41.03/10.69 YES 41.03/10.71 41.03/10.71 Problem: 41.03/10.71 b(b(x1)) -> c(c(c(c(x1)))) 41.03/10.71 c(x1) -> x1 41.03/10.71 b(c(b(x1))) -> b(b(b(x1))) 41.03/10.71 41.03/10.71 Proof: 41.03/10.71 DP Processor: 41.03/10.71 DPs: 41.03/10.71 b#(b(x1)) -> c#(x1) 41.03/10.71 b#(b(x1)) -> c#(c(x1)) 41.03/10.71 b#(b(x1)) -> c#(c(c(x1))) 41.03/10.71 b#(b(x1)) -> c#(c(c(c(x1)))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) 41.03/10.71 TRS: 41.03/10.71 b(b(x1)) -> c(c(c(c(x1)))) 41.03/10.71 c(x1) -> x1 41.03/10.71 b(c(b(x1))) -> b(b(b(x1))) 41.03/10.71 TDG Processor: 41.03/10.71 DPs: 41.03/10.71 b#(b(x1)) -> c#(x1) 41.03/10.71 b#(b(x1)) -> c#(c(x1)) 41.03/10.71 b#(b(x1)) -> c#(c(c(x1))) 41.03/10.71 b#(b(x1)) -> c#(c(c(c(x1)))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) 41.03/10.71 TRS: 41.03/10.71 b(b(x1)) -> c(c(c(c(x1)))) 41.03/10.71 c(x1) -> x1 41.03/10.71 b(c(b(x1))) -> b(b(b(x1))) 41.03/10.71 graph: 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(c(b(x1))) -> b#(b(b(x1))) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(c(b(x1))) -> b#(b(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(c(c(x1)))) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(c(x1))) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(c(b(x1))) -> b#(b(b(x1))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(c(b(x1))) -> b#(b(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(c(c(x1)))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(c(x1))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(x1)) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1) 41.03/10.71 SCC Processor: 41.03/10.71 #sccs: 1 41.03/10.71 #rules: 2 41.03/10.71 #arcs: 12/36 41.03/10.71 DPs: 41.03/10.71 b#(c(b(x1))) -> b#(b(b(x1))) 41.03/10.71 b#(c(b(x1))) -> b#(b(x1)) 41.03/10.71 TRS: 41.03/10.71 b(b(x1)) -> c(c(c(c(x1)))) 41.03/10.71 c(x1) -> x1 41.03/10.71 b(c(b(x1))) -> b(b(b(x1))) 41.03/10.71 Root-Labeling Processor: 41.03/10.71 DPs: 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1))) 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1))) 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(c)(x1))) 41.03/10.71 TRS: 41.03/10.71 f4(b)(b(b)(b(f4)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.03/10.71 f4(b)(b(b)(b(b)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.03/10.71 f4(b)(b(b)(b(c)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.03/10.71 b(b)(b(b)(b(f4)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.03/10.71 b(b)(b(b)(b(b)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.03/10.71 b(b)(b(b)(b(c)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.03/10.71 c(b)(b(b)(b(f4)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.03/10.71 c(b)(b(b)(b(b)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.03/10.71 c(b)(b(b)(b(c)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.03/10.71 f4(c)(c(f4)(x1)) -> f4(f4)(x1) 41.03/10.71 f4(c)(c(b)(x1)) -> f4(b)(x1) 41.03/10.71 f4(c)(c(c)(x1)) -> f4(c)(x1) 41.03/10.71 b(c)(c(f4)(x1)) -> b(f4)(x1) 41.03/10.71 b(c)(c(b)(x1)) -> b(b)(x1) 41.03/10.71 b(c)(c(c)(x1)) -> b(c)(x1) 41.03/10.71 c(c)(c(f4)(x1)) -> c(f4)(x1) 41.03/10.71 c(c)(c(b)(x1)) -> c(b)(x1) 41.03/10.71 c(c)(c(c)(x1)) -> c(c)(x1) 41.03/10.71 b(c)(c(b)(b(f4)(x1))) -> b(b)(b(b)(b(f4)(x1))) 41.03/10.71 b(c)(c(b)(b(b)(x1))) -> b(b)(b(b)(b(b)(x1))) 41.03/10.71 b(c)(c(b)(b(c)(x1))) -> b(b)(b(b)(b(c)(x1))) 41.03/10.71 Polynomial Interpretation Processor: 41.03/10.71 dimension: 1 41.03/10.71 interpretation: 41.03/10.71 [f4(f4)](x0) = x0, 41.03/10.71 41.03/10.71 [c(f4)](x0) = x0 + 1, 41.03/10.71 41.03/10.71 [c(c)](x0) = x0, 41.03/10.71 41.03/10.71 [b(c)](x0) = x0, 41.03/10.71 41.03/10.71 [b(b)](x0) = x0, 41.03/10.71 41.03/10.71 [f4(b)](x0) = x0 + 1, 41.03/10.71 41.03/10.71 [b(f4)](x0) = x0 + 1, 41.03/10.71 41.03/10.71 [c(b)](x0) = x0, 41.03/10.71 41.03/10.71 [f4(c)](x0) = x0 + 1, 41.03/10.71 41.03/10.71 [b{#,(f4)}](x0) = x0 + 1 41.03/10.71 orientation: 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 3 >= x1 + 3 = b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.03/10.71 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.03/10.71 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.03/10.71 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 3 >= x1 + 3 = b{#,(f4)}(f4(b)(b(f4)(x1))) 41.03/10.71 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(x1))) 41.03/10.71 41.03/10.71 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(c)(x1))) 41.21/10.86 41.21/10.86 f4(b)(b(b)(b(f4)(x1))) = x1 + 2 >= x1 + 2 = f4(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 41.21/10.86 f4(b)(b(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = f4(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 41.21/10.86 f4(b)(b(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = f4(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 41.21/10.86 b(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 41.21/10.86 b(b)(b(b)(b(b)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 41.21/10.86 b(b)(b(b)(b(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 41.21/10.86 c(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = c(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 41.21/10.86 c(b)(b(b)(b(b)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 41.21/10.86 c(b)(b(b)(b(c)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 41.21/10.86 f4(c)(c(f4)(x1)) = x1 + 2 >= x1 = f4(f4)(x1) 41.21/10.86 41.21/10.86 f4(c)(c(b)(x1)) = x1 + 1 >= x1 + 1 = f4(b)(x1) 41.21/10.86 41.21/10.86 f4(c)(c(c)(x1)) = x1 + 1 >= x1 + 1 = f4(c)(x1) 41.21/10.86 41.21/10.86 b(c)(c(f4)(x1)) = x1 + 1 >= x1 + 1 = b(f4)(x1) 41.21/10.86 41.21/10.86 b(c)(c(b)(x1)) = x1 >= x1 = b(b)(x1) 41.21/10.86 41.21/10.86 b(c)(c(c)(x1)) = x1 >= x1 = b(c)(x1) 41.21/10.86 41.21/10.86 c(c)(c(f4)(x1)) = x1 + 1 >= x1 + 1 = c(f4)(x1) 41.21/10.86 41.21/10.86 c(c)(c(b)(x1)) = x1 >= x1 = c(b)(x1) 41.21/10.86 41.21/10.86 c(c)(c(c)(x1)) = x1 >= x1 = c(c)(x1) 41.21/10.86 41.21/10.86 b(c)(c(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(f4)(x1))) 41.21/10.86 41.21/10.86 b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(b)(b(b)(x1))) 41.21/10.86 41.21/10.86 b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(b)(b(b)(b(c)(x1))) 41.21/10.86 problem: 41.21/10.86 DPs: 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1))) 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1))) 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(c)(x1))) 41.21/10.86 TRS: 41.21/10.86 f4(b)(b(b)(b(f4)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 f4(b)(b(b)(b(b)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 f4(b)(b(b)(b(c)(x1))) -> f4(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 b(b)(b(b)(b(f4)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 b(b)(b(b)(b(b)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 b(b)(b(b)(b(c)(x1))) -> b(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 c(b)(b(b)(b(f4)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.21/10.86 c(b)(b(b)(b(b)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.21/10.86 c(b)(b(b)(b(c)(x1))) -> c(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.21/10.86 f4(c)(c(b)(x1)) -> f4(b)(x1) 41.21/10.86 f4(c)(c(c)(x1)) -> f4(c)(x1) 41.21/10.86 b(c)(c(f4)(x1)) -> b(f4)(x1) 41.21/10.86 b(c)(c(b)(x1)) -> b(b)(x1) 41.21/10.86 b(c)(c(c)(x1)) -> b(c)(x1) 41.21/10.86 c(c)(c(f4)(x1)) -> c(f4)(x1) 41.21/10.86 c(c)(c(b)(x1)) -> c(b)(x1) 41.21/10.86 c(c)(c(c)(x1)) -> c(c)(x1) 41.21/10.86 b(c)(c(b)(b(f4)(x1))) -> b(b)(b(b)(b(f4)(x1))) 41.21/10.86 b(c)(c(b)(b(b)(x1))) -> b(b)(b(b)(b(b)(x1))) 41.21/10.86 b(c)(c(b)(b(c)(x1))) -> b(b)(b(b)(b(c)(x1))) 41.21/10.86 Polynomial Interpretation Processor: 41.21/10.86 dimension: 1 41.21/10.86 interpretation: 41.21/10.86 [c(f4)](x0) = x0, 41.21/10.86 41.21/10.86 [c(c)](x0) = x0, 41.21/10.86 41.21/10.86 [b(c)](x0) = x0 + 1, 41.21/10.86 41.21/10.86 [b(b)](x0) = x0 + 1, 41.21/10.86 41.21/10.86 [f4(b)](x0) = x0, 41.21/10.86 41.21/10.86 [b(f4)](x0) = x0 + 1, 41.21/10.86 41.21/10.86 [c(b)](x0) = x0 + 1, 41.21/10.86 41.21/10.86 [f4(c)](x0) = x0, 41.21/10.86 41.21/10.86 [b{#,(f4)}](x0) = x0 41.21/10.86 orientation: 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.21/10.86 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.21/10.86 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.21/10.86 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(b)(b(f4)(x1))) 41.21/10.86 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(b)(b(b)(x1))) 41.21/10.86 41.21/10.86 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(b)(b(c)(x1))) 41.39/11.00 41.39/11.00 f4(b)(b(b)(b(f4)(x1))) = x1 + 2 >= x1 = f4(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.39/11.00 41.39/11.00 f4(b)(b(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = f4(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.39/11.00 41.39/11.00 f4(b)(b(b)(b(c)(x1))) = x1 + 2 >= x1 = f4(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.39/11.00 41.39/11.00 b(b)(b(b)(b(f4)(x1))) = x1 + 3 >= x1 + 1 = b(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.39/11.00 41.39/11.00 b(b)(b(b)(b(b)(x1))) = x1 + 3 >= x1 + 2 = b(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.39/11.00 41.39/11.00 b(b)(b(b)(b(c)(x1))) = x1 + 3 >= x1 + 1 = b(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.39/11.00 41.39/11.00 c(b)(b(b)(b(f4)(x1))) = x1 + 3 >= x1 = c(c)(c(c)(c(c)(c(c)(c(f4)(x1))))) 41.39/11.00 41.39/11.00 c(b)(b(b)(b(b)(x1))) = x1 + 3 >= x1 + 1 = c(c)(c(c)(c(c)(c(c)(c(b)(x1))))) 41.39/11.00 41.39/11.00 c(b)(b(b)(b(c)(x1))) = x1 + 3 >= x1 = c(c)(c(c)(c(c)(c(c)(c(c)(x1))))) 41.39/11.00 41.39/11.00 f4(c)(c(b)(x1)) = x1 + 1 >= x1 = f4(b)(x1) 41.39/11.00 41.39/11.00 f4(c)(c(c)(x1)) = x1 >= x1 = f4(c)(x1) 41.39/11.00 41.39/11.00 b(c)(c(f4)(x1)) = x1 + 1 >= x1 + 1 = b(f4)(x1) 41.39/11.00 41.39/11.00 b(c)(c(b)(x1)) = x1 + 2 >= x1 + 1 = b(b)(x1) 41.39/11.00 41.39/11.00 b(c)(c(c)(x1)) = x1 + 1 >= x1 + 1 = b(c)(x1) 41.39/11.00 41.39/11.00 c(c)(c(f4)(x1)) = x1 >= x1 = c(f4)(x1) 41.39/11.00 41.39/11.00 c(c)(c(b)(x1)) = x1 + 1 >= x1 + 1 = c(b)(x1) 41.39/11.00 41.39/11.00 c(c)(c(c)(x1)) = x1 >= x1 = c(c)(x1) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(f4)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(f4)(x1))) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(b)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(b)(x1))) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(c)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(c)(x1))) 41.39/11.00 problem: 41.39/11.00 DPs: 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.00 TRS: 41.39/11.00 f4(c)(c(c)(x1)) -> f4(c)(x1) 41.39/11.00 b(c)(c(f4)(x1)) -> b(f4)(x1) 41.39/11.00 b(c)(c(c)(x1)) -> b(c)(x1) 41.39/11.00 c(c)(c(f4)(x1)) -> c(f4)(x1) 41.39/11.00 c(c)(c(b)(x1)) -> c(b)(x1) 41.39/11.00 c(c)(c(c)(x1)) -> c(c)(x1) 41.39/11.00 b(c)(c(b)(b(f4)(x1))) -> b(b)(b(b)(b(f4)(x1))) 41.39/11.00 b(c)(c(b)(b(b)(x1))) -> b(b)(b(b)(b(b)(x1))) 41.39/11.00 b(c)(c(b)(b(c)(x1))) -> b(b)(b(b)(b(c)(x1))) 41.39/11.00 Usable Rule Processor: 41.39/11.00 DPs: 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.00 TRS: 41.39/11.00 b(c)(c(f4)(x1)) -> b(f4)(x1) 41.39/11.00 b(c)(c(c)(x1)) -> b(c)(x1) 41.39/11.00 b(c)(c(b)(b(f4)(x1))) -> b(b)(b(b)(b(f4)(x1))) 41.39/11.00 b(c)(c(b)(b(b)(x1))) -> b(b)(b(b)(b(b)(x1))) 41.39/11.00 b(c)(c(b)(b(c)(x1))) -> b(b)(b(b)(b(c)(x1))) 41.39/11.00 Polynomial Interpretation Processor: 41.39/11.00 dimension: 1 41.39/11.00 interpretation: 41.39/11.00 [c(f4)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [c(c)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [b(c)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [b(b)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [f4(b)](x0) = x0, 41.39/11.00 41.39/11.00 [b(f4)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [c(b)](x0) = x0 + 1, 41.39/11.00 41.39/11.00 [f4(c)](x0) = x0, 41.39/11.00 41.39/11.00 [b{#,(f4)}](x0) = x0 41.39/11.00 orientation: 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.00 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.00 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.00 41.39/11.00 b(c)(c(f4)(x1)) = x1 + 2 >= x1 + 1 = b(f4)(x1) 41.39/11.00 41.39/11.00 b(c)(c(c)(x1)) = x1 + 2 >= x1 + 1 = b(c)(x1) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(f4)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(f4)(x1))) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(b)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(b)(x1))) 41.39/11.00 41.39/11.00 b(c)(c(b)(b(c)(x1))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(c)(x1))) 41.39/11.00 problem: 41.39/11.00 DPs: 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.00 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.02 TRS: 41.39/11.02 b(c)(c(b)(b(f4)(x1))) -> b(b)(b(b)(b(f4)(x1))) 41.39/11.02 b(c)(c(b)(b(b)(x1))) -> b(b)(b(b)(b(b)(x1))) 41.39/11.02 b(c)(c(b)(b(c)(x1))) -> b(b)(b(b)(b(c)(x1))) 41.39/11.02 Polynomial Interpretation Processor: 41.39/11.02 dimension: 1 41.39/11.02 interpretation: 41.39/11.02 [b(c)](x0) = x0, 41.39/11.02 41.39/11.02 [b(b)](x0) = x0, 41.39/11.02 41.39/11.02 [f4(b)](x0) = x0 + 1, 41.39/11.02 41.39/11.02 [b(f4)](x0) = x0 + 1, 41.39/11.02 41.39/11.02 [c(b)](x0) = x0 + 1, 41.39/11.02 41.39/11.02 [f4(c)](x0) = x0, 41.39/11.02 41.39/11.02 [b{#,(f4)}](x0) = x0 + 1 41.39/11.02 orientation: 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 3 >= x1 + 3 = b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.02 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.02 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.02 41.39/11.02 b(c)(c(b)(b(f4)(x1))) = x1 + 2 >= x1 + 1 = b(b)(b(b)(b(f4)(x1))) 41.39/11.02 41.39/11.02 b(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 = b(b)(b(b)(b(b)(x1))) 41.39/11.02 41.39/11.02 b(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 = b(b)(b(b)(b(c)(x1))) 41.39/11.02 problem: 41.39/11.02 DPs: 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.02 TRS: 41.39/11.02 41.39/11.02 Polynomial Interpretation Processor: 41.39/11.02 dimension: 1 41.39/11.02 interpretation: 41.39/11.02 [b(c)](x0) = x0, 41.39/11.02 41.39/11.02 [b(b)](x0) = x0, 41.39/11.02 41.39/11.02 [f4(b)](x0) = x0, 41.39/11.02 41.39/11.02 [b(f4)](x0) = x0, 41.39/11.02 41.39/11.02 [c(b)](x0) = x0 + 1, 41.39/11.02 41.39/11.02 [f4(c)](x0) = x0, 41.39/11.02 41.39/11.02 [b{#,(f4)}](x0) = x0 41.39/11.02 orientation: 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(f4)(x1)))) = x1 + 1 >= x1 = b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) 41.39/11.02 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(b)(x1)))) = x1 + 1 >= x1 = b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) 41.39/11.02 41.39/11.02 b{#,(f4)}(f4(c)(c(b)(b(c)(x1)))) = x1 + 1 >= x1 = b{#,(f4)}(f4(b)(b(b)(b(c)(x1)))) 41.39/11.02 problem: 41.39/11.02 DPs: 41.39/11.02 41.39/11.02 TRS: 41.39/11.02 41.39/11.02 Qed 41.39/11.02 EOF