YES Problem: a(x1) -> x1 a(a(x1)) -> a(b(a(c(a(x1))))) c(b(x1)) -> a(c(x1)) Proof: DP Processor: DPs: a#(a(x1)) -> c#(a(x1)) a#(a(x1)) -> a#(c(a(x1))) a#(a(x1)) -> a#(b(a(c(a(x1))))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(b(a(c(a(x1))))) c(b(x1)) -> a(c(x1)) TDG Processor: DPs: a#(a(x1)) -> c#(a(x1)) a#(a(x1)) -> a#(c(a(x1))) a#(a(x1)) -> a#(b(a(c(a(x1))))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(b(a(c(a(x1))))) c(b(x1)) -> a(c(x1)) graph: c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(c(a(x1))))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(a(x1))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(a(x1)) a#(a(x1)) -> c#(a(x1)) -> c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(a(x1)) -> c#(b(x1)) -> c#(x1) a#(a(x1)) -> a#(b(a(c(a(x1))))) -> a#(a(x1)) -> a#(b(a(c(a(x1))))) a#(a(x1)) -> a#(b(a(c(a(x1))))) -> a#(a(x1)) -> a#(c(a(x1))) a#(a(x1)) -> a#(b(a(c(a(x1))))) -> a#(a(x1)) -> c#(a(x1)) a#(a(x1)) -> a#(c(a(x1))) -> a#(a(x1)) -> a#(b(a(c(a(x1))))) a#(a(x1)) -> a#(c(a(x1))) -> a#(a(x1)) -> a#(c(a(x1))) a#(a(x1)) -> a#(c(a(x1))) -> a#(a(x1)) -> c#(a(x1)) Root-Labeling Processor: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(f5)(x1)) -> f5(f5)(x1) f5(a)(a(a)(x1)) -> f5(a)(x1) f5(a)(a(b)(x1)) -> f5(b)(x1) f5(a)(a(c)(x1)) -> f5(c)(x1) a(a)(a(f5)(x1)) -> a(f5)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f5)(x1)) -> b(f5)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f5)(x1)) -> c(f5)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(f5)(x1))) -> f5(a)(a(c)(c(f5)(x1))) f5(c)(c(b)(b(a)(x1))) -> f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) -> f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) -> f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(f5)(x1))) -> a(a)(a(c)(c(f5)(x1))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(f5)(x1))) -> b(a)(a(c)(c(f5)(x1))) b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(f5)(x1))) -> c(a)(a(c)(c(f5)(x1))) c(c)(c(b)(b(a)(x1))) -> c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) -> c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) -> c(a)(a(c)(c(c)(x1))) TDG Processor: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(f5)(x1)) -> f5(f5)(x1) f5(a)(a(a)(x1)) -> f5(a)(x1) f5(a)(a(b)(x1)) -> f5(b)(x1) f5(a)(a(c)(x1)) -> f5(c)(x1) a(a)(a(f5)(x1)) -> a(f5)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f5)(x1)) -> b(f5)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f5)(x1)) -> c(f5)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(f5)(x1))) -> f5(a)(a(c)(c(f5)(x1))) f5(c)(c(b)(b(a)(x1))) -> f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) -> f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) -> f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(f5)(x1))) -> a(a)(a(c)(c(f5)(x1))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(f5)(x1))) -> b(a)(a(c)(c(f5)(x1))) b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(f5)(x1))) -> c(a)(a(c)(c(f5)(x1))) c(c)(c(b)(b(a)(x1))) -> c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) -> c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) -> c(a)(a(c)(c(c)(x1))) graph: c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) -> a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0 + 1, [f5(b)](x0) = x0 + 1, [a(f5)](x0) = x0 + 1, [b(a)](x0) = x0, [c(f5)](x0) = x0, [b(b)](x0) = x0, [b(f5)](x0) = x0, [c(b)](x0) = x0, [a(a)](x0) = x0, [f5(a)](x0) = x0 + 1, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0, [c{#,(f5)}](x0) = x0, [f5(c)](x0) = x0 + 1, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(c)(x1))) f5(a)(a(f5)(x1)) = x1 + 2 >= x1 + 1 = f5(f5)(x1) f5(a)(a(a)(x1)) = x1 + 1 >= x1 + 1 = f5(a)(x1) f5(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = f5(b)(x1) f5(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = f5(c)(x1) a(a)(a(f5)(x1)) = x1 + 1 >= x1 + 1 = a(f5)(x1) a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(x1) a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) b(a)(a(f5)(x1)) = x1 + 1 >= x1 = b(f5)(x1) b(a)(a(a)(x1)) = x1 >= x1 = b(a)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(f5)(x1)) = x1 + 1 >= x1 = c(f5)(x1) c(a)(a(a)(x1)) = x1 >= x1 = c(a)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(a(c)(c(f5)(x1))) f5(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(f5)(x1))) = x1 >= x1 = a(a)(a(c)(c(f5)(x1))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(f5)(x1))) = x1 >= x1 = b(a)(a(c)(c(f5)(x1))) b(c)(c(b)(b(a)(x1))) = x1 >= x1 = b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(f5)(x1))) = x1 >= x1 = c(a)(a(c)(c(f5)(x1))) c(c)(c(b)(b(a)(x1))) = x1 >= x1 = c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) = x1 >= x1 = c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) = x1 >= x1 = c(a)(a(c)(c(c)(x1))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) -> a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(a)(x1)) -> f5(a)(x1) f5(a)(a(b)(x1)) -> f5(b)(x1) f5(a)(a(c)(x1)) -> f5(c)(x1) a(a)(a(f5)(x1)) -> a(f5)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(f5)(x1))) -> f5(a)(a(c)(c(f5)(x1))) f5(c)(c(b)(b(a)(x1))) -> f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) -> f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) -> f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(f5)(x1))) -> a(a)(a(c)(c(f5)(x1))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(f5)(x1))) -> b(a)(a(c)(c(f5)(x1))) b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(f5)(x1))) -> c(a)(a(c)(c(f5)(x1))) c(c)(c(b)(b(a)(x1))) -> c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) -> c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) -> c(a)(a(c)(c(c)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0 + 1, [f5(b)](x0) = x0, [a(f5)](x0) = x0, [b(a)](x0) = x0, [c(f5)](x0) = x0, [b(b)](x0) = x0, [b(f5)](x0) = x0 + 1, [c(b)](x0) = x0, [a(a)](x0) = x0, [f5(a)](x0) = x0, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0, [c{#,(f5)}](x0) = x0, [f5(c)](x0) = x0, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 >= x1 = c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(f5)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(f5)(x1))) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(c)(x1))) f5(a)(a(a)(x1)) = x1 >= x1 = f5(a)(x1) f5(a)(a(b)(x1)) = x1 >= x1 = f5(b)(x1) f5(a)(a(c)(x1)) = x1 >= x1 = f5(c)(x1) a(a)(a(f5)(x1)) = x1 >= x1 = a(f5)(x1) a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(x1) a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) b(a)(a(a)(x1)) = x1 >= x1 = b(a)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(a)(x1)) = x1 >= x1 = c(a)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(f5)(x1))) = x1 + 1 >= x1 = f5(a)(a(c)(c(f5)(x1))) f5(c)(c(b)(b(a)(x1))) = x1 >= x1 = f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) = x1 >= x1 = f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) = x1 >= x1 = f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(f5)(x1))) = x1 + 1 >= x1 = a(a)(a(c)(c(f5)(x1))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(f5)(x1))) = x1 + 1 >= x1 = b(a)(a(c)(c(f5)(x1))) b(c)(c(b)(b(a)(x1))) = x1 >= x1 = b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(f5)(x1))) = x1 + 1 >= x1 = c(a)(a(c)(c(f5)(x1))) c(c)(c(b)(b(a)(x1))) = x1 >= x1 = c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) = x1 >= x1 = c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) = x1 >= x1 = c(a)(a(c)(c(c)(x1))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) -> c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(a)(x1)) -> f5(a)(x1) f5(a)(a(b)(x1)) -> f5(b)(x1) f5(a)(a(c)(x1)) -> f5(c)(x1) a(a)(a(f5)(x1)) -> a(f5)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(a)(x1))) -> f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) -> f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) -> f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(a)(x1))) -> c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) -> c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) -> c(a)(a(c)(c(c)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(f5)](x0) = x0, [f5(b)](x0) = x0, [a(f5)](x0) = x0, [b(a)](x0) = x0, [b(b)](x0) = x0, [b(f5)](x0) = x0 + 1, [c(b)](x0) = x0, [a(a)](x0) = x0, [f5(a)](x0) = x0, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0, [c{#,(f5)}](x0) = x0, [f5(c)](x0) = x0, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(f5)(x1))) = x1 + 1 >= x1 = c{#,(f5)}(f5(f5)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 >= x1 = c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(c)(x1))) f5(a)(a(a)(x1)) = x1 >= x1 = f5(a)(x1) f5(a)(a(b)(x1)) = x1 >= x1 = f5(b)(x1) f5(a)(a(c)(x1)) = x1 >= x1 = f5(c)(x1) a(a)(a(f5)(x1)) = x1 >= x1 = a(f5)(x1) a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(x1) a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) b(a)(a(a)(x1)) = x1 >= x1 = b(a)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(a)(x1)) = x1 >= x1 = c(a)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(a)(x1))) = x1 >= x1 = f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) = x1 >= x1 = f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) = x1 >= x1 = f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(a)(x1))) = x1 >= x1 = b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(a)(x1))) = x1 >= x1 = c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) = x1 >= x1 = c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) = x1 >= x1 = c(a)(a(c)(c(c)(x1))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) -> c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(a)(x1)) -> f5(a)(x1) f5(a)(a(b)(x1)) -> f5(b)(x1) f5(a)(a(c)(x1)) -> f5(c)(x1) a(a)(a(f5)(x1)) -> a(f5)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(a)(x1))) -> f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) -> f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) -> f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(a)(x1))) -> c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) -> c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) -> c(a)(a(c)(c(c)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(b)](x0) = x0, [a(f5)](x0) = x0, [b(a)](x0) = x0, [b(b)](x0) = x0 + 1, [c(b)](x0) = x0 + 1, [a(a)](x0) = x0 + 1, [f5(a)](x0) = x0, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0 + 1, [c{#,(f5)}](x0) = x0, [f5(c)](x0) = x0, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 + 1 >= x1 = c{#,(f5)}(f5(b)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 >= x1 = a{#,(f5)}(f5(c)(c(c)(x1))) f5(a)(a(a)(x1)) = x1 + 1 >= x1 = f5(a)(x1) f5(a)(a(b)(x1)) = x1 + 1 >= x1 = f5(b)(x1) f5(a)(a(c)(x1)) = x1 >= x1 = f5(c)(x1) a(a)(a(f5)(x1)) = x1 + 1 >= x1 = a(f5)(x1) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(x1) a(a)(a(b)(x1)) = x1 + 2 >= x1 + 1 = a(b)(x1) a(a)(a(c)(x1)) = x1 + 1 >= x1 = a(c)(x1) b(a)(a(a)(x1)) = x1 + 1 >= x1 = b(a)(x1) b(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(a)(x1)) = x1 + 1 >= x1 = c(a)(x1) c(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) f5(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 = f5(a)(a(c)(c(a)(x1))) f5(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = f5(a)(a(c)(c(b)(x1))) f5(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 = f5(a)(a(c)(c(c)(x1))) a(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(c)(c(c)(x1))) b(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 = b(a)(a(c)(c(a)(x1))) b(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = b(a)(a(c)(c(b)(x1))) b(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 = b(a)(a(c)(c(c)(x1))) c(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 = c(a)(a(c)(c(a)(x1))) c(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 1 = c(a)(a(c)(c(b)(x1))) c(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 = c(a)(a(c)(c(c)(x1))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) -> c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) -> a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) -> a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) -> a{#,(f5)}(f5(c)(c(c)(x1))) TRS: f5(a)(a(c)(x1)) -> f5(c)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(b)](x0) = x0 + 1, [a(f5)](x0) = x0 + 1, [b(a)](x0) = x0, [b(b)](x0) = x0, [c(b)](x0) = x0, [a(a)](x0) = x0, [f5(a)](x0) = x0 + 1, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0, [c{#,(f5)}](x0) = x0, [f5(c)](x0) = x0, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f5)}(f5(c)(c(a)(a(f5)(x1)))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(a)(x1)))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(b)(x1)))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(a)(a(c)(x1)))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f5)}(f5(a)(x1)) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 + 1 >= x1 = c{#,(f5)}(f5(c)(x1)) c{#,(f5)}(f5(b)(b(a)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(a)(x1))) c{#,(f5)}(f5(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(b)(x1))) c{#,(f5)}(f5(b)(b(c)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(c)(c(c)(x1))) f5(a)(a(c)(x1)) = x1 + 1 >= x1 = f5(c)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(a)(a(c)(c(c)(x1))) problem: DPs: a{#,(f5)}(f5(a)(a(f5)(x1))) -> c{#,(f5)}(f5(a)(a(f5)(x1))) a{#,(f5)}(f5(a)(a(a)(x1))) -> c{#,(f5)}(f5(a)(a(a)(x1))) a{#,(f5)}(f5(a)(a(b)(x1))) -> c{#,(f5)}(f5(a)(a(b)(x1))) a{#,(f5)}(f5(a)(a(c)(x1))) -> c{#,(f5)}(f5(a)(a(c)(x1))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) TRS: b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) SCC Processor: #sccs: 2 #rules: 5 #arcs: 208/81 DPs: a{#,(f5)}(f5(a)(a(c)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) -> a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) TRS: b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(b)](x0) = x0, [a(f5)](x0) = x0, [b(a)](x0) = x0, [b(b)](x0) = x0, [c(b)](x0) = x0, [a(a)](x0) = x0, [f5(a)](x0) = x0 + 1, [b(c)](x0) = x0, [c(a)](x0) = x0, [a(c)](x0) = x0, [c(c)](x0) = x0, [a(b)](x0) = x0, [a{#,(f5)}](x0) = x0 orientation: a{#,(f5)}(f5(a)(a(c)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(c)(x1)))))) a{#,(f5)}(f5(a)(a(f5)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(f5)(x1)))))) a{#,(f5)}(f5(a)(a(a)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(a)(x1)))))) a{#,(f5)}(f5(a)(a(b)(x1))) = x1 + 1 >= x1 = a{#,(f5)}(f5(b)(b(a)(a(c)(c(a)(a(b)(x1)))))) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(a)(a(f5)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(a)(a(c)(c(c)(x1))) problem: DPs: TRS: b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) Qed DPs: c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) TRS: b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f5)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(f5)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(a)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(b)(x1))))) a(a)(a(c)(x1)) -> a(b)(b(a)(a(c)(c(a)(a(c)(x1))))) a(c)(c(b)(b(a)(x1))) -> a(a)(a(c)(c(a)(x1))) a(c)(c(b)(b(b)(x1))) -> a(a)(a(c)(c(b)(x1))) a(c)(c(b)(b(c)(x1))) -> a(a)(a(c)(c(c)(x1))) Usable Rule Processor: DPs: c{#,(f5)}(f5(b)(b(a)(x1))) -> c{#,(f5)}(f5(a)(x1)) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [f5(b)](x0) = x0 + 1, [b(a)](x0) = x0, [f5(a)](x0) = x0, [c{#,(f5)}](x0) = x0 orientation: c{#,(f5)}(f5(b)(b(a)(x1))) = x1 + 1 >= x1 = c{#,(f5)}(f5(a)(x1)) problem: DPs: TRS: Qed