40.89/10.74 YES 40.89/10.74 40.89/10.74 Problem: 40.89/10.74 a(x1) -> x1 40.89/10.74 a(a(x1)) -> a(b(x1)) 40.89/10.74 b(x1) -> x1 40.89/10.74 c(b(x1)) -> a(b(c(c(x1)))) 40.89/10.74 40.89/10.74 Proof: 40.89/10.74 DP Processor: 40.89/10.74 DPs: 40.89/10.74 a#(a(x1)) -> b#(x1) 40.89/10.74 a#(a(x1)) -> a#(b(x1)) 40.89/10.74 c#(b(x1)) -> c#(x1) 40.89/10.74 c#(b(x1)) -> c#(c(x1)) 40.89/10.74 c#(b(x1)) -> b#(c(c(x1))) 40.89/10.74 c#(b(x1)) -> a#(b(c(c(x1)))) 40.89/10.74 TRS: 40.89/10.74 a(x1) -> x1 40.89/10.74 a(a(x1)) -> a(b(x1)) 40.89/10.74 b(x1) -> x1 40.89/10.74 c(b(x1)) -> a(b(c(c(x1)))) 40.89/10.74 TDG Processor: 40.89/10.74 DPs: 40.89/10.74 a#(a(x1)) -> b#(x1) 40.89/10.74 a#(a(x1)) -> a#(b(x1)) 40.89/10.74 c#(b(x1)) -> c#(x1) 40.89/10.74 c#(b(x1)) -> c#(c(x1)) 40.89/10.74 c#(b(x1)) -> b#(c(c(x1))) 40.89/10.74 c#(b(x1)) -> a#(b(c(c(x1)))) 40.89/10.74 TRS: 40.89/10.74 a(x1) -> x1 40.89/10.74 a(a(x1)) -> a(b(x1)) 40.89/10.74 b(x1) -> x1 40.89/10.74 c(b(x1)) -> a(b(c(c(x1)))) 40.89/10.74 graph: 40.89/10.74 c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(c(c(x1)))) 40.89/10.74 c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> b#(c(c(x1))) 40.89/10.74 c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) 40.89/10.74 c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1) 40.89/10.74 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(c(x1)))) 40.89/10.74 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(c(x1))) 40.89/10.74 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1)) 40.89/10.75 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 40.89/10.75 c#(b(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> a#(b(x1)) 40.89/10.75 c#(b(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> b#(x1) 40.89/10.75 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) 40.89/10.75 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1) 40.89/10.75 SCC Processor: 40.89/10.75 #sccs: 2 40.89/10.75 #rules: 3 40.89/10.75 #arcs: 12/36 40.89/10.75 DPs: 40.89/10.75 c#(b(x1)) -> c#(c(x1)) 40.89/10.75 c#(b(x1)) -> c#(x1) 40.89/10.75 TRS: 40.89/10.75 a(x1) -> x1 40.89/10.75 a(a(x1)) -> a(b(x1)) 40.89/10.75 b(x1) -> x1 40.89/10.75 c(b(x1)) -> a(b(c(c(x1)))) 40.89/10.75 Root-Labeling Processor: 40.89/10.75 DPs: 40.89/10.75 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) 40.89/10.75 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) 40.89/10.75 c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) 40.89/10.75 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) 40.89/10.75 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) 40.89/10.75 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) 40.89/10.75 c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) 40.89/10.75 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) 40.89/10.75 TRS: 40.89/10.75 f6(a)(a(f6)(x1)) -> f6(f6)(x1) 40.89/10.75 f6(a)(a(a)(x1)) -> f6(a)(x1) 40.89/10.75 f6(a)(a(b)(x1)) -> f6(b)(x1) 40.89/10.75 f6(a)(a(c)(x1)) -> f6(c)(x1) 40.89/10.75 a(a)(a(f6)(x1)) -> a(f6)(x1) 40.89/10.75 a(a)(a(a)(x1)) -> a(a)(x1) 40.89/10.75 a(a)(a(b)(x1)) -> a(b)(x1) 40.89/10.75 a(a)(a(c)(x1)) -> a(c)(x1) 40.89/10.75 b(a)(a(f6)(x1)) -> b(f6)(x1) 40.89/10.75 b(a)(a(a)(x1)) -> b(a)(x1) 40.89/10.75 b(a)(a(b)(x1)) -> b(b)(x1) 40.89/10.75 b(a)(a(c)(x1)) -> b(c)(x1) 40.89/10.75 c(a)(a(f6)(x1)) -> c(f6)(x1) 40.89/10.75 c(a)(a(a)(x1)) -> c(a)(x1) 40.89/10.75 c(a)(a(b)(x1)) -> c(b)(x1) 40.89/10.75 c(a)(a(c)(x1)) -> c(c)(x1) 40.89/10.75 a(a)(a(f6)(x1)) -> a(b)(b(f6)(x1)) 40.89/10.75 a(a)(a(a)(x1)) -> a(b)(b(a)(x1)) 40.89/10.75 a(a)(a(b)(x1)) -> a(b)(b(b)(x1)) 40.89/10.75 a(a)(a(c)(x1)) -> a(b)(b(c)(x1)) 40.89/10.75 f6(b)(b(f6)(x1)) -> f6(f6)(x1) 40.89/10.75 f6(b)(b(a)(x1)) -> f6(a)(x1) 40.89/10.75 f6(b)(b(b)(x1)) -> f6(b)(x1) 40.89/10.75 f6(b)(b(c)(x1)) -> f6(c)(x1) 40.89/10.75 a(b)(b(f6)(x1)) -> a(f6)(x1) 40.89/10.75 a(b)(b(a)(x1)) -> a(a)(x1) 40.89/10.75 a(b)(b(b)(x1)) -> a(b)(x1) 40.89/10.75 a(b)(b(c)(x1)) -> a(c)(x1) 40.89/10.75 b(b)(b(f6)(x1)) -> b(f6)(x1) 56.33/10.75 b(b)(b(a)(x1)) -> b(a)(x1) 56.33/10.75 b(b)(b(b)(x1)) -> b(b)(x1) 56.33/10.75 b(b)(b(c)(x1)) -> b(c)(x1) 56.33/10.75 c(b)(b(f6)(x1)) -> c(f6)(x1) 56.33/10.75 c(b)(b(a)(x1)) -> c(a)(x1) 56.33/10.75 c(b)(b(b)(x1)) -> c(b)(x1) 56.33/10.75 c(b)(b(c)(x1)) -> c(c)(x1) 56.33/10.75 f6(c)(c(b)(b(f6)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.33/10.75 f6(c)(c(b)(b(a)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.33/10.75 f6(c)(c(b)(b(b)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.33/10.75 f6(c)(c(b)(b(c)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.33/10.75 a(c)(c(b)(b(f6)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.33/10.75 a(c)(c(b)(b(a)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.33/10.75 a(c)(c(b)(b(b)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.33/10.75 a(c)(c(b)(b(c)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.33/10.75 b(c)(c(b)(b(f6)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.33/10.75 b(c)(c(b)(b(a)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.33/10.75 b(c)(c(b)(b(b)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.33/10.75 b(c)(c(b)(b(c)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.33/10.75 c(c)(c(b)(b(f6)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.41/10.82 c(c)(c(b)(b(a)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.41/10.82 c(c)(c(b)(b(b)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.41/10.82 c(c)(c(b)(b(c)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.41/10.82 Polynomial Interpretation Processor: 56.41/10.82 dimension: 1 56.41/10.82 interpretation: 56.41/10.82 [a(c)](x0) = x0, 56.41/10.82 56.41/10.82 [a(b)](x0) = x0, 56.41/10.82 56.41/10.82 [a(a)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [a(f6)](x0) = x0, 56.41/10.82 56.41/10.82 [f6(a)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [f6(f6)](x0) = x0, 56.41/10.82 56.41/10.82 [c(c)](x0) = x0, 56.41/10.82 56.41/10.82 [b(c)](x0) = x0, 56.41/10.82 56.41/10.82 [c(b)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [b(b)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [c(a)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [b(a)](x0) = x0 + 1, 56.41/10.82 56.41/10.82 [c(f6)](x0) = x0, 56.41/10.82 56.41/10.82 [f6(c)](x0) = x0, 56.41/10.82 56.41/10.82 [b(f6)](x0) = x0, 56.41/10.82 56.41/10.82 [f6(b)](x0) = x0, 56.41/10.82 56.41/10.82 [c{#,(f6)}](x0) = x0 56.41/10.82 orientation: 56.41/10.82 c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 >= x1 = c{#,(f6)}(f6(c)(c(f6)(x1))) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f6)}(f6(c)(c(a)(x1))) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f6)}(f6(c)(c(b)(x1))) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(c)(x1))) = x1 >= x1 = c{#,(f6)}(f6(c)(c(c)(x1))) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 >= x1 = c{#,(f6)}(f6(f6)(x1)) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f6)}(f6(a)(x1)) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(b)(x1)) 56.41/10.82 56.41/10.82 c{#,(f6)}(f6(b)(b(c)(x1))) = x1 >= x1 = c{#,(f6)}(f6(c)(x1)) 56.41/10.82 56.41/10.82 f6(a)(a(f6)(x1)) = x1 + 1 >= x1 = f6(f6)(x1) 56.41/10.82 56.41/10.82 f6(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = f6(a)(x1) 56.41/10.82 56.41/10.82 f6(a)(a(b)(x1)) = x1 + 1 >= x1 = f6(b)(x1) 56.41/10.82 56.41/10.82 f6(a)(a(c)(x1)) = x1 + 1 >= x1 = f6(c)(x1) 56.41/10.82 56.41/10.82 a(a)(a(f6)(x1)) = x1 + 1 >= x1 = a(f6)(x1) 56.41/10.82 56.41/10.82 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(x1) 56.41/10.82 56.41/10.82 a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(x1) 56.41/10.82 56.41/10.82 a(a)(a(c)(x1)) = x1 + 1 >= x1 = a(c)(x1) 56.41/10.82 56.41/10.82 b(a)(a(f6)(x1)) = x1 + 1 >= x1 = b(f6)(x1) 56.41/10.82 56.41/10.82 b(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = b(a)(x1) 56.41/10.82 56.41/10.82 b(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = b(b)(x1) 56.41/10.82 56.41/10.82 b(a)(a(c)(x1)) = x1 + 1 >= x1 = b(c)(x1) 56.41/10.82 56.41/10.82 c(a)(a(f6)(x1)) = x1 + 1 >= x1 = c(f6)(x1) 56.41/10.82 56.41/10.82 c(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = c(a)(x1) 56.41/10.82 56.41/10.82 c(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = c(b)(x1) 56.41/10.82 56.41/10.82 c(a)(a(c)(x1)) = x1 + 1 >= x1 = c(c)(x1) 56.41/10.82 56.41/10.82 a(a)(a(f6)(x1)) = x1 + 1 >= x1 = a(b)(b(f6)(x1)) 56.41/10.82 56.41/10.82 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(x1)) 56.41/10.82 56.41/10.82 a(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(b)(x1)) 56.41/10.82 56.41/10.82 a(a)(a(c)(x1)) = x1 + 1 >= x1 = a(b)(b(c)(x1)) 56.41/10.82 56.41/10.82 f6(b)(b(f6)(x1)) = x1 >= x1 = f6(f6)(x1) 56.41/10.82 56.41/10.82 f6(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(x1) 56.41/10.82 56.41/10.82 f6(b)(b(b)(x1)) = x1 + 1 >= x1 = f6(b)(x1) 56.41/10.82 56.41/10.82 f6(b)(b(c)(x1)) = x1 >= x1 = f6(c)(x1) 56.41/10.82 56.41/10.82 a(b)(b(f6)(x1)) = x1 >= x1 = a(f6)(x1) 56.41/10.82 56.41/10.82 a(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = a(a)(x1) 56.41/10.82 56.41/10.82 a(b)(b(b)(x1)) = x1 + 1 >= x1 = a(b)(x1) 56.41/10.82 56.41/10.82 a(b)(b(c)(x1)) = x1 >= x1 = a(c)(x1) 56.41/10.82 56.41/10.82 b(b)(b(f6)(x1)) = x1 + 1 >= x1 = b(f6)(x1) 56.41/10.82 56.41/10.82 b(b)(b(a)(x1)) = x1 + 2 >= x1 + 1 = b(a)(x1) 56.41/10.82 56.41/10.82 b(b)(b(b)(x1)) = x1 + 2 >= x1 + 1 = b(b)(x1) 56.41/10.82 56.41/10.82 b(b)(b(c)(x1)) = x1 + 1 >= x1 = b(c)(x1) 56.41/10.82 56.41/10.82 c(b)(b(f6)(x1)) = x1 + 1 >= x1 = c(f6)(x1) 56.41/10.82 56.41/10.82 c(b)(b(a)(x1)) = x1 + 2 >= x1 + 1 = c(a)(x1) 56.41/10.82 56.41/10.82 c(b)(b(b)(x1)) = x1 + 2 >= x1 + 1 = c(b)(x1) 56.41/10.82 56.41/10.82 c(b)(b(c)(x1)) = x1 + 1 >= x1 = c(c)(x1) 56.41/10.82 56.41/10.82 f6(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.41/10.82 56.41/10.82 f6(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.41/10.82 56.41/10.82 f6(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.41/10.82 56.41/10.82 f6(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.41/10.82 56.41/10.82 a(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 56.55/10.98 a(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 56.55/10.98 a(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 56.55/10.98 a(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 56.55/10.98 b(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 56.55/10.98 b(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 56.55/10.98 b(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 56.55/10.98 b(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 56.55/10.98 c(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 56.55/10.98 c(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 56.55/10.98 c(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 56.55/10.98 c(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 problem: 56.55/10.98 DPs: 56.55/10.98 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) 56.55/10.98 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) 56.55/10.98 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) 56.55/10.98 TRS: 56.55/10.98 b(a)(a(b)(x1)) -> b(b)(x1) 56.55/10.98 c(a)(a(b)(x1)) -> c(b)(x1) 56.55/10.98 a(a)(a(b)(x1)) -> a(b)(b(b)(x1)) 56.55/10.98 f6(b)(b(f6)(x1)) -> f6(f6)(x1) 56.55/10.98 f6(b)(b(a)(x1)) -> f6(a)(x1) 56.55/10.98 f6(b)(b(c)(x1)) -> f6(c)(x1) 56.55/10.98 a(b)(b(f6)(x1)) -> a(f6)(x1) 56.55/10.98 a(b)(b(a)(x1)) -> a(a)(x1) 56.55/10.98 a(b)(b(c)(x1)) -> a(c)(x1) 56.55/10.98 f6(c)(c(b)(b(f6)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 f6(c)(c(b)(b(a)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 f6(c)(c(b)(b(b)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 f6(c)(c(b)(b(c)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 a(c)(c(b)(b(f6)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 a(c)(c(b)(b(a)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 a(c)(c(b)(b(b)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 a(c)(c(b)(b(c)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 b(c)(c(b)(b(f6)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 b(c)(c(b)(b(a)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 b(c)(c(b)(b(b)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 b(c)(c(b)(b(c)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 c(c)(c(b)(b(f6)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 c(c)(c(b)(b(a)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 c(c)(c(b)(b(b)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 c(c)(c(b)(b(c)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 Usable Rule Processor: 56.55/10.98 DPs: 56.55/10.98 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) 56.55/10.98 c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) 56.55/10.98 c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) 56.55/10.98 c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) 56.55/10.98 TRS: 56.55/10.98 c(a)(a(b)(x1)) -> c(b)(x1) 56.55/10.98 f6(c)(c(b)(b(f6)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 f6(c)(c(b)(b(a)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 f6(c)(c(b)(b(b)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 f6(c)(c(b)(b(c)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 a(b)(b(c)(x1)) -> a(c)(x1) 56.55/10.98 a(c)(c(b)(b(f6)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.55/10.98 a(c)(c(b)(b(a)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.55/10.98 a(c)(c(b)(b(b)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.55/10.98 a(c)(c(b)(b(c)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.55/10.98 a(a)(a(b)(x1)) -> a(b)(b(b)(x1)) 56.55/10.98 c(c)(c(b)(b(f6)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 c(c)(c(b)(b(a)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 c(c)(c(b)(b(b)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 c(c)(c(b)(b(c)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 b(c)(c(b)(b(f6)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 b(c)(c(b)(b(a)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 b(c)(c(b)(b(b)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 b(c)(c(b)(b(c)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 b(a)(a(b)(x1)) -> b(b)(x1) 56.77/11.19 a(b)(b(f6)(x1)) -> a(f6)(x1) 56.77/11.19 a(b)(b(a)(x1)) -> a(a)(x1) 56.77/11.19 Polynomial Interpretation Processor: 56.77/11.19 dimension: 1 56.77/11.19 interpretation: 56.77/11.19 [a(c)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [a(b)](x0) = x0, 56.77/11.19 56.77/11.19 [a(a)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [a(f6)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [f6(a)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [f6(f6)](x0) = x0, 56.77/11.19 56.77/11.19 [c(c)](x0) = x0, 56.77/11.19 56.77/11.19 [b(c)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [c(b)](x0) = x0, 56.77/11.19 56.77/11.19 [b(b)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [c(a)](x0) = x0, 56.77/11.19 56.77/11.19 [b(a)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [c(f6)](x0) = x0, 56.77/11.19 56.77/11.19 [f6(c)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [b(f6)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [f6(b)](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [c{#,(f6)}](x0) = x0 56.77/11.19 orientation: 56.77/11.19 c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(c(f6)(x1))) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(c(a)(x1))) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(c(b)(x1))) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(c(c)(x1))) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 2 >= x1 = c{#,(f6)}(f6(f6)(x1)) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(a)(x1)) 56.77/11.19 56.77/11.19 c{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(x1)) 56.77/11.19 56.77/11.19 c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) 56.77/11.19 56.77/11.19 f6(c)(c(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 56.77/11.19 f6(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 56.77/11.19 f6(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 56.77/11.19 f6(c)(c(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 56.77/11.19 a(b)(b(c)(x1)) = x1 + 1 >= x1 + 1 = a(c)(x1) 56.77/11.19 56.77/11.19 a(c)(c(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 56.77/11.19 a(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 56.77/11.19 a(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 56.77/11.19 a(c)(c(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 56.77/11.19 a(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(b)(x1)) 56.77/11.19 56.77/11.19 c(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 56.77/11.19 c(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 56.77/11.19 c(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 56.77/11.19 c(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 56.77/11.19 b(c)(c(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 56.77/11.19 b(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 56.77/11.19 b(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 56.77/11.19 b(c)(c(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 56.77/11.19 b(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = b(b)(x1) 56.77/11.19 56.77/11.19 a(b)(b(f6)(x1)) = x1 + 1 >= x1 + 1 = a(f6)(x1) 56.77/11.19 56.77/11.19 a(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = a(a)(x1) 56.77/11.19 problem: 56.77/11.19 DPs: 56.77/11.19 56.77/11.19 TRS: 56.77/11.19 c(a)(a(b)(x1)) -> c(b)(x1) 56.77/11.19 f6(c)(c(b)(b(f6)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 f6(c)(c(b)(b(a)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 f6(c)(c(b)(b(b)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 f6(c)(c(b)(b(c)(x1))) -> f6(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 a(b)(b(c)(x1)) -> a(c)(x1) 56.77/11.19 a(c)(c(b)(b(f6)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 a(c)(c(b)(b(a)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 a(c)(c(b)(b(b)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 a(c)(c(b)(b(c)(x1))) -> a(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 a(a)(a(b)(x1)) -> a(b)(b(b)(x1)) 56.77/11.19 c(c)(c(b)(b(f6)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 c(c)(c(b)(b(a)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 c(c)(c(b)(b(b)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 c(c)(c(b)(b(c)(x1))) -> c(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 b(c)(c(b)(b(f6)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(f6)(x1))))) 56.77/11.19 b(c)(c(b)(b(a)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(a)(x1))))) 56.77/11.19 b(c)(c(b)(b(b)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(b)(x1))))) 56.77/11.19 b(c)(c(b)(b(c)(x1))) -> b(a)(a(b)(b(c)(c(c)(c(c)(x1))))) 56.77/11.19 b(a)(a(b)(x1)) -> b(b)(x1) 56.77/11.19 a(b)(b(f6)(x1)) -> a(f6)(x1) 56.77/11.19 a(b)(b(a)(x1)) -> a(a)(x1) 56.77/11.19 Qed 56.77/11.19 56.77/11.19 DPs: 56.77/11.19 a#(a(x1)) -> a#(b(x1)) 56.77/11.19 TRS: 56.77/11.19 a(x1) -> x1 56.77/11.19 a(a(x1)) -> a(b(x1)) 56.77/11.19 b(x1) -> x1 56.77/11.19 c(b(x1)) -> a(b(c(c(x1)))) 56.77/11.19 Usable Rule Processor: 56.77/11.19 DPs: 56.77/11.19 a#(a(x1)) -> a#(b(x1)) 56.77/11.19 TRS: 56.77/11.19 b(x1) -> x1 56.77/11.19 Polynomial Interpretation Processor: 56.77/11.19 dimension: 1 56.77/11.19 interpretation: 56.77/11.19 [a#](x0) = x0, 56.77/11.19 56.77/11.19 [b](x0) = x0 + 1, 56.77/11.19 56.77/11.19 [a](x0) = x0 + 1 56.77/11.19 orientation: 56.77/11.19 a#(a(x1)) = x1 + 1 >= x1 + 1 = a#(b(x1)) 56.77/11.19 56.77/11.19 b(x1) = x1 + 1 >= x1 = x1 56.77/11.19 problem: 56.77/11.19 DPs: 56.77/11.19 a#(a(x1)) -> a#(b(x1)) 56.77/11.19 TRS: 56.77/11.19 56.77/11.19 Polynomial Interpretation Processor: 56.77/11.19 dimension: 1 56.77/11.19 interpretation: 56.77/11.19 [a#](x0) = x0, 56.77/11.19 56.77/11.19 [b](x0) = x0, 56.77/11.19 56.77/11.19 [a](x0) = x0 + 1 56.77/11.19 orientation: 56.77/11.19 a#(a(x1)) = x1 + 1 >= x1 = a#(b(x1)) 56.77/11.19 problem: 56.77/11.19 DPs: 56.77/11.19 56.77/11.19 TRS: 56.77/11.19 56.77/11.19 Qed 56.77/11.20 EOF