YES Problem: a(b(x1)) -> x1 a(c(x1)) -> c(c(x1)) b(c(x1)) -> a(b(a(b(x1)))) Proof: DP Processor: DPs: b#(c(x1)) -> b#(x1) b#(c(x1)) -> a#(b(x1)) b#(c(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(b(a(b(x1)))) TRS: a(b(x1)) -> x1 a(c(x1)) -> c(c(x1)) b(c(x1)) -> a(b(a(b(x1)))) TDG Processor: DPs: b#(c(x1)) -> b#(x1) b#(c(x1)) -> a#(b(x1)) b#(c(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(b(a(b(x1)))) TRS: a(b(x1)) -> x1 a(c(x1)) -> c(c(x1)) b(c(x1)) -> a(b(a(b(x1)))) graph: b#(c(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> a#(b(a(b(x1)))) b#(c(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> b#(a(b(x1))) b#(c(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> a#(b(x1)) b#(c(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(a(b(x1)))) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(a(b(x1))) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1)) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) SCC Processor: #sccs: 1 #rules: 2 #arcs: 8/16 DPs: b#(c(x1)) -> b#(a(b(x1))) b#(c(x1)) -> b#(x1) TRS: a(b(x1)) -> x1 a(c(x1)) -> c(c(x1)) b(c(x1)) -> a(b(a(b(x1)))) Root-Labeling Processor: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(c)(x1)) TRS: f5(a)(a(b)(b(f5)(x1))) -> f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) f5(a)(a(b)(b(b)(x1))) -> f5(b)(x1) f5(a)(a(b)(b(c)(x1))) -> f5(c)(x1) a(a)(a(b)(b(f5)(x1))) -> a(f5)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(b)(x1))) -> a(b)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) f5(a)(a(c)(c(f5)(x1))) -> f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) f5(b)(b(c)(c(f5)(x1))) -> f5(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) f5(b)(b(c)(c(a)(x1))) -> f5(a)(a(b)(b(a)(a(b)(b(a)(x1))))) f5(b)(b(c)(c(b)(x1))) -> f5(a)(a(b)(b(a)(a(b)(b(b)(x1))))) f5(b)(b(c)(c(c)(x1))) -> f5(a)(a(b)(b(a)(a(b)(b(c)(x1))))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) b(b)(b(c)(c(f5)(x1))) -> b(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) b(b)(b(c)(c(a)(x1))) -> b(a)(a(b)(b(a)(a(b)(b(a)(x1))))) b(b)(b(c)(c(b)(x1))) -> b(a)(a(b)(b(a)(a(b)(b(b)(x1))))) b(b)(b(c)(c(c)(x1))) -> b(a)(a(b)(b(a)(a(b)(b(c)(x1))))) c(b)(b(c)(c(f5)(x1))) -> c(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) c(b)(b(c)(c(a)(x1))) -> c(a)(a(b)(b(a)(a(b)(b(a)(x1))))) c(b)(b(c)(c(b)(x1))) -> c(a)(a(b)(b(a)(a(b)(b(b)(x1))))) c(b)(b(c)(c(c)(x1))) -> c(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0, [b(b)](x0) = x0 + 1, [c(f5)](x0) = x0, [c(c)](x0) = x0, [a(f5)](x0) = x0, [f5(b)](x0) = x0 + 1, [b(c)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0, [c(b)](x0) = x0 + 1, [c(a)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 >= x1 = b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(c)(x1)) f5(a)(a(b)(b(f5)(x1))) = x1 >= x1 = f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) f5(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = f5(b)(x1) f5(a)(a(b)(b(c)(x1))) = x1 >= x1 = f5(c)(x1) a(a)(a(b)(b(f5)(x1))) = x1 >= x1 = a(f5)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 = a(b)(x1) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 >= x1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 >= x1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 >= x1 = c(c)(x1) f5(a)(a(c)(c(f5)(x1))) = x1 >= x1 = f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) = x1 >= x1 = f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) = x1 >= x1 = f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) = x1 >= x1 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 >= x1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 >= x1 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(x1))) f5(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = f5(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) f5(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 = f5(a)(a(b)(b(a)(a(b)(b(a)(x1))))) f5(b)(b(c)(c(b)(x1))) = x1 + 2 >= x1 + 1 = f5(a)(a(b)(b(a)(a(b)(b(b)(x1))))) f5(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 = f5(a)(a(b)(b(a)(a(b)(b(c)(x1))))) a(b)(b(c)(c(f5)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) b(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = b(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) b(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 = b(a)(a(b)(b(a)(a(b)(b(a)(x1))))) b(b)(b(c)(c(b)(x1))) = x1 + 2 >= x1 + 1 = b(a)(a(b)(b(a)(a(b)(b(b)(x1))))) b(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 = b(a)(a(b)(b(a)(a(b)(b(c)(x1))))) c(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 = c(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) c(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 = c(a)(a(b)(b(a)(a(b)(b(a)(x1))))) c(b)(b(c)(c(b)(x1))) = x1 + 2 >= x1 + 1 = c(a)(a(b)(b(a)(a(b)(b(b)(x1))))) c(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 = c(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(c)(x1)) TRS: f5(a)(a(b)(b(f5)(x1))) -> f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) f5(a)(a(b)(b(b)(x1))) -> f5(b)(x1) f5(a)(a(b)(b(c)(x1))) -> f5(c)(x1) a(a)(a(b)(b(f5)(x1))) -> a(f5)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) f5(a)(a(c)(c(f5)(x1))) -> f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0, [b(b)](x0) = x0 + 1, [c(f5)](x0) = x0, [c(c)](x0) = x0, [a(f5)](x0) = x0, [f5(b)](x0) = x0, [b(c)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0, [c(b)](x0) = x0 + 1, [c(a)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 >= x1 = b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(b)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(c)(x1)) f5(a)(a(b)(b(f5)(x1))) = x1 >= x1 = f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) f5(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 = f5(b)(x1) f5(a)(a(b)(b(c)(x1))) = x1 >= x1 = f5(c)(x1) a(a)(a(b)(b(f5)(x1))) = x1 >= x1 = a(f5)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 >= x1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 >= x1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 >= x1 = c(c)(x1) f5(a)(a(c)(c(f5)(x1))) = x1 >= x1 = f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) = x1 >= x1 = f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) = x1 >= x1 = f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) = x1 >= x1 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 >= x1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 >= x1 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(c)(x1)) TRS: f5(a)(a(b)(b(f5)(x1))) -> f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) f5(a)(a(b)(b(c)(x1))) -> f5(c)(x1) a(a)(a(b)(b(f5)(x1))) -> a(f5)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) f5(a)(a(c)(c(f5)(x1))) -> f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) -> f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) -> f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) -> f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0 + 1, [b(b)](x0) = x0, [c(f5)](x0) = x0 + 1, [c(c)](x0) = x0 + 1, [a(f5)](x0) = x0 + 1, [b(c)](x0) = x0, [a(c)](x0) = x0 + 1, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0 + 1, [c(b)](x0) = x0 + 1, [c(a)](x0) = x0 + 1, [b(f5)](x0) = x0, [f5(a)](x0) = x0 + 1, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(x1)) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(c)(x1)) f5(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(x1) f5(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 = f5(c)(x1) a(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = a(f5)(x1) a(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 >= x1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = c(c)(x1) f5(a)(a(c)(c(f5)(x1))) = x1 + 3 >= x1 + 2 = f5(c)(c(c)(c(f5)(x1))) f5(a)(a(c)(c(a)(x1))) = x1 + 3 >= x1 + 2 = f5(c)(c(c)(c(a)(x1))) f5(a)(a(c)(c(b)(x1))) = x1 + 3 >= x1 + 2 = f5(c)(c(c)(c(b)(x1))) f5(a)(a(c)(c(c)(x1))) = x1 + 3 >= x1 + 2 = f5(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(f5)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) TRS: f5(a)(a(b)(b(f5)(x1))) -> f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(f5)(x1))) -> a(f5)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0 + 1, [b(b)](x0) = x0, [c(f5)](x0) = x0 + 1, [c(c)](x0) = x0, [a(f5)](x0) = x0, [b(c)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0, [c(b)](x0) = x0, [c(a)](x0) = x0, [b(f5)](x0) = x0 + 1, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 + 1 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(x1)) f5(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) a(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 = a(f5)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 >= x1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 >= x1 = c(c)(x1) a(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) TRS: f5(a)(a(b)(b(f5)(x1))) -> f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0, [b(b)](x0) = x0, [c(f5)](x0) = x0 + 1, [c(c)](x0) = x0, [b(c)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0, [c(b)](x0) = x0, [c(a)](x0) = x0, [b(f5)](x0) = x0 + 1, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(f5)(x1)) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 >= x1 = b{#,(f5)}(f5(a)(x1)) f5(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 = f5(f5)(x1) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 >= x1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 >= x1 = c(c)(x1) a(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 >= x1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 >= x1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 >= x1 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 >= x1 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 >= x1 = c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(f5)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) -> b{#,(f5)}(f5(a)(x1)) TRS: f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) c(a)(a(b)(b(b)(x1))) -> c(b)(x1) c(a)(a(b)(b(c)(x1))) -> c(c)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) -> c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) -> c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) -> c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) -> c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b(b)](x0) = x0 + 1, [c(f5)](x0) = x0 + 1, [c(c)](x0) = x0, [b(c)](x0) = x0 + 1, [a(c)](x0) = x0 + 1, [a(b)](x0) = x0, [f5(c)](x0) = x0 + 1, [a(a)](x0) = x0, [c(b)](x0) = x0, [c(a)](x0) = x0, [b(f5)](x0) = x0 + 1, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(f5)(x1))) = x1 + 2 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(f5)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(a)(x1)))) b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) b{#,(f5)}(f5(c)(c(a)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(a)(x1)) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) c(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 = c(b)(x1) c(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 = c(c)(x1) a(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(c)(x1))) c(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 1 = c(c)(c(c)(c(f5)(x1))) c(a)(a(c)(c(a)(x1))) = x1 + 1 >= x1 = c(c)(c(c)(c(a)(x1))) c(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 = c(c)(c(c)(c(b)(x1))) c(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 = c(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(f5)(x1))) = x1 + 2 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(f5)(x1))))) a(b)(b(c)(c(a)(x1))) = x1 + 1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(a)(x1))))) a(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(b)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) TRS: f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(b)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b(b)](x0) = x0, [c(f5)](x0) = x0, [c(c)](x0) = x0, [b(c)](x0) = x0, [a(c)](x0) = x0, [a(b)](x0) = x0, [f5(c)](x0) = x0 + 1, [a(a)](x0) = x0, [c(b)](x0) = x0 + 1, [c(a)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0 + 1, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(b)(x1))) = x1 + 2 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(b)(x1)))) b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) f5(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 >= x1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 >= x1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) a(a)(a(c)(c(f5)(x1))) = x1 >= x1 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 >= x1 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 >= x1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 >= x1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 >= x1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 >= x1 = b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(b)(x1))) = x1 + 1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(b)(x1))))) a(b)(b(c)(c(c)(x1))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) TRS: f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(f5)(x1))) -> c(f5)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b(b)](x0) = x0, [c(f5)](x0) = x0 + 1, [c(c)](x0) = x0, [b(c)](x0) = x0 + 1, [a(c)](x0) = x0 + 1, [a(b)](x0) = x0, [f5(c)](x0) = x0 + 1, [a(a)](x0) = x0, [c(b)](x0) = x0, [c(a)](x0) = x0 + 1, [b(f5)](x0) = x0 + 1, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 + 1 orientation: b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = b(c)(x1) c(a)(a(b)(b(f5)(x1))) = x1 + 2 >= x1 + 1 = c(f5)(x1) c(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c(a)(x1) a(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: b{#,(f5)}(f5(c)(c(c)(x1))) -> b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) TRS: f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b(b)](x0) = x0, [c(f5)](x0) = x0, [c(c)](x0) = x0 + 1, [b(c)](x0) = x0, [a(c)](x0) = x0 + 1, [a(b)](x0) = x0, [f5(c)](x0) = x0, [a(a)](x0) = x0 + 1, [c(b)](x0) = x0, [c(a)](x0) = x0, [b(f5)](x0) = x0, [f5(a)](x0) = x0, [b(a)](x0) = x0, [b{#,(f5)}](x0) = x0 orientation: b{#,(f5)}(f5(c)(c(c)(x1))) = x1 + 1 >= x1 = b{#,(f5)}(f5(a)(a(b)(b(c)(x1)))) f5(a)(a(b)(b(a)(x1))) = x1 >= x1 = f5(a)(x1) a(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a(a)(x1) a(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(c)(x1) b(a)(a(b)(b(f5)(x1))) = x1 >= x1 = b(f5)(x1) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(a)(x1) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(b)(x1) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(x1) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(a)(x1) a(a)(a(c)(c(f5)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) problem: DPs: TRS: f5(a)(a(b)(b(a)(x1))) -> f5(a)(x1) a(a)(a(b)(b(a)(x1))) -> a(a)(x1) a(a)(a(b)(b(c)(x1))) -> a(c)(x1) b(a)(a(b)(b(f5)(x1))) -> b(f5)(x1) b(a)(a(b)(b(a)(x1))) -> b(a)(x1) b(a)(a(b)(b(b)(x1))) -> b(b)(x1) b(a)(a(b)(b(c)(x1))) -> b(c)(x1) c(a)(a(b)(b(a)(x1))) -> c(a)(x1) a(a)(a(c)(c(f5)(x1))) -> a(c)(c(c)(c(f5)(x1))) a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) b(a)(a(c)(c(f5)(x1))) -> b(c)(c(c)(c(f5)(x1))) b(a)(a(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) b(a)(a(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) b(a)(a(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) a(b)(b(c)(c(c)(x1))) -> a(a)(a(b)(b(a)(a(b)(b(c)(x1))))) Qed