YES Problem: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) a(a(c(c(x1)))) -> c(c(a(a(b(b(x1)))))) Proof: String Reversal Processor: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) DP Processor: DPs: b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) TDG Processor: DPs: b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) graph: c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(a(a(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(a(a(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(b(b(x1))) -> c#(c(b(b(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) EDG Processor: DPs: b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) graph: c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(a(a(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> b#(a(a(c(c(x1))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) SCC Processor: #sccs: 1 #rules: 12 #arcs: 78/196 DPs: c#(c(a(a(x1)))) -> c#(c(x1)) c#(c(a(a(x1)))) -> b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) Arctic Interpretation Processor: dimension: 1 interpretation: [c#](x0) = 4x0, [b#](x0) = x0 + 4, [c](x0) = x0 + 0, [a](x0) = 2x0 + 8, [b](x0) = x0 + 0 orientation: c#(c(a(a(x1)))) = 8x1 + 14 >= 4x1 + 4 = c#(c(x1)) c#(c(a(a(x1)))) = 8x1 + 14 >= 4x1 + 10 = b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) = 4x1 + 10 >= 4x1 + 4 = c#(c(b(b(x1)))) c#(c(a(a(x1)))) = 8x1 + 14 >= 4x1 = c#(x1) c#(c(b(b(x1)))) = 4x1 + 4 >= x1 + 4 = b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) = 4x1 + 10 >= x1 + 4 = b#(b(x1)) b#(b(a(a(x1)))) = 4x1 + 10 >= x1 + 4 = b#(x1) c#(c(b(b(x1)))) = 4x1 + 4 >= x1 + 4 = b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) = 4x1 + 4 >= x1 + 4 = b#(b(c(c(x1)))) c#(c(b(b(x1)))) = 4x1 + 4 >= x1 + 4 = b#(c(c(x1))) c#(c(b(b(x1)))) = 4x1 + 4 >= 4x1 + 4 = c#(c(x1)) c#(c(b(b(x1)))) = 4x1 + 4 >= 4x1 = c#(x1) b(b(a(a(x1)))) = 4x1 + 10 >= 4x1 + 10 = a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) = x1 + 0 >= x1 + 0 = b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) = 4x1 + 10 >= 4x1 + 10 = b(b(a(a(c(c(x1)))))) problem: DPs: b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) EDG Processor: DPs: b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) graph: c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) -> b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(b(c(c(x1))))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [c#](x0) = 8x0, [b#](x0) = 6x0, [c](x0) = x0, [a](x0) = 1x0, [b](x0) = x0 orientation: b#(b(a(a(x1)))) = 8x1 >= 8x1 = c#(c(b(b(x1)))) c#(c(b(b(x1)))) = 8x1 >= 6x1 = b#(b(b(b(c(c(x1)))))) c#(c(b(b(x1)))) = 8x1 >= 6x1 = b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) = 8x1 >= 6x1 = b#(b(c(c(x1)))) c#(c(b(b(x1)))) = 8x1 >= 6x1 = b#(c(c(x1))) c#(c(b(b(x1)))) = 8x1 >= 8x1 = c#(c(x1)) c#(c(b(b(x1)))) = 8x1 >= 8x1 = c#(x1) b(b(a(a(x1)))) = 2x1 >= 2x1 = a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) = x1 >= x1 = b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) = 2x1 >= 2x1 = b(b(a(a(c(c(x1)))))) problem: DPs: b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) EDG Processor: DPs: b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) graph: c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(x1) b#(b(a(a(x1)))) -> c#(c(b(b(x1)))) -> c#(c(b(b(x1)))) -> c#(c(x1)) SCC Processor: #sccs: 1 #rules: 2 #arcs: 6/9 DPs: c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) Arctic Interpretation Processor: dimension: 1 interpretation: [c#](x0) = 8x0, [c](x0) = 8x0, [a](x0) = 0, [b](x0) = x0 orientation: c#(c(b(b(x1)))) = 16x1 >= 16x1 = c#(c(x1)) c#(c(b(b(x1)))) = 16x1 >= 8x1 = c#(x1) b(b(a(a(x1)))) = 0 >= 0 = a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) = 16x1 >= 16x1 = b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) = 16 >= 0 = b(b(a(a(c(c(x1)))))) problem: DPs: c#(c(b(b(x1)))) -> c#(c(x1)) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) EDG Processor: DPs: c#(c(b(b(x1)))) -> c#(c(x1)) TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) graph: c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) LPO Processor: argument filtering: pi(b) = [0] pi(a) = [] pi(c) = [0] pi(c#) = [0] precedence: c > b > c# ~ a problem: DPs: TRS: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) -> b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) -> b(b(a(a(c(c(x1)))))) Qed