/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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 usable rules: 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)))))) interpretation: [c#](x0) = x0, [b#](x0) = x0, [c](x0) = x0, [a](x0) = 1x0, [b](x0) = x0 orientation: c#(c(a(a(x1)))) = 2x1 >= x1 = c#(c(x1)) c#(c(a(a(x1)))) = 2x1 >= 2x1 = b#(b(a(a(c(c(x1)))))) b#(b(a(a(x1)))) = 2x1 >= x1 = c#(c(b(b(x1)))) c#(c(a(a(x1)))) = 2x1 >= x1 = c#(x1) c#(c(b(b(x1)))) = x1 >= x1 = b#(b(b(b(c(c(x1)))))) b#(b(a(a(x1)))) = 2x1 >= x1 = b#(b(x1)) b#(b(a(a(x1)))) = 2x1 >= x1 = b#(x1) c#(c(b(b(x1)))) = x1 >= x1 = b#(b(b(c(c(x1))))) c#(c(b(b(x1)))) = x1 >= x1 = b#(b(c(c(x1)))) c#(c(b(b(x1)))) = x1 >= x1 = b#(c(c(x1))) c#(c(b(b(x1)))) = x1 >= x1 = c#(c(x1)) c#(c(b(b(x1)))) = x1 >= x1 = 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: c#(c(a(a(x1)))) -> b#(b(a(a(c(c(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)))))) Restore Modifier: DPs: c#(c(a(a(x1)))) -> b#(b(a(a(c(c(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: c#(c(a(a(x1)))) -> b#(b(a(a(c(c(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(a(a(x1)))) -> b#(b(a(a(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(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(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) SCC Processor: #sccs: 1 #rules: 2 #arcs: 14/49 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 usable rules: 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)))))) interpretation: [c#](x0) = x0, [c](x0) = 1x0 + 1, [a](x0) = 0, [b](x0) = x0 + 0 orientation: c#(c(b(b(x1)))) = 1x1 + 1 >= 1x1 + 1 = c#(c(x1)) c#(c(b(b(x1)))) = 1x1 + 1 >= x1 = c#(x1) b(b(a(a(x1)))) = 0 >= 0 = a(a(c(c(b(b(x1)))))) c(c(b(b(x1)))) = 2x1 + 2 >= 2x1 + 2 = b(b(b(b(c(c(x1)))))) c(c(a(a(x1)))) = 2 >= 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)))))) Restore Modifier: 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] usable rules: 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)))))) 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