YES Problem: a(x1) -> x1 a(b(x1)) -> c(b(x1)) b(x1) -> a(a(c(x1))) c(c(x1)) -> b(x1) Proof: DP Processor: DPs: a#(b(x1)) -> c#(b(x1)) b#(x1) -> c#(x1) b#(x1) -> a#(c(x1)) b#(x1) -> a#(a(c(x1))) c#(c(x1)) -> b#(x1) TRS: a(x1) -> x1 a(b(x1)) -> c(b(x1)) b(x1) -> a(a(c(x1))) c(c(x1)) -> b(x1) TDG Processor: DPs: a#(b(x1)) -> c#(b(x1)) b#(x1) -> c#(x1) b#(x1) -> a#(c(x1)) b#(x1) -> a#(a(c(x1))) c#(c(x1)) -> b#(x1) TRS: a(x1) -> x1 a(b(x1)) -> c(b(x1)) b(x1) -> a(a(c(x1))) c(c(x1)) -> b(x1) graph: b#(x1) -> c#(x1) -> c#(c(x1)) -> b#(x1) b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> c#(b(x1)) b#(x1) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(b(x1)) c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(a(c(x1))) c#(c(x1)) -> b#(x1) -> b#(x1) -> a#(c(x1)) c#(c(x1)) -> b#(x1) -> b#(x1) -> c#(x1) a#(b(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1) Root-Labeling Processor: DPs: a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) TRS: f6(a)(a(f6)(x1)) -> f6(f6)(x1) f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(b)(x1)) -> f6(b)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f6)(x1)) -> c(f6)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) -> a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) -> a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) -> a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) -> a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) -> c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) -> c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) -> c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) -> c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) -> f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) -> f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) -> f6(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(f6)(x1)) -> a(a)(a(a)(a(c)(c(f6)(x1)))) a(b)(b(a)(x1)) -> a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(b)(x1)) -> a(a)(a(a)(a(c)(c(b)(x1)))) a(b)(b(c)(x1)) -> a(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) -> c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) -> c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) -> c(a)(a(a)(a(c)(c(c)(x1)))) f6(c)(c(c)(c(f6)(x1))) -> f6(b)(b(f6)(x1)) f6(c)(c(c)(c(a)(x1))) -> f6(b)(b(a)(x1)) f6(c)(c(c)(c(b)(x1))) -> f6(b)(b(b)(x1)) f6(c)(c(c)(c(c)(x1))) -> f6(b)(b(c)(x1)) a(c)(c(c)(c(f6)(x1))) -> a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) -> a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) -> a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) -> a(b)(b(c)(x1)) b(c)(c(c)(c(f6)(x1))) -> b(b)(b(f6)(x1)) b(c)(c(c)(c(a)(x1))) -> b(b)(b(a)(x1)) b(c)(c(c)(c(b)(x1))) -> b(b)(b(b)(x1)) b(c)(c(c)(c(c)(x1))) -> b(b)(b(c)(x1)) c(c)(c(c)(c(f6)(x1))) -> c(b)(b(f6)(x1)) c(c)(c(c)(c(a)(x1))) -> c(b)(b(a)(x1)) c(c)(c(c)(c(b)(x1))) -> c(b)(b(b)(x1)) c(c)(c(c)(c(c)(x1))) -> c(b)(b(c)(x1)) TDG Processor: DPs: a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) TRS: f6(a)(a(f6)(x1)) -> f6(f6)(x1) f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(b)(x1)) -> f6(b)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f6)(x1)) -> c(f6)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) -> a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) -> a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) -> a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) -> a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) -> c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) -> c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) -> c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) -> c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) -> f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) -> f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) -> f6(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(f6)(x1)) -> a(a)(a(a)(a(c)(c(f6)(x1)))) a(b)(b(a)(x1)) -> a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(b)(x1)) -> a(a)(a(a)(a(c)(c(b)(x1)))) a(b)(b(c)(x1)) -> a(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) -> c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) -> c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) -> c(a)(a(a)(a(c)(c(c)(x1)))) f6(c)(c(c)(c(f6)(x1))) -> f6(b)(b(f6)(x1)) f6(c)(c(c)(c(a)(x1))) -> f6(b)(b(a)(x1)) f6(c)(c(c)(c(b)(x1))) -> f6(b)(b(b)(x1)) f6(c)(c(c)(c(c)(x1))) -> f6(b)(b(c)(x1)) a(c)(c(c)(c(f6)(x1))) -> a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) -> a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) -> a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) -> a(b)(b(c)(x1)) b(c)(c(c)(c(f6)(x1))) -> b(b)(b(f6)(x1)) b(c)(c(c)(c(a)(x1))) -> b(b)(b(a)(x1)) b(c)(c(c)(c(b)(x1))) -> b(b)(b(b)(x1)) b(c)(c(c)(c(c)(x1))) -> b(b)(b(c)(x1)) c(c)(c(c)(c(f6)(x1))) -> c(b)(b(f6)(x1)) c(c)(c(c)(c(a)(x1))) -> c(b)(b(a)(x1)) c(c)(c(c)(c(b)(x1))) -> c(b)(b(b)(x1)) c(c)(c(c)(c(c)(x1))) -> c(b)(b(c)(x1)) graph: b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) -> a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) -> a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) -> a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) -> a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) -> b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) Polynomial Interpretation Processor: dimension: 1 interpretation: [c(f6)](x0) = x0, [f6(f6)](x0) = x0 + 1, [f6(b)](x0) = x0 + 1, [f6(a)](x0) = x0 + 1, [c(c)](x0) = x0, [c(a)](x0) = x0, [f6(c)](x0) = x0 + 1, [a(c)](x0) = x0, [c{#,(f6)}](x0) = x0 + 1, [a{#,(f6)}](x0) = x0 + 1, [c(b)](x0) = x0, [a(b)](x0) = x0, [b{#,(f6)}](x0) = x0 + 1, [b(b)](x0) = x0, [a(f6)](x0) = x0 + 1, [a(a)](x0) = x0, [b(a)](x0) = x0, [b(f6)](x0) = x0, [b(c)](x0) = x0 orientation: a{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(c)(x1)) f6(a)(a(f6)(x1)) = x1 + 2 >= x1 + 1 = f6(f6)(x1) f6(a)(a(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(x1) f6(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = f6(b)(x1) f6(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = f6(c)(x1) a(a)(a(f6)(x1)) = x1 + 1 >= x1 + 1 = a(f6)(x1) a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(x1) a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) b(a)(a(f6)(x1)) = x1 + 1 >= x1 = b(f6)(x1) b(a)(a(a)(x1)) = x1 >= x1 = b(a)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) c(a)(a(f6)(x1)) = x1 + 1 >= x1 = c(f6)(x1) c(a)(a(a)(x1)) = x1 >= x1 = c(a)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) f6(a)(a(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) = x1 >= x1 = a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) = x1 >= x1 = a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) = x1 >= x1 = a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) = x1 >= x1 = a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) = x1 >= x1 = b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) = x1 >= x1 = b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) = x1 >= x1 = b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) = x1 >= x1 = b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) = x1 >= x1 = c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) = x1 >= x1 = c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) = x1 >= x1 = c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) = x1 >= x1 = c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(f6)(x1)) = x1 >= x1 = a(a)(a(a)(a(c)(c(f6)(x1)))) a(b)(b(a)(x1)) = x1 >= x1 = a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(b)(x1)) = x1 >= x1 = a(a)(a(a)(a(c)(c(b)(x1)))) a(b)(b(c)(x1)) = x1 >= x1 = a(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) = x1 >= x1 = b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) = x1 >= x1 = b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) = x1 >= x1 = b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) = x1 >= x1 = b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) = x1 >= x1 = c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) = x1 >= x1 = c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) = x1 >= x1 = c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) = x1 >= x1 = c(a)(a(a)(a(c)(c(c)(x1)))) f6(c)(c(c)(c(f6)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(f6)(x1)) f6(c)(c(c)(c(a)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(a)(x1)) f6(c)(c(c)(c(b)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(b)(x1)) f6(c)(c(c)(c(c)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(c)(x1)) a(c)(c(c)(c(f6)(x1))) = x1 >= x1 = a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) = x1 >= x1 = a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) = x1 >= x1 = a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) = x1 >= x1 = a(b)(b(c)(x1)) b(c)(c(c)(c(f6)(x1))) = x1 >= x1 = b(b)(b(f6)(x1)) b(c)(c(c)(c(a)(x1))) = x1 >= x1 = b(b)(b(a)(x1)) b(c)(c(c)(c(b)(x1))) = x1 >= x1 = b(b)(b(b)(x1)) b(c)(c(c)(c(c)(x1))) = x1 >= x1 = b(b)(b(c)(x1)) c(c)(c(c)(c(f6)(x1))) = x1 >= x1 = c(b)(b(f6)(x1)) c(c)(c(c)(c(a)(x1))) = x1 >= x1 = c(b)(b(a)(x1)) c(c)(c(c)(c(b)(x1))) = x1 >= x1 = c(b)(b(b)(x1)) c(c)(c(c)(c(c)(x1))) = x1 >= x1 = c(b)(b(c)(x1)) problem: DPs: a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) TRS: f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(b)(x1)) -> f6(b)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(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) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) -> a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) -> a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) -> a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) -> a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) -> c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) -> c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) -> c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) -> c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) -> f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) -> f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) -> f6(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(f6)(x1)) -> a(a)(a(a)(a(c)(c(f6)(x1)))) a(b)(b(a)(x1)) -> a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(b)(x1)) -> a(a)(a(a)(a(c)(c(b)(x1)))) a(b)(b(c)(x1)) -> a(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) -> c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) -> c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) -> c(a)(a(a)(a(c)(c(c)(x1)))) f6(c)(c(c)(c(f6)(x1))) -> f6(b)(b(f6)(x1)) f6(c)(c(c)(c(a)(x1))) -> f6(b)(b(a)(x1)) f6(c)(c(c)(c(b)(x1))) -> f6(b)(b(b)(x1)) f6(c)(c(c)(c(c)(x1))) -> f6(b)(b(c)(x1)) a(c)(c(c)(c(f6)(x1))) -> a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) -> a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) -> a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) -> a(b)(b(c)(x1)) b(c)(c(c)(c(f6)(x1))) -> b(b)(b(f6)(x1)) b(c)(c(c)(c(a)(x1))) -> b(b)(b(a)(x1)) b(c)(c(c)(c(b)(x1))) -> b(b)(b(b)(x1)) b(c)(c(c)(c(c)(x1))) -> b(b)(b(c)(x1)) c(c)(c(c)(c(f6)(x1))) -> c(b)(b(f6)(x1)) c(c)(c(c)(c(a)(x1))) -> c(b)(b(a)(x1)) c(c)(c(c)(c(b)(x1))) -> c(b)(b(b)(x1)) c(c)(c(c)(c(c)(x1))) -> c(b)(b(c)(x1)) Polynomial Interpretation Processor: dimension: 1 interpretation: [c(f6)](x0) = x0, [f6(f6)](x0) = x0, [f6(b)](x0) = x0 + 1, [f6(a)](x0) = x0 + 1, [c(c)](x0) = x0 + 1, [c(a)](x0) = x0 + 1, [f6(c)](x0) = x0 + 1, [a(c)](x0) = x0, [c{#,(f6)}](x0) = x0, [a{#,(f6)}](x0) = x0, [c(b)](x0) = x0 + 1, [a(b)](x0) = x0 + 1, [b{#,(f6)}](x0) = x0 + 1, [b(b)](x0) = x0 + 1, [a(f6)](x0) = x0 + 1, [a(a)](x0) = x0, [b(a)](x0) = x0 + 1, [b(f6)](x0) = x0, [b(c)](x0) = x0 + 1 orientation: a{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = x1 + 1 >= x1 = c{#,(f6)}(f6(f6)(x1)) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(a)(x1)) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(b)(x1)) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(c)(x1)) b{#,(f6)}(f6(f6)(x1)) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) = x1 + 2 >= x1 + 2 = a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f6)}(f6(c)(x1)) f6(a)(a(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(x1) f6(a)(a(b)(x1)) = x1 + 2 >= x1 + 1 = f6(b)(x1) f6(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = f6(c)(x1) a(a)(a(f6)(x1)) = x1 + 1 >= x1 + 1 = a(f6)(x1) a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = a(b)(x1) a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) b(a)(a(a)(x1)) = x1 + 1 >= x1 + 1 = b(a)(x1) b(a)(a(b)(x1)) = x1 + 2 >= x1 + 1 = b(b)(x1) b(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = b(c)(x1) c(a)(a(a)(x1)) = x1 + 1 >= x1 + 1 = c(a)(x1) c(a)(a(b)(x1)) = x1 + 2 >= x1 + 1 = c(b)(x1) c(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = c(c)(x1) f6(a)(a(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) = x1 + 3 >= x1 + 3 = f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) = x1 + 3 >= x1 + 3 = f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) = x1 + 3 >= x1 + 3 = f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) = x1 + 3 >= x1 + 3 = b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) = x1 + 3 >= x1 + 3 = b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) = x1 + 3 >= x1 + 3 = b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) = x1 + 3 >= x1 + 3 = c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) = x1 + 2 >= x1 + 2 = f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) = x1 + 2 >= x1 + 2 = f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) = x1 + 2 >= x1 + 2 = f6(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(f6)(x1)) = x1 + 1 >= x1 = a(a)(a(a)(a(c)(c(f6)(x1)))) a(b)(b(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(b)(x1)) = x1 + 2 >= x1 + 1 = a(a)(a(a)(a(c)(c(b)(x1)))) a(b)(b(c)(x1)) = x1 + 2 >= x1 + 1 = a(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) = x1 + 1 >= x1 + 1 = b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) = x1 + 2 >= x1 + 2 = b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) = x1 + 1 >= x1 + 1 = c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) = x1 + 2 >= x1 + 2 = c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) = x1 + 2 >= x1 + 2 = c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) = x1 + 2 >= x1 + 2 = c(a)(a(a)(a(c)(c(c)(x1)))) f6(c)(c(c)(c(f6)(x1))) = x1 + 2 >= x1 + 1 = f6(b)(b(f6)(x1)) f6(c)(c(c)(c(a)(x1))) = x1 + 3 >= x1 + 2 = f6(b)(b(a)(x1)) f6(c)(c(c)(c(b)(x1))) = x1 + 3 >= x1 + 2 = f6(b)(b(b)(x1)) f6(c)(c(c)(c(c)(x1))) = x1 + 3 >= x1 + 2 = f6(b)(b(c)(x1)) a(c)(c(c)(c(f6)(x1))) = x1 + 1 >= x1 + 1 = a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) = x1 + 2 >= x1 + 2 = a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = a(b)(b(c)(x1)) b(c)(c(c)(c(f6)(x1))) = x1 + 2 >= x1 + 1 = b(b)(b(f6)(x1)) b(c)(c(c)(c(a)(x1))) = x1 + 3 >= x1 + 2 = b(b)(b(a)(x1)) b(c)(c(c)(c(b)(x1))) = x1 + 3 >= x1 + 2 = b(b)(b(b)(x1)) b(c)(c(c)(c(c)(x1))) = x1 + 3 >= x1 + 2 = b(b)(b(c)(x1)) c(c)(c(c)(c(f6)(x1))) = x1 + 2 >= x1 + 1 = c(b)(b(f6)(x1)) c(c)(c(c)(c(a)(x1))) = x1 + 3 >= x1 + 2 = c(b)(b(a)(x1)) c(c)(c(c)(c(b)(x1))) = x1 + 3 >= x1 + 2 = c(b)(b(b)(x1)) c(c)(c(c)(c(c)(x1))) = x1 + 3 >= x1 + 2 = c(b)(b(c)(x1)) problem: DPs: a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) -> b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) -> b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) -> b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) -> b{#,(f6)}(f6(c)(x1)) TRS: f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(c)(x1)) -> c(c)(x1) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) -> a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) -> a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) -> a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) -> a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) -> c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) -> c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) -> c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) -> c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) -> f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) -> f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) -> f6(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) -> c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) -> c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) -> c(a)(a(a)(a(c)(c(c)(x1)))) a(c)(c(c)(c(f6)(x1))) -> a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) -> a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) -> a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) -> a(b)(b(c)(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(c)(x1)) -> b(c)(x1) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) interpretation: [c(f6)](x0) = 0, [f6(f6)](x0) = 0, [f6(b)](x0) = 1, [f6(a)](x0) = 0, [c(c)](x0) = 0, [c(a)](x0) = 0, [f6(c)](x0) = 0, [a(c)](x0) = 0, [c{#,(f6)}](x0) = 1, [a{#,(f6)}](x0) = x0, [c(b)](x0) = 0, [a(b)](x0) = 0, [b{#,(f6)}](x0) = 0, [b(b)](x0) = 0, [a(f6)](x0) = 0, [a(a)](x0) = 0, [b(a)](x0) = 0, [b(f6)](x0) = 0, [b(c)](x0) = 0 orientation: a{#,(f6)}(f6(b)(b(f6)(x1))) = 1 >= 1 = c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) = 1 >= 1 = c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) = 1 >= 1 = c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) = 1 >= 1 = c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = 0 >= 0 = a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) = 0 >= 0 = a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) = 0 >= 0 = a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) = 0 >= 0 = a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) = 0 >= 0 = a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) = 0 >= 0 = a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) = 0 >= 0 = a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) = 0 >= 0 = a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) c{#,(f6)}(f6(c)(c(f6)(x1))) = 1 >= 0 = b{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(c)(c(a)(x1))) = 1 >= 0 = b{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(c)(c(b)(x1))) = 1 >= 0 = b{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(c)(c(c)(x1))) = 1 >= 0 = b{#,(f6)}(f6(c)(x1)) f6(a)(a(a)(x1)) = 0 >= 0 = f6(a)(x1) f6(a)(a(c)(x1)) = 0 >= 0 = f6(c)(x1) a(a)(a(f6)(x1)) = 0 >= 0 = a(f6)(x1) a(a)(a(a)(x1)) = 0 >= 0 = a(a)(x1) a(a)(a(b)(x1)) = 0 >= 0 = a(b)(x1) a(a)(a(c)(x1)) = 0 >= 0 = a(c)(x1) b(a)(a(a)(x1)) = 0 >= 0 = b(a)(x1) b(a)(a(c)(x1)) = 0 >= 0 = b(c)(x1) c(a)(a(a)(x1)) = 0 >= 0 = c(a)(x1) c(a)(a(c)(x1)) = 0 >= 0 = c(c)(x1) f6(a)(a(b)(b(f6)(x1))) = 0 >= 0 = f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) = 0 >= 0 = f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) = 0 >= 0 = f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) = 0 >= 0 = f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) = 0 >= 0 = a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) = 0 >= 0 = a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) = 0 >= 0 = a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) = 0 >= 0 = a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) = 0 >= 0 = b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) = 0 >= 0 = b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) = 0 >= 0 = b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) = 0 >= 0 = b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) = 0 >= 0 = c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) = 0 >= 0 = c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) = 0 >= 0 = c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) = 0 >= 0 = c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) = 1 >= 0 = f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) = 1 >= 0 = f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) = 1 >= 0 = f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) = 1 >= 0 = f6(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) = 0 >= 0 = b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) = 0 >= 0 = b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) = 0 >= 0 = b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) = 0 >= 0 = b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) = 0 >= 0 = c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) = 0 >= 0 = c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) = 0 >= 0 = c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) = 0 >= 0 = c(a)(a(a)(a(c)(c(c)(x1)))) a(c)(c(c)(c(f6)(x1))) = 0 >= 0 = a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) = 0 >= 0 = a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) = 0 >= 0 = a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) = 0 >= 0 = a(b)(b(c)(x1)) problem: DPs: a{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(b)(b(f6)(x1))) a{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(b)(b(a)(x1))) a{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(b(b)(x1))) a{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(b)(b(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(c)(c(f6)(x1))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(c)(c(a)(x1))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(c)(c(b)(x1))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(c)(c(c)(x1))) b{#,(f6)}(f6(f6)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(f6)(x1)))) b{#,(f6)}(f6(a)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(a)(x1)))) b{#,(f6)}(f6(b)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(b)(x1)))) b{#,(f6)}(f6(c)(x1)) -> a{#,(f6)}(f6(a)(a(c)(c(c)(x1)))) TRS: f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(c)(x1)) -> c(c)(x1) f6(a)(a(b)(b(f6)(x1))) -> f6(c)(c(b)(b(f6)(x1))) f6(a)(a(b)(b(a)(x1))) -> f6(c)(c(b)(b(a)(x1))) f6(a)(a(b)(b(b)(x1))) -> f6(c)(c(b)(b(b)(x1))) f6(a)(a(b)(b(c)(x1))) -> f6(c)(c(b)(b(c)(x1))) a(a)(a(b)(b(f6)(x1))) -> a(c)(c(b)(b(f6)(x1))) a(a)(a(b)(b(a)(x1))) -> a(c)(c(b)(b(a)(x1))) a(a)(a(b)(b(b)(x1))) -> a(c)(c(b)(b(b)(x1))) a(a)(a(b)(b(c)(x1))) -> a(c)(c(b)(b(c)(x1))) b(a)(a(b)(b(f6)(x1))) -> b(c)(c(b)(b(f6)(x1))) b(a)(a(b)(b(a)(x1))) -> b(c)(c(b)(b(a)(x1))) b(a)(a(b)(b(b)(x1))) -> b(c)(c(b)(b(b)(x1))) b(a)(a(b)(b(c)(x1))) -> b(c)(c(b)(b(c)(x1))) c(a)(a(b)(b(f6)(x1))) -> c(c)(c(b)(b(f6)(x1))) c(a)(a(b)(b(a)(x1))) -> c(c)(c(b)(b(a)(x1))) c(a)(a(b)(b(b)(x1))) -> c(c)(c(b)(b(b)(x1))) c(a)(a(b)(b(c)(x1))) -> c(c)(c(b)(b(c)(x1))) f6(b)(b(f6)(x1)) -> f6(a)(a(a)(a(c)(c(f6)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(a(a)(a(c)(c(a)(x1)))) f6(b)(b(b)(x1)) -> f6(a)(a(a)(a(c)(c(b)(x1)))) f6(b)(b(c)(x1)) -> f6(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(f6)(x1)) -> b(a)(a(a)(a(c)(c(f6)(x1)))) b(b)(b(a)(x1)) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(b)(x1)) -> b(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(c)(x1)) -> b(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(f6)(x1)) -> c(a)(a(a)(a(c)(c(f6)(x1)))) c(b)(b(a)(x1)) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(b)(x1)) -> c(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(c)(x1)) -> c(a)(a(a)(a(c)(c(c)(x1)))) a(c)(c(c)(c(f6)(x1))) -> a(b)(b(f6)(x1)) a(c)(c(c)(c(a)(x1))) -> a(b)(b(a)(x1)) a(c)(c(c)(c(b)(x1))) -> a(b)(b(b)(x1)) a(c)(c(c)(c(c)(x1))) -> a(b)(b(c)(x1)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 112/144