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