/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Proof: DP Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) TDG Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(x1) EDG Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> a#(b(b(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(x1) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(b(x1))) b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(b(a(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) SCC Processor: #sccs: 2 #rules: 9 #arcs: 54/196 DPs: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> a#(x1) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> b#(x1) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) interpretation: [b](x0) = 6x0, [b#](x0) = x0, [a](x0) = 6x0, [a#](x0) = x0 orientation: b#(a(b(b(x1)))) = 18x1 >= 18x1 = b#(a(b(a(x1)))) b#(a(b(b(x1)))) = 18x1 >= 6x1 = b#(a(x1)) b#(a(b(b(x1)))) = 18x1 >= x1 = a#(x1) a#(a(a(b(x1)))) = 18x1 >= 18x1 = b#(a(b(b(x1)))) a#(a(a(a(x1)))) = 18x1 >= 12x1 = b#(a(b(x1))) a#(a(a(a(x1)))) = 18x1 >= x1 = b#(x1) a(a(a(a(x1)))) = 24x1 >= 24x1 = a(b(a(b(x1)))) b(b(a(b(x1)))) = 24x1 >= 24x1 = b(b(b(b(x1)))) a(a(a(b(x1)))) = 24x1 >= 24x1 = b(a(b(b(x1)))) b(a(b(b(x1)))) = 24x1 >= 24x1 = b(a(b(a(x1)))) problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) graph: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) a#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: b#(a(b(b(x1)))) -> b#(a(b(a(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Matrix Interpretation Processor: dim=4 interpretation: [0 1 0 0] [0] [0 0 0 1] [1] [b](x0) = [0 0 0 0]x0 + [0] [0 0 0 0] [0], [b#](x0) = [1 0 0 0]x0, [1 0 0 0] [0] [0 0 0 1] [0] [a](x0) = [0 0 0 0]x0 + [1] [0 0 1 0] [0] orientation: b#(a(b(b(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = b#(a(b(a(x1)))) [1 0 0 0] [0] [0] [0 0 0 0] [1] [0] a(a(a(a(x1)))) = [0 0 0 0]x1 + [1] >= [1] = a(b(a(b(x1)))) [0 0 0 0] [1] [0] [1] [1] [1] [1] b(b(a(b(x1)))) = [0] >= [0] = b(b(b(b(x1)))) [0] [0] [0 1 0 0] [0] [0] [0 0 0 0] [1] [1] a(a(a(b(x1)))) = [0 0 0 0]x1 + [1] >= [0] = b(a(b(b(x1)))) [0 0 0 0] [1] [0] [0] [0] [1] [1] b(a(b(b(x1)))) = [0] >= [0] = b(a(b(a(x1)))) [0] [0] problem: DPs: TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Qed DPs: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) interpretation: [b](x0) = 1x0, [b#](x0) = x0, [a](x0) = 1x0 orientation: b#(b(a(b(x1)))) = 3x1 >= 3x1 = b#(b(b(b(x1)))) b#(b(a(b(x1)))) = 3x1 >= 2x1 = b#(b(b(x1))) b#(b(a(b(x1)))) = 3x1 >= 1x1 = b#(b(x1)) a(a(a(a(x1)))) = 4x1 >= 4x1 = a(b(a(b(x1)))) b(b(a(b(x1)))) = 4x1 >= 4x1 = b(b(b(b(x1)))) a(a(a(b(x1)))) = 4x1 >= 4x1 = b(a(b(b(x1)))) b(a(b(b(x1)))) = 4x1 >= 4x1 = b(a(b(a(x1)))) problem: DPs: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Restore Modifier: DPs: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) EDG Processor: DPs: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(b(b(x1)))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4} transitions: a0(2) -> 1* a0(1) -> 1* b0(1) -> 2* b0(3) -> 5* b0(6) -> 7* b0(2) -> 2* b0(5) -> 6* b{#,0}(7) -> 4* 2 -> 1,3 1 -> 3* problem: DPs: TRS: a(a(a(a(x1)))) -> a(b(a(b(x1)))) b(b(a(b(x1)))) -> b(b(b(b(x1)))) a(a(a(b(x1)))) -> b(a(b(b(x1)))) b(a(b(b(x1)))) -> b(a(b(a(x1)))) Qed