 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) = x1 >= x1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) 47.14/13.08 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) = x1 + 1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 47.14/13.08 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 47.14/13.08 a(b)(b(b)(b(b)(b(f14)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(f14)(x1)))) 47.14/13.08 47.14/13.08 a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(a)(x1)))) 47.14/13.08 47.14/13.08 a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(b)(x1)))) 47.14/13.08 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) = x1 + 1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) 47.14/13.08 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 47.14/13.08 b(b)(b(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(b)(x1)))) 47.14/13.08 47.14/13.08 b(b)(b(a)(a(a)(a(f14)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(a)(a(f14)(x1)))) 47.14/13.08 47.14/13.08 b(b)(b(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(a)(x1)))) 47.14/13.08 problem: 47.14/13.08 DPs: 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.14/13.08 b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) 47.14/13.08 TRS: 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 47.14/13.08 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 47.14/13.08 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.14/13.08 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.14/13.08 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.14/13.08 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.14/13.08 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.48/13.38 Polynomial Interpretation Processor: 47.48/13.38 dimension: 1 47.48/13.38 usable rules: 47.48/13.38 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.48/13.38 interpretation: 47.48/13.38 [b(f14)](x0) = 0, 47.48/13.38 47.48/13.38 [a(f14)](x0) = 0, 47.48/13.38 47.48/13.38 [f14(b)](x0) = x0, 47.48/13.38 47.48/13.38 [b{#,(f14)}](x0) = x0 + 1, 47.48/13.38 47.48/13.38 [b(a)](x0) = x0 + 1, 47.48/13.38 47.48/13.38 [a(b)](x0) = x0 + 1, 47.48/13.38 47.48/13.38 [a(a)](x0) = x0, 47.48/13.38 47.48/13.38 [b(b)](x0) = 1 47.48/13.38 orientation: 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = 2 >= 2 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.48/13.38 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 + 2 >= 2 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.48/13.38 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) = x1 + 3 >= 2 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) 47.48/13.38 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 2 >= x1 + 4 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.48/13.38 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 2 >= 4 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.48/13.38 47.48/13.38 a(b)(b(b)(b(b)(b(f14)(x1)))) = 2 >= 1 = a(a)(a(a)(a(b)(b(f14)(x1)))) 47.48/13.38 47.48/13.38 a(b)(b(b)(b(b)(b(a)(x1)))) = 2 >= x1 + 2 = a(a)(a(a)(a(b)(b(a)(x1)))) 47.48/13.38 47.48/13.38 a(b)(b(b)(b(b)(b(b)(x1)))) = 2 >= 2 = a(a)(a(a)(a(b)(b(b)(x1)))) 47.48/13.38 47.48/13.38 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 3 >= 1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.48/13.38 47.48/13.38 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 3 >= 1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.48/13.38 47.48/13.38 b(b)(b(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(b)(x1)))) 47.48/13.38 47.48/13.38 b(b)(b(a)(a(a)(a(f14)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(f14)(x1)))) 47.48/13.38 47.48/13.38 b(b)(b(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(a)(x1)))) 47.48/13.38 problem: 47.48/13.38 DPs: 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.48/13.38 TRS: 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.48/13.38 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 47.48/13.38 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 47.48/13.38 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 47.48/13.38 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.48/13.38 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.48/13.38 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.48/13.38 Polynomial Interpretation Processor: 47.48/13.38 dimension: 1 47.48/13.38 usable rules: 47.48/13.38 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.48/13.38 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.48/13.38 interpretation: 47.48/13.38 [b(f14)](x0) = 0, 47.48/13.38 47.48/13.38 [a(f14)](x0) = 1, 47.48/13.38 47.48/13.38 [f14(b)](x0) = x0, 47.48/13.38 47.48/13.38 [b{#,(f14)}](x0) = x0, 47.48/13.38 47.48/13.38 [b(a)](x0) = x0, 47.48/13.38 47.48/13.38 [a(b)](x0) = 0, 47.48/13.38 47.48/13.38 [a(a)](x0) = x0, 47.48/13.38 47.48/13.38 [b(b)](x0) = 0 47.48/13.38 orientation: 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = 1 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) 47.48/13.38 47.48/13.38 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.48/13.38 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.48/13.38 47.48/13.38 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.48/13.38 47.48/13.38 a(b)(b(b)(b(b)(b(f14)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(f14)(x1)))) 47.64/13.58 47.64/13.58 a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(a)(x1)))) 47.64/13.58 47.64/13.58 a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(a)(a(b)(b(b)(x1)))) 47.64/13.58 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(f14)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f14)(x1)))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) 47.64/13.58 problem: 47.64/13.58 DPs: 47.64/13.58 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.64/13.58 TRS: 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 47.64/13.58 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 47.64/13.58 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.64/13.58 Polynomial Interpretation Processor: 47.64/13.58 dimension: 1 47.64/13.58 usable rules: 47.64/13.58 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.64/13.58 interpretation: 47.64/13.58 [b(f14)](x0) = 0, 47.64/13.58 47.64/13.58 [a(f14)](x0) = 0, 47.64/13.58 47.64/13.58 [f14(b)](x0) = x0 + 1, 47.64/13.58 47.64/13.58 [b{#,(f14)}](x0) = x0, 47.64/13.58 47.64/13.58 [b(a)](x0) = x0 + 1, 47.64/13.58 47.64/13.58 [a(b)](x0) = 0, 47.64/13.58 47.64/13.58 [a(a)](x0) = x0 + 1, 47.64/13.58 47.64/13.58 [b(b)](x0) = 0 47.64/13.58 orientation: 47.64/13.58 b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 + 4 >= 1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) 47.64/13.58 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 47.64/13.58 a(b)(b(b)(b(b)(b(f14)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(f14)(x1)))) 47.64/13.58 47.64/13.58 a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(a)(x1)))) 47.64/13.58 47.64/13.58 a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(b)(x1)))) 47.64/13.58 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(f14)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f14)(x1)))) 47.64/13.58 47.64/13.58 b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) 47.64/13.58 problem: 47.64/13.58 DPs: 47.64/13.58 47.64/13.58 TRS: 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) 47.64/13.58 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 47.64/13.58 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) 47.64/13.58 b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) 47.64/13.58 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) 47.64/13.58 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) 47.64/13.58 Qed 47.64/13.59 EOF