YES Problem: a(x1) -> x1 a(a(x1)) -> a(b(c(x1))) b(x1) -> x1 c(b(x1)) -> b(a(c(x1))) Proof: DP Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> b#(a(c(x1))) TRS: a(x1) -> x1 a(a(x1)) -> a(b(c(x1))) b(x1) -> x1 c(b(x1)) -> b(a(c(x1))) TDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> b#(a(c(x1))) TRS: a(x1) -> x1 a(a(x1)) -> a(b(c(x1))) b(x1) -> x1 c(b(x1)) -> b(a(c(x1))) graph: c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(c(x1))) 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(c(x1))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1)) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(c(x1))) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1) SCC Processor: #sccs: 1 #rules: 4 #arcs: 12/36 DPs: c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(b(c(x1))) TRS: a(x1) -> x1 a(a(x1)) -> a(b(c(x1))) b(x1) -> x1 c(b(x1)) -> b(a(c(x1))) Root-Labeling Processor: DPs: c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) TRS: f6(a)(a(f6)(x1)) -> f6(f6)(x1) f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(b)(x1)) -> f6(b)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f6)(x1)) -> c(f6)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(a)(x1)) -> a(b)(b(c)(c(a)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) f6(b)(b(f6)(x1)) -> f6(f6)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) f6(b)(b(b)(x1)) -> f6(b)(x1) f6(b)(b(c)(x1)) -> f6(c)(x1) a(b)(b(f6)(x1)) -> a(f6)(x1) a(b)(b(a)(x1)) -> a(a)(x1) a(b)(b(b)(x1)) -> a(b)(x1) a(b)(b(c)(x1)) -> a(c)(x1) b(b)(b(f6)(x1)) -> b(f6)(x1) b(b)(b(a)(x1)) -> b(a)(x1) b(b)(b(b)(x1)) -> b(b)(x1) b(b)(b(c)(x1)) -> b(c)(x1) c(b)(b(f6)(x1)) -> c(f6)(x1) c(b)(b(a)(x1)) -> c(a)(x1) c(b)(b(b)(x1)) -> c(b)(x1) c(b)(b(c)(x1)) -> c(c)(x1) f6(c)(c(b)(b(f6)(x1))) -> f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) -> f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) -> f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) -> f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) TDG Processor: DPs: c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) TRS: f6(a)(a(f6)(x1)) -> f6(f6)(x1) f6(a)(a(a)(x1)) -> f6(a)(x1) f6(a)(a(b)(x1)) -> f6(b)(x1) f6(a)(a(c)(x1)) -> f6(c)(x1) a(a)(a(f6)(x1)) -> a(f6)(x1) a(a)(a(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(x1) a(a)(a(c)(x1)) -> a(c)(x1) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(a)(x1)) -> b(a)(x1) b(a)(a(b)(x1)) -> b(b)(x1) b(a)(a(c)(x1)) -> b(c)(x1) c(a)(a(f6)(x1)) -> c(f6)(x1) c(a)(a(a)(x1)) -> c(a)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(a)(x1)) -> a(b)(b(c)(c(a)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) f6(b)(b(f6)(x1)) -> f6(f6)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) f6(b)(b(b)(x1)) -> f6(b)(x1) f6(b)(b(c)(x1)) -> f6(c)(x1) a(b)(b(f6)(x1)) -> a(f6)(x1) a(b)(b(a)(x1)) -> a(a)(x1) a(b)(b(b)(x1)) -> a(b)(x1) a(b)(b(c)(x1)) -> a(c)(x1) b(b)(b(f6)(x1)) -> b(f6)(x1) b(b)(b(a)(x1)) -> b(a)(x1) b(b)(b(b)(x1)) -> b(b)(x1) b(b)(b(c)(x1)) -> b(c)(x1) c(b)(b(f6)(x1)) -> c(f6)(x1) c(b)(b(a)(x1)) -> c(a)(x1) c(b)(b(b)(x1)) -> c(b)(x1) c(b)(b(c)(x1)) -> c(c)(x1) f6(c)(c(b)(b(f6)(x1))) -> f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) -> f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) -> f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) -> f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) graph: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) -> a{#,(f6)}(f6(a)(a(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> a{#,(f6)}(f6(c)(c(c)(x1))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(c)(x1))) -> c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(b)(x1))) -> c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) -> c{#,(f6)}(f6(b)(b(f6)(x1))) -> c{#,(f6)}(f6(f6)(x1)) Polynomial Interpretation Processor: dimension: 1 interpretation: [c(a)](x0) = x0, [f6(c)](x0) = x0, [f6(b)](x0) = x0, [a{#,(f6)}](x0) = x0, [a(f6)](x0) = x0, [c(b)](x0) = x0, [c(f6)](x0) = x0, [a(a)](x0) = x0 + 1, [f6(f6)](x0) = x0, [c{#,(f6)}](x0) = x0, [c(c)](x0) = x0, [b(c)](x0) = x0 + 1, [f6(a)](x0) = x0 + 1, [a(b)](x0) = x0, [a(c)](x0) = x0, [b(a)](x0) = x0 + 1, [b(f6)](x0) = x0 + 1, [b(b)](x0) = x0 + 1 orientation: c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(f6)(x1)) c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c{#,(f6)}(f6(a)(x1)) c{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(b)(x1)) c{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(c)(x1)) c{#,(f6)}(f6(b)(b(f6)(x1))) = x1 + 1 >= x1 = a{#,(f6)}(f6(c)(c(f6)(x1))) c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 1 >= x1 = a{#,(f6)}(f6(c)(c(a)(x1))) c{#,(f6)}(f6(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f6)}(f6(c)(c(b)(x1))) c{#,(f6)}(f6(b)(b(c)(x1))) = x1 + 1 >= x1 = a{#,(f6)}(f6(c)(c(c)(x1))) a{#,(f6)}(f6(a)(a(f6)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(f6)(x1)) a{#,(f6)}(f6(a)(a(a)(x1))) = x1 + 2 >= x1 + 1 = c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(b)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(b)(x1)) a{#,(f6)}(f6(a)(a(c)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(c)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(a)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(a)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) f6(a)(a(f6)(x1)) = x1 + 1 >= x1 = f6(f6)(x1) f6(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = f6(a)(x1) f6(a)(a(b)(x1)) = x1 + 1 >= x1 = f6(b)(x1) f6(a)(a(c)(x1)) = x1 + 1 >= x1 = f6(c)(x1) a(a)(a(f6)(x1)) = x1 + 1 >= x1 = a(f6)(x1) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(x1) a(a)(a(b)(x1)) = x1 + 1 >= x1 = a(b)(x1) a(a)(a(c)(x1)) = x1 + 1 >= x1 = a(c)(x1) b(a)(a(f6)(x1)) = x1 + 1 >= x1 + 1 = b(f6)(x1) b(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = b(a)(x1) b(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = b(b)(x1) b(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = b(c)(x1) c(a)(a(f6)(x1)) = x1 >= x1 = c(f6)(x1) c(a)(a(a)(x1)) = x1 + 1 >= 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(f6)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(c)(c(f6)(x1))) a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(b)(b(c)(c(a)(x1))) a(a)(a(b)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(c)(c(c)(x1))) f6(b)(b(f6)(x1)) = x1 + 1 >= x1 = f6(f6)(x1) f6(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(x1) f6(b)(b(b)(x1)) = x1 + 1 >= x1 = f6(b)(x1) f6(b)(b(c)(x1)) = x1 + 1 >= x1 = f6(c)(x1) a(b)(b(f6)(x1)) = x1 + 1 >= x1 = a(f6)(x1) a(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = a(a)(x1) a(b)(b(b)(x1)) = x1 + 1 >= x1 = a(b)(x1) a(b)(b(c)(x1)) = x1 + 1 >= x1 = a(c)(x1) b(b)(b(f6)(x1)) = x1 + 2 >= x1 + 1 = b(f6)(x1) b(b)(b(a)(x1)) = x1 + 2 >= x1 + 1 = b(a)(x1) b(b)(b(b)(x1)) = x1 + 2 >= x1 + 1 = b(b)(x1) b(b)(b(c)(x1)) = x1 + 2 >= x1 + 1 = b(c)(x1) c(b)(b(f6)(x1)) = x1 + 1 >= x1 = c(f6)(x1) c(b)(b(a)(x1)) = x1 + 1 >= x1 = c(a)(x1) c(b)(b(b)(x1)) = x1 + 1 >= x1 = c(b)(x1) c(b)(b(c)(x1)) = x1 + 1 >= x1 = c(c)(x1) f6(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 + 1 = c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) = x1 + 1 >= x1 + 1 = c(b)(b(a)(a(c)(c(c)(x1)))) problem: DPs: c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) TRS: b(a)(a(f6)(x1)) -> b(f6)(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(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) f6(b)(b(a)(x1)) -> f6(a)(x1) a(b)(b(a)(x1)) -> a(a)(x1) f6(c)(c(b)(b(f6)(x1))) -> f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) -> f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) -> f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) -> f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) SCC Processor: #sccs: 2 #rules: 4 #arcs: 128/16 DPs: c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) TRS: b(a)(a(f6)(x1)) -> b(f6)(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(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) f6(b)(b(a)(x1)) -> f6(a)(x1) a(b)(b(a)(x1)) -> a(a)(x1) f6(c)(c(b)(b(f6)(x1))) -> f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) -> f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) -> f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) -> f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) Usable Rule Processor: DPs: c{#,(f6)}(f6(b)(b(a)(x1))) -> c{#,(f6)}(f6(a)(x1)) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [f6(b)](x0) = x0 + 1, [c{#,(f6)}](x0) = x0, [f6(a)](x0) = x0, [b(a)](x0) = x0 orientation: c{#,(f6)}(f6(b)(b(a)(x1))) = x1 + 1 >= x1 = c{#,(f6)}(f6(a)(x1)) problem: DPs: TRS: Qed DPs: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) TRS: b(a)(a(f6)(x1)) -> b(f6)(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(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) f6(b)(b(a)(x1)) -> f6(a)(x1) a(b)(b(a)(x1)) -> a(a)(x1) f6(c)(c(b)(b(f6)(x1))) -> f6(b)(b(a)(a(c)(c(f6)(x1)))) f6(c)(c(b)(b(a)(x1))) -> f6(b)(b(a)(a(c)(c(a)(x1)))) f6(c)(c(b)(b(b)(x1))) -> f6(b)(b(a)(a(c)(c(b)(x1)))) f6(c)(c(b)(b(c)(x1))) -> f6(b)(b(a)(a(c)(c(c)(x1)))) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) Usable Rule Processor: DPs: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) TRS: c(c)(c(b)(b(f6)(x1))) -> c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) -> b(c)(x1) b(c)(c(b)(b(f6)(x1))) -> b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(f6)(x1)) -> c(f6)(x1) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(c)(c(b)(b(f6)(x1))) -> a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) -> a(a)(x1) a(a)(a(f6)(x1)) -> a(b)(b(c)(c(f6)(x1))) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(b)(x1)) -> b(b)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) Polynomial Interpretation Processor: dimension: 1 interpretation: [c(a)](x0) = x0, [f6(b)](x0) = x0, [a{#,(f6)}](x0) = x0, [a(f6)](x0) = x0 + 1, [c(b)](x0) = x0, [c(f6)](x0) = x0, [a(a)](x0) = x0, [c(c)](x0) = x0, [b(c)](x0) = x0, [f6(a)](x0) = x0, [a(b)](x0) = x0, [a(c)](x0) = x0, [b(a)](x0) = x0, [b(f6)](x0) = x0 + 1, [b(b)](x0) = x0 orientation: a{#,(f6)}(f6(a)(a(c)(x1))) = x1 >= x1 = a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(f6)(x1))) = x1 + 1 >= x1 = a{#,(f6)}(f6(b)(b(c)(c(f6)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) = x1 >= x1 = a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 = c(b)(b(a)(a(c)(c(f6)(x1)))) c(c)(c(b)(b(a)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) b(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 = b(b)(b(a)(a(c)(c(f6)(x1)))) b(c)(c(b)(b(a)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(f6)(x1)) = x1 + 1 >= x1 = c(f6)(x1) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(c)(c(b)(b(f6)(x1))) = x1 + 1 >= x1 = a(b)(b(a)(a(c)(c(f6)(x1)))) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(f6)(x1)) = x1 + 1 >= x1 = a(b)(b(c)(c(f6)(x1))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(c)(c(c)(x1))) b(a)(a(f6)(x1)) = x1 + 1 >= x1 + 1 = b(f6)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) f6(b)(b(a)(x1)) = x1 >= x1 = f6(a)(x1) problem: DPs: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) TRS: c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) -> b(c)(x1) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) b(a)(a(f6)(x1)) -> b(f6)(x1) b(a)(a(b)(x1)) -> b(b)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) Polynomial Interpretation Processor: dimension: 1 interpretation: [c(a)](x0) = x0, [f6(b)](x0) = x0, [a{#,(f6)}](x0) = x0 + 1, [a(f6)](x0) = x0 + 1, [c(b)](x0) = x0, [a(a)](x0) = x0, [c(c)](x0) = x0, [b(c)](x0) = x0, [f6(a)](x0) = x0, [a(b)](x0) = x0, [a(c)](x0) = x0, [b(a)](x0) = x0, [b(f6)](x0) = x0, [b(b)](x0) = x0 orientation: a{#,(f6)}(f6(a)(a(c)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c(c)(c(b)(b(a)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) = x1 >= x1 = c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) = x1 >= x1 = b(c)(x1) b(c)(c(b)(b(a)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) = x1 >= x1 = b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) = x1 >= x1 = c(b)(x1) c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) a(c)(c(b)(b(a)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) = x1 >= x1 = a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) = x1 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) = x1 >= x1 = a(b)(b(c)(c(c)(x1))) b(a)(a(f6)(x1)) = x1 + 1 >= x1 = b(f6)(x1) b(a)(a(b)(x1)) = x1 >= x1 = b(b)(x1) f6(b)(b(a)(x1)) = x1 >= x1 = f6(a)(x1) problem: DPs: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) TRS: c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) -> b(c)(x1) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) b(a)(a(b)(x1)) -> b(b)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) Polynomial Interpretation Processor: dimension: 1 usable rules: c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(x1) interpretation: [c(a)](x0) = 0, [f6(b)](x0) = x0, [a{#,(f6)}](x0) = x0, [c(b)](x0) = 0, [a(a)](x0) = 0, [c(c)](x0) = 1, [b(c)](x0) = x0, [f6(a)](x0) = x0, [a(b)](x0) = 1, [a(c)](x0) = 1, [b(a)](x0) = x0 + 1, [b(b)](x0) = 0 orientation: a{#,(f6)}(f6(a)(a(c)(x1))) = 1 >= 1 = a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) a{#,(f6)}(f6(a)(a(b)(x1))) = 1 >= 0 = a{#,(f6)}(f6(b)(b(c)(c(b)(x1)))) c(c)(c(b)(b(a)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) = 2 >= x1 = b(c)(x1) b(c)(c(b)(b(a)(x1))) = 0 >= 0 = b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) = 0 >= 0 = b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) = 0 >= 0 = b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) = 0 >= 0 = c(b)(x1) c(a)(a(c)(x1)) = 0 >= 1 = c(c)(x1) a(c)(c(b)(b(a)(x1))) = 1 >= 1 = a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) = 1 >= 1 = a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) = 1 >= 1 = a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) = 1 >= 0 = a(a)(x1) a(a)(a(b)(x1)) = 0 >= 1 = a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) = 0 >= 1 = a(b)(b(c)(c(c)(x1))) b(a)(a(b)(x1)) = 2 >= 0 = b(b)(x1) f6(b)(b(a)(x1)) = x1 + 1 >= x1 = f6(a)(x1) problem: DPs: a{#,(f6)}(f6(a)(a(c)(x1))) -> a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) TRS: c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) -> b(c)(x1) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) b(a)(a(b)(x1)) -> b(b)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) Polynomial Interpretation Processor: dimension: 1 usable rules: b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) f6(b)(b(a)(x1)) -> f6(a)(x1) interpretation: [c(a)](x0) = 0, [f6(b)](x0) = x0, [a{#,(f6)}](x0) = x0 + 1, [c(b)](x0) = 0, [a(a)](x0) = x0, [c(c)](x0) = 1, [b(c)](x0) = 1, [f6(a)](x0) = x0 + 1, [a(b)](x0) = 0, [a(c)](x0) = 1, [b(a)](x0) = x0 + 1, [b(b)](x0) = 1 orientation: a{#,(f6)}(f6(a)(a(c)(x1))) = 3 >= 2 = a{#,(f6)}(f6(b)(b(c)(c(c)(x1)))) c(c)(c(b)(b(a)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) = 1 >= 0 = c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) = 2 >= 1 = b(c)(x1) b(c)(c(b)(b(a)(x1))) = 1 >= 1 = b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) = 1 >= 1 = b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) = 1 >= 1 = b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) = 0 >= 0 = c(b)(x1) c(a)(a(c)(x1)) = 0 >= 1 = c(c)(x1) a(c)(c(b)(b(a)(x1))) = 1 >= 0 = a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) = 1 >= 0 = a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) = 1 >= 0 = a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) = 0 >= x1 = a(a)(x1) a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) = 1 >= 0 = a(b)(b(c)(c(c)(x1))) b(a)(a(b)(x1)) = 1 >= 1 = b(b)(x1) f6(b)(b(a)(x1)) = x1 + 1 >= x1 + 1 = f6(a)(x1) problem: DPs: TRS: c(c)(c(b)(b(a)(x1))) -> c(b)(b(a)(a(c)(c(a)(x1)))) c(c)(c(b)(b(b)(x1))) -> c(b)(b(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(x1))) -> c(b)(b(a)(a(c)(c(c)(x1)))) b(a)(a(c)(x1)) -> b(c)(x1) b(c)(c(b)(b(a)(x1))) -> b(b)(b(a)(a(c)(c(a)(x1)))) b(c)(c(b)(b(b)(x1))) -> b(b)(b(a)(a(c)(c(b)(x1)))) b(c)(c(b)(b(c)(x1))) -> b(b)(b(a)(a(c)(c(c)(x1)))) c(a)(a(b)(x1)) -> c(b)(x1) c(a)(a(c)(x1)) -> c(c)(x1) a(c)(c(b)(b(a)(x1))) -> a(b)(b(a)(a(c)(c(a)(x1)))) a(c)(c(b)(b(b)(x1))) -> a(b)(b(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(x1))) -> a(b)(b(a)(a(c)(c(c)(x1)))) a(b)(b(a)(x1)) -> a(a)(x1) a(a)(a(b)(x1)) -> a(b)(b(c)(c(b)(x1))) a(a)(a(c)(x1)) -> a(b)(b(c)(c(c)(x1))) b(a)(a(b)(x1)) -> b(b)(x1) f6(b)(b(a)(x1)) -> f6(a)(x1) Qed