YES Problem: b(b(b(x1))) -> a(x1) a(a(x1)) -> a(b(a(x1))) b(c(x1)) -> c(a(a(x1))) a(c(x1)) -> c(b(b(x1))) a(a(a(x1))) -> b(a(a(x1))) Proof: DP Processor: DPs: b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(x1) b#(c(x1)) -> a#(a(x1)) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) a#(a(a(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> a(x1) a(a(x1)) -> a(b(a(x1))) b(c(x1)) -> c(a(a(x1))) a(c(x1)) -> c(b(b(x1))) a(a(a(x1))) -> b(a(a(x1))) TDG Processor: DPs: b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(x1) b#(c(x1)) -> a#(a(x1)) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) a#(a(a(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> a(x1) a(a(x1)) -> a(b(a(x1))) b(c(x1)) -> c(a(a(x1))) a(c(x1)) -> c(b(b(x1))) a(a(a(x1))) -> b(a(a(x1))) graph: a#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(x1)) a#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(x1) a#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(x1) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(x1)) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1) a#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) a#(a(a(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(x1)) a#(a(a(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1) a#(a(a(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(a(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(c(x1)) -> b#(b(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(c(x1)) -> b#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(a(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1) b#(c(x1)) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(a(a(x1))) b#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1) b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1)) b#(c(x1)) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1))) b#(c(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(x1) -> a#(c(x1)) -> b#(b(x1)) b#(b(b(x1))) -> a#(x1) -> a#(c(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) Polynomial Interpretation Processor: dimension: 1 interpretation: [a#](x0) = x0, [a](x0) = x0, [b#](x0) = x0, [b](x0) = x0, [c](x0) = x0 + 1 orientation: b#(b(b(x1))) = x1 >= x1 = a#(x1) a#(a(x1)) = x1 >= x1 = b#(a(x1)) a#(a(x1)) = x1 >= x1 = a#(b(a(x1))) b#(c(x1)) = x1 + 1 >= x1 = a#(x1) b#(c(x1)) = x1 + 1 >= x1 = a#(a(x1)) a#(c(x1)) = x1 + 1 >= x1 = b#(x1) a#(c(x1)) = x1 + 1 >= x1 = b#(b(x1)) a#(a(a(x1))) = x1 >= x1 = b#(a(a(x1))) b(b(b(x1))) = x1 >= x1 = a(x1) a(a(x1)) = x1 >= x1 = a(b(a(x1))) b(c(x1)) = x1 + 1 >= x1 + 1 = c(a(a(x1))) a(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1))) a(a(a(x1))) = x1 >= x1 = b(a(a(x1))) problem: DPs: b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> a(x1) a(a(x1)) -> a(b(a(x1))) b(c(x1)) -> c(a(a(x1))) a(c(x1)) -> c(b(b(x1))) a(a(a(x1))) -> b(a(a(x1))) Root-Labeling Processor: DPs: b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(f5)(x1)))) -> f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) -> b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) -> a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) -> c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) f5(b)(b(c)(c(f5)(x1))) -> f5(c)(c(a)(a(a)(a(f5)(x1)))) f5(b)(b(c)(c(b)(x1))) -> f5(c)(c(a)(a(a)(a(b)(x1)))) f5(b)(b(c)(c(a)(x1))) -> f5(c)(c(a)(a(a)(a(a)(x1)))) f5(b)(b(c)(c(c)(x1))) -> f5(c)(c(a)(a(a)(a(c)(x1)))) b(b)(b(c)(c(f5)(x1))) -> b(c)(c(a)(a(a)(a(f5)(x1)))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(f5)(x1))) -> a(c)(c(a)(a(a)(a(f5)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(f5)(x1))) -> c(c)(c(a)(a(a)(a(f5)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) f5(a)(a(c)(c(f5)(x1))) -> f5(c)(c(b)(b(b)(b(f5)(x1)))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(b)(b(b)(b(b)(x1)))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(b)(b(b)(b(a)(x1)))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(b)(b(b)(b(c)(x1)))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(b)(b(b)(b(f5)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(b)(b(b)(b(f5)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(b)(b(b)(b(f5)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) TDG Processor: DPs: b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(f5)(x1)))) -> f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) -> b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) -> a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) -> c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) f5(b)(b(c)(c(f5)(x1))) -> f5(c)(c(a)(a(a)(a(f5)(x1)))) f5(b)(b(c)(c(b)(x1))) -> f5(c)(c(a)(a(a)(a(b)(x1)))) f5(b)(b(c)(c(a)(x1))) -> f5(c)(c(a)(a(a)(a(a)(x1)))) f5(b)(b(c)(c(c)(x1))) -> f5(c)(c(a)(a(a)(a(c)(x1)))) b(b)(b(c)(c(f5)(x1))) -> b(c)(c(a)(a(a)(a(f5)(x1)))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(f5)(x1))) -> a(c)(c(a)(a(a)(a(f5)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(f5)(x1))) -> c(c)(c(a)(a(a)(a(f5)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) f5(a)(a(c)(c(f5)(x1))) -> f5(c)(c(b)(b(b)(b(f5)(x1)))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(b)(b(b)(b(b)(x1)))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(b)(b(b)(b(a)(x1)))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(b)(b(b)(b(c)(x1)))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(b)(b(b)(b(f5)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(b)(b(b)(b(f5)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(b)(b(b)(b(f5)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) graph: a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a(a)](x0) = x0, [f5(c)](x0) = x0, [b(b)](x0) = x0, [a(f5)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [c(f5)](x0) = x0 + 1, [a{#,(f5)}](x0) = x0, [f5(b)](x0) = x0, [c(b)](x0) = x0, [b(c)](x0) = x0, [b(a)](x0) = x0, [c(c)](x0) = x0, [f5(f5)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) = x1 >= x1 = a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) f5(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(x1))) f5(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = f5(c)(c(a)(a(a)(a(f5)(x1)))) f5(b)(b(c)(c(b)(x1))) = x1 >= x1 = f5(c)(c(a)(a(a)(a(b)(x1)))) f5(b)(b(c)(c(a)(x1))) = x1 >= x1 = f5(c)(c(a)(a(a)(a(a)(x1)))) f5(b)(b(c)(c(c)(x1))) = x1 >= x1 = f5(c)(c(a)(a(a)(a(c)(x1)))) b(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = b(c)(c(a)(a(a)(a(f5)(x1)))) b(b)(b(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = a(c)(c(a)(a(a)(a(f5)(x1)))) a(b)(b(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = c(c)(c(a)(a(a)(a(f5)(x1)))) c(b)(b(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(c)(x1)))) f5(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 = f5(c)(c(b)(b(b)(b(f5)(x1)))) f5(a)(a(c)(c(b)(x1))) = x1 >= x1 = f5(c)(c(b)(b(b)(b(b)(x1)))) f5(a)(a(c)(c(a)(x1))) = x1 >= x1 = f5(c)(c(b)(b(b)(b(a)(x1)))) f5(a)(a(c)(c(c)(x1))) = x1 >= x1 = f5(c)(c(b)(b(b)(b(c)(x1)))) b(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 = b(c)(c(b)(b(b)(b(f5)(x1)))) b(a)(a(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 = a(c)(c(b)(b(b)(b(f5)(x1)))) a(a)(a(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 = c(c)(c(b)(b(b)(b(f5)(x1)))) c(a)(a(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) -> a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) -> a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(f5)(x1)))) -> f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) -> b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) -> a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) -> c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) f5(b)(b(c)(c(b)(x1))) -> f5(c)(c(a)(a(a)(a(b)(x1)))) f5(b)(b(c)(c(a)(x1))) -> f5(c)(c(a)(a(a)(a(a)(x1)))) f5(b)(b(c)(c(c)(x1))) -> f5(c)(c(a)(a(a)(a(c)(x1)))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(b)(b(b)(b(b)(x1)))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(b)(b(b)(b(a)(x1)))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(b)(b(b)(b(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a(a)](x0) = x0, [f5(c)](x0) = x0, [b(b)](x0) = x0, [a(f5)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [a{#,(f5)}](x0) = x0, [f5(b)](x0) = x0 + 1, [c(b)](x0) = x0, [b(c)](x0) = x0, [b(a)](x0) = x0, [c(c)](x0) = x0, [f5(f5)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0 + 1, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 = a{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(b)(b(b)(b(c)(x1)))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) f5(b)(b(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 + 1 = f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = x1 + 1 >= x1 + 1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) = x1 >= x1 = c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(x1))) f5(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 = f5(c)(c(a)(a(a)(a(b)(x1)))) f5(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 = f5(c)(c(a)(a(a)(a(a)(x1)))) f5(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 = f5(c)(c(a)(a(a)(a(c)(x1)))) b(b)(b(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(c)(x1)))) f5(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 = f5(c)(c(b)(b(b)(b(b)(x1)))) f5(a)(a(c)(c(a)(x1))) = x1 + 1 >= x1 = f5(c)(c(b)(b(b)(b(a)(x1)))) f5(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 = f5(c)(c(b)(b(b)(b(c)(x1)))) b(a)(a(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = x1 + 1 >= x1 + 1 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = x1 + 1 >= x1 + 1 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(f5)(x1)))) -> f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) -> b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) -> a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) -> c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a(a)](x0) = x0, [b(b)](x0) = x0, [a(f5)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [a{#,(f5)}](x0) = x0 + 1, [f5(b)](x0) = x0, [c(b)](x0) = x0, [b(c)](x0) = x0, [b(a)](x0) = x0, [c(c)](x0) = x0, [b(f5)](x0) = x0 + 1, [f5(a)](x0) = x0, [b{#,(f5)}](x0) = x0 + 1 orientation: b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) f5(b)(b(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 = f5(a)(a(f5)(x1)) f5(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 = b(a)(a(f5)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 = a(a)(a(f5)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(f5)(x1)))) = x1 + 1 >= x1 = c(a)(a(f5)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = x1 >= x1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = x1 >= x1 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) -> a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) -> a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) interpretation: [a(a)](x0) = x0 + 1, [b(b)](x0) = x0 + 1, [a(f5)](x0) = 1, [c(a)](x0) = 1, [a(c)](x0) = 1, [a(b)](x0) = x0, [a{#,(f5)}](x0) = x0, [f5(b)](x0) = x0, [c(b)](x0) = 0, [b(c)](x0) = 1, [b(a)](x0) = x0, [c(c)](x0) = 0, [f5(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(b)(b(b)(b(b)(x1)))) = x1 + 2 >= x1 = a{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 = a{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) = 1 >= 1 = b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = 1 >= 1 = b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = 1 >= 1 = a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = 1 >= 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) = 2 >= 2 = b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 + 2 = b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) = 2 >= 2 = b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) f5(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 1 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = 3 >= 1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = 4 >= 1 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = 3 >= 2 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 1 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 1 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = 2 >= 1 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = 2 >= 1 = a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) = 2 >= 1 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = 2 >= 1 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = 2 >= 1 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = 1 >= 1 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = 1 >= 1 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = 1 >= 1 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) = 1 >= 1 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = 1 >= 1 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = 1 >= 1 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = 2 >= 1 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = 2 >= 1 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = 2 >= 1 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = 3 >= 2 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = 3 >= 2 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = 3 >= 3 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = 3 >= 3 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = 4 >= 2 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = 4 >= 2 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> b{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> b{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> b{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) -> b{#,(f5)}(f5(a)(a(a)(a(c)(x1)))) TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 128/144 DPs: a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) interpretation: [a(a)](x0) = 0, [b(b)](x0) = 0, [a(f5)](x0) = 1, [c(a)](x0) = 0, [a(c)](x0) = 0, [a(b)](x0) = 0, [a{#,(f5)}](x0) = x0, [f5(b)](x0) = 0, [c(b)](x0) = 0, [b(c)](x0) = 1, [b(a)](x0) = 0, [c(c)](x0) = 0, [f5(a)](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(c)(x1))) = 0 >= 0 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = 1 >= 0 = a{#,(f5)}(f5(b)(b(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = 0 >= 0 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = 0 >= 0 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) f5(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 0 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 0 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 0 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 0 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = 0 >= 0 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = 0 >= 0 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = 0 >= 0 = a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) = 0 >= 1 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = 0 >= 1 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = 0 >= 1 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) = 0 >= 1 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = 0 >= 1 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = 0 >= 1 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = 0 >= 0 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = 0 >= 0 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = 0 >= 0 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = 0 >= 0 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = 0 >= 0 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = 0 >= 0 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = 0 >= 0 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = 0 >= 0 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = 0 >= 0 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = 0 >= 0 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = 0 >= 0 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = 0 >= 0 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = 0 >= 0 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = 0 >= 0 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) interpretation: [a(a)](x0) = 1, [b(b)](x0) = 1, [a(f5)](x0) = 0, [c(a)](x0) = x0 + 1, [a(c)](x0) = 0, [a(b)](x0) = 1, [a{#,(f5)}](x0) = x0, [f5(b)](x0) = x0, [c(b)](x0) = 0, [b(c)](x0) = 0, [b(a)](x0) = x0, [c(c)](x0) = 0, [f5(a)](x0) = 1 orientation: a{#,(f5)}(f5(a)(a(c)(x1))) = 1 >= 0 = a{#,(f5)}(f5(b)(b(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = 1 >= 1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = 1 >= 1 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) f5(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = 1 >= 1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = 1 >= 0 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = 1 >= 1 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 2 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 2 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = 1 >= 1 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = 1 >= 1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = 1 >= 1 = a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = 1 >= 0 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = 1 >= 0 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = 1 >= 0 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = 0 >= 0 = c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = 1 >= 0 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = 1 >= 1 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = 1 >= 1 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = 1 >= 1 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = 1 >= 1 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = 2 >= 0 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = 2 >= 0 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = 2 >= 0 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = 2 >= 0 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) interpretation: [a(a)](x0) = x0 + 1, [b(b)](x0) = x0 + 1, [a(f5)](x0) = 0, [c(a)](x0) = 1, [a(c)](x0) = 0, [a(b)](x0) = x0, [a{#,(f5)}](x0) = x0 + 1, [f5(b)](x0) = x0, [c(b)](x0) = 0, [b(c)](x0) = 0, [b(a)](x0) = x0, [c(c)](x0) = x0 + 1, [f5(a)](x0) = x0 + 1 orientation: a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 3 >= x1 + 2 = a{#,(f5)}(f5(b)(b(a)(a(a)(x1)))) f5(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) = 2 >= 1 = f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 = b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) = 3 >= 0 = b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) = 2 >= 1 = a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 1 = c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 1 = c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) = 0 >= 1 = c(a)(a(c)(x1)) a(a)(a(f5)(x1)) = 1 >= 0 = a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) = 1 >= 0 = a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) = 1 >= 0 = b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) = 0 >= 0 = a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) = 0 >= 2 = c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) = 0 >= 2 = c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) = 0 >= 2 = c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) = 1 >= 0 = a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) = 1 >= 1 = c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) = 1 >= 1 = c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) = 1 >= 1 = c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) = 3 >= 1 = f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) = 3 >= 1 = f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) = 2 >= 2 = b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) = 2 >= 2 = b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) = 3 >= 1 = a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 1 = a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) = 3 >= 1 = a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) = 1 >= 0 = c(b)(b(a)(a(a)(a(c)(x1)))) problem: DPs: TRS: f5(b)(b(b)(b(b)(b(b)(x1)))) -> f5(a)(a(b)(x1)) f5(b)(b(b)(b(b)(b(a)(x1)))) -> f5(a)(a(a)(x1)) f5(b)(b(b)(b(b)(b(c)(x1)))) -> f5(a)(a(c)(x1)) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1)) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1)) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(a)(a(c)(x1)) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1)) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1)) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(a)(a(c)(x1)) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(a)(a(b)(x1)) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(a)(a(a)(x1)) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(a)(a(c)(x1)) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(f5)(x1))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(x1))) b(b)(b(c)(c(b)(x1))) -> b(c)(c(a)(a(a)(a(b)(x1)))) b(b)(b(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(a(a)(x1)))) b(b)(b(c)(c(c)(x1))) -> b(c)(c(a)(a(a)(a(c)(x1)))) a(b)(b(c)(c(b)(x1))) -> a(c)(c(a)(a(a)(a(b)(x1)))) a(b)(b(c)(c(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) a(b)(b(c)(c(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) c(b)(b(c)(c(b)(x1))) -> c(c)(c(a)(a(a)(a(b)(x1)))) c(b)(b(c)(c(a)(x1))) -> c(c)(c(a)(a(a)(a(a)(x1)))) c(b)(b(c)(c(c)(x1))) -> c(c)(c(a)(a(a)(a(c)(x1)))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(b(b)(x1)))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(b)(b(b)(b(a)(x1)))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(b)(b(b)(b(c)(x1)))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(b)(b(b)(b(b)(x1)))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(b)(b(b)(b(a)(x1)))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(b)(b(b)(b(c)(x1)))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(b)(b(b)(b(b)(x1)))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(b)(b(b)(b(a)(x1)))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(b)(b(b)(b(c)(x1)))) f5(a)(a(a)(a(a)(a(f5)(x1)))) -> f5(b)(b(a)(a(a)(a(f5)(x1)))) f5(a)(a(a)(a(a)(a(b)(x1)))) -> f5(b)(b(a)(a(a)(a(b)(x1)))) f5(a)(a(a)(a(a)(a(a)(x1)))) -> f5(b)(b(a)(a(a)(a(a)(x1)))) f5(a)(a(a)(a(a)(a(c)(x1)))) -> f5(b)(b(a)(a(a)(a(c)(x1)))) b(a)(a(a)(a(a)(a(f5)(x1)))) -> b(b)(b(a)(a(a)(a(f5)(x1)))) b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(a)(a(a)(a(b)(x1)))) b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(a)(a(a)(a(a)(x1)))) b(a)(a(a)(a(a)(a(c)(x1)))) -> b(b)(b(a)(a(a)(a(c)(x1)))) a(a)(a(a)(a(a)(a(f5)(x1)))) -> a(b)(b(a)(a(a)(a(f5)(x1)))) a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(a)(a(a)(a(b)(x1)))) a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(a)(a(a)(a(a)(x1)))) a(a)(a(a)(a(a)(a(c)(x1)))) -> a(b)(b(a)(a(a)(a(c)(x1)))) c(a)(a(a)(a(a)(a(f5)(x1)))) -> c(b)(b(a)(a(a)(a(f5)(x1)))) c(a)(a(a)(a(a)(a(b)(x1)))) -> c(b)(b(a)(a(a)(a(b)(x1)))) c(a)(a(a)(a(a)(a(a)(x1)))) -> c(b)(b(a)(a(a)(a(a)(x1)))) c(a)(a(a)(a(a)(a(c)(x1)))) -> c(b)(b(a)(a(a)(a(c)(x1)))) Qed