/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Proof: DP Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) TDG Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) graph: b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) EDG Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) graph: b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(b(b(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(a(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) interpretation: [b](x0) = 1x0 + 0, [b#](x0) = x0 + 0, [a](x0) = 1x0 + 0, [a#](x0) = x0 + 0 orientation: a#(a(b(a(x1)))) = 3x1 + 2 >= x1 + 0 = b#(x1) a#(a(b(a(x1)))) = 3x1 + 2 >= 1x1 + 0 = b#(b(x1)) a#(a(b(a(x1)))) = 3x1 + 2 >= 2x1 + 1 = b#(b(b(x1))) a#(a(b(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(b(b(b(x1)))) b#(b(b(b(x1)))) = 3x1 + 2 >= x1 + 0 = a#(x1) b#(b(b(b(x1)))) = 3x1 + 2 >= 1x1 + 0 = a#(a(x1)) b#(b(b(b(x1)))) = 3x1 + 2 >= 2x1 + 1 = b#(a(a(x1))) b#(b(b(b(x1)))) = 3x1 + 2 >= 3x1 + 2 = b#(b(a(a(x1)))) a#(a(b(b(x1)))) = 3x1 + 2 >= x1 + 0 = a#(x1) a#(a(b(b(x1)))) = 3x1 + 2 >= 1x1 + 0 = b#(a(x1)) a#(a(b(b(x1)))) = 3x1 + 2 >= 2x1 + 1 = b#(b(a(x1))) a#(a(b(b(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(b(b(a(x1)))) b#(a(a(a(x1)))) = 3x1 + 2 >= x1 + 0 = b#(x1) b#(a(a(a(x1)))) = 3x1 + 2 >= 1x1 + 0 = a#(b(x1)) b#(a(a(a(x1)))) = 3x1 + 2 >= 2x1 + 1 = b#(a(b(x1))) b#(a(a(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(b(a(b(x1)))) a(a(b(a(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b(b(b(x1)))) b(b(b(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = b(b(a(a(x1)))) a(a(b(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b(b(a(x1)))) b(a(a(a(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b(a(b(x1)))) problem: DPs: a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Restore Modifier: DPs: a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) EDG Processor: DPs: a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) graph: b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) SCC Processor: #sccs: 2 #rules: 3 #arcs: 8/16 DPs: b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4} transitions: a0(3) -> 5* a0(2) -> 1* a0(5) -> 6* a0(1) -> 1* b0(1) -> 2* b0(6) -> 7* b0(2) -> 2* b{#,0}(7) -> 4* 2 -> 3* 1 -> 2,7,6,3 problem: DPs: TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Qed DPs: a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(b(x1)))) -> a#(b(b(a(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Matrix Interpretation Processor: dim=4 interpretation: [0 0 0 0] [0 0 0 0] [b](x0) = [0 0 0 0]x0 [0 0 1 0] , [0 0 0 0] [0] [0 0 0 1] [0] [a](x0) = [0 1 0 0]x0 + [0] [0 0 0 0] [1], [a#](x0) = [0 0 0 1]x0 orientation: a#(a(b(a(x1)))) = [1] >= [0] = a#(b(b(b(x1)))) a#(a(b(b(x1)))) = [1] >= [0] = a#(b(b(a(x1)))) [0 0 0 0] [0] [0] [0 0 0 0] [1] [0] a(a(b(a(x1)))) = [0 1 0 0]x1 + [0] >= [0] = a(b(b(b(x1)))) [0 0 0 0] [1] [1] [0] [0] [0] [0] b(b(b(b(x1)))) = [0] >= [0] = b(b(a(a(x1)))) [0] [0] [0] [0] [1] [0] a(a(b(b(x1)))) = [0] >= [0] = a(b(b(a(x1)))) [1] [1] [0] [0] [0] [0] b(a(a(a(x1)))) = [0] >= [0] = a(b(a(b(x1)))) [1] [1] problem: DPs: TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(a(b(x1)))) Qed