/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Proof: DP Processor: DPs: a13#(x1) -> a12#(x1) a13#(x1) -> a23#(a12(x1)) a13#(x1) -> a12#(a23(a12(x1))) a14#(x1) -> a12#(x1) a14#(x1) -> a23#(a12(x1)) a14#(x1) -> a34#(a23(a12(x1))) a14#(x1) -> a23#(a34(a23(a12(x1)))) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) a15#(x1) -> a12#(x1) a15#(x1) -> a23#(a12(x1)) a15#(x1) -> a34#(a23(a12(x1))) a15#(x1) -> a45#(a34(a23(a12(x1)))) a15#(x1) -> a34#(a45(a34(a23(a12(x1))))) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) a16#(x1) -> a12#(x1) a16#(x1) -> a23#(a12(x1)) a16#(x1) -> a34#(a23(a12(x1))) a16#(x1) -> a45#(a34(a23(a12(x1)))) a16#(x1) -> a56#(a45(a34(a23(a12(x1))))) a16#(x1) -> a45#(a56(a45(a34(a23(a12(x1)))))) a16#(x1) -> a34#(a45(a56(a45(a34(a23(a12(x1))))))) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24#(x1) -> a23#(x1) a24#(x1) -> a34#(a23(x1)) a24#(x1) -> a23#(a34(a23(x1))) a25#(x1) -> a23#(x1) a25#(x1) -> a34#(a23(x1)) a25#(x1) -> a45#(a34(a23(x1))) a25#(x1) -> a34#(a45(a34(a23(x1)))) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) a26#(x1) -> a23#(x1) a26#(x1) -> a34#(a23(x1)) a26#(x1) -> a45#(a34(a23(x1))) a26#(x1) -> a56#(a45(a34(a23(x1)))) a26#(x1) -> a45#(a56(a45(a34(a23(x1))))) a26#(x1) -> a34#(a45(a56(a45(a34(a23(x1)))))) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) a35#(x1) -> a34#(x1) a35#(x1) -> a45#(a34(x1)) a35#(x1) -> a34#(a45(a34(x1))) a36#(x1) -> a34#(x1) a36#(x1) -> a45#(a34(x1)) a36#(x1) -> a56#(a45(a34(x1))) a36#(x1) -> a45#(a56(a45(a34(x1)))) a36#(x1) -> a34#(a45(a56(a45(a34(x1))))) a46#(x1) -> a45#(x1) a46#(x1) -> a56#(a45(x1)) a46#(x1) -> a45#(a56(a45(x1))) a12#(a34(x1)) -> a12#(x1) a12#(a34(x1)) -> a34#(a12(x1)) a12#(a45(x1)) -> a12#(x1) a12#(a45(x1)) -> a45#(a12(x1)) a12#(a56(x1)) -> a12#(x1) a12#(a56(x1)) -> a56#(a12(x1)) a23#(a45(x1)) -> a23#(x1) a23#(a45(x1)) -> a45#(a23(x1)) a23#(a56(x1)) -> a23#(x1) a23#(a56(x1)) -> a56#(a23(x1)) a34#(a56(x1)) -> a34#(x1) a34#(a56(x1)) -> a56#(a34(x1)) TRS: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) TDG Processor: DPs: a13#(x1) -> a12#(x1) a13#(x1) -> a23#(a12(x1)) a13#(x1) -> a12#(a23(a12(x1))) a14#(x1) -> a12#(x1) a14#(x1) -> a23#(a12(x1)) a14#(x1) -> a34#(a23(a12(x1))) a14#(x1) -> a23#(a34(a23(a12(x1)))) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) a15#(x1) -> a12#(x1) a15#(x1) -> a23#(a12(x1)) a15#(x1) -> a34#(a23(a12(x1))) a15#(x1) -> a45#(a34(a23(a12(x1)))) a15#(x1) -> a34#(a45(a34(a23(a12(x1))))) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) a16#(x1) -> a12#(x1) a16#(x1) -> a23#(a12(x1)) a16#(x1) -> a34#(a23(a12(x1))) a16#(x1) -> a45#(a34(a23(a12(x1)))) a16#(x1) -> a56#(a45(a34(a23(a12(x1))))) a16#(x1) -> a45#(a56(a45(a34(a23(a12(x1)))))) a16#(x1) -> a34#(a45(a56(a45(a34(a23(a12(x1))))))) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24#(x1) -> a23#(x1) a24#(x1) -> a34#(a23(x1)) a24#(x1) -> a23#(a34(a23(x1))) a25#(x1) -> a23#(x1) a25#(x1) -> a34#(a23(x1)) a25#(x1) -> a45#(a34(a23(x1))) a25#(x1) -> a34#(a45(a34(a23(x1)))) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) a26#(x1) -> a23#(x1) a26#(x1) -> a34#(a23(x1)) a26#(x1) -> a45#(a34(a23(x1))) a26#(x1) -> a56#(a45(a34(a23(x1)))) a26#(x1) -> a45#(a56(a45(a34(a23(x1))))) a26#(x1) -> a34#(a45(a56(a45(a34(a23(x1)))))) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) a35#(x1) -> a34#(x1) a35#(x1) -> a45#(a34(x1)) a35#(x1) -> a34#(a45(a34(x1))) a36#(x1) -> a34#(x1) a36#(x1) -> a45#(a34(x1)) a36#(x1) -> a56#(a45(a34(x1))) a36#(x1) -> a45#(a56(a45(a34(x1)))) a36#(x1) -> a34#(a45(a56(a45(a34(x1))))) a46#(x1) -> a45#(x1) a46#(x1) -> a56#(a45(x1)) a46#(x1) -> a45#(a56(a45(x1))) a12#(a34(x1)) -> a12#(x1) a12#(a34(x1)) -> a34#(a12(x1)) a12#(a45(x1)) -> a12#(x1) a12#(a45(x1)) -> a45#(a12(x1)) a12#(a56(x1)) -> a12#(x1) a12#(a56(x1)) -> a56#(a12(x1)) a23#(a45(x1)) -> a23#(x1) a23#(a45(x1)) -> a45#(a23(x1)) a23#(a56(x1)) -> a23#(x1) a23#(a56(x1)) -> a56#(a23(x1)) a34#(a56(x1)) -> a34#(x1) a34#(a56(x1)) -> a56#(a34(x1)) TRS: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) graph: a36#(x1) -> a34#(a45(a56(a45(a34(x1))))) -> a34#(a56(x1)) -> a56#(a34(x1)) a36#(x1) -> a34#(a45(a56(a45(a34(x1))))) -> a34#(a56(x1)) -> a34#(x1) a36#(x1) -> a34#(x1) -> a34#(a56(x1)) -> a56#(a34(x1)) a36#(x1) -> a34#(x1) -> a34#(a56(x1)) -> a34#(x1) a35#(x1) -> a34#(a45(a34(x1))) -> a34#(a56(x1)) -> a56#(a34(x1)) a35#(x1) -> a34#(a45(a34(x1))) -> a34#(a56(x1)) -> a34#(x1) a35#(x1) -> a34#(x1) -> a34#(a56(x1)) -> a56#(a34(x1)) a35#(x1) -> a34#(x1) -> a34#(a56(x1)) -> a34#(x1) a34#(a56(x1)) -> a34#(x1) -> a34#(a56(x1)) -> a56#(a34(x1)) a34#(a56(x1)) -> a34#(x1) -> a34#(a56(x1)) -> a34#(x1) a26#(x1) -> a34#(a45(a56(a45(a34(a23(x1)))))) -> a34#(a56(x1)) -> a56#(a34(x1)) a26#(x1) -> a34#(a45(a56(a45(a34(a23(x1)))))) -> a34#(a56(x1)) -> a34#(x1) a26#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a56#(a34(x1)) a26#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a34#(x1) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) -> a23#(a56(x1)) -> a56#(a23(x1)) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) -> a23#(a56(x1)) -> a23#(x1) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) -> a23#(a45(x1)) -> a45#(a23(x1)) a26#(x1) -> a23#(a34(a45(a56(a45(a34(a23(x1))))))) -> a23#(a45(x1)) -> a23#(x1) a26#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a56#(a23(x1)) a26#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a23#(x1) a26#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a45#(a23(x1)) a26#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a23#(x1) a25#(x1) -> a34#(a45(a34(a23(x1)))) -> a34#(a56(x1)) -> a56#(a34(x1)) a25#(x1) -> a34#(a45(a34(a23(x1)))) -> a34#(a56(x1)) -> a34#(x1) a25#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a56#(a34(x1)) a25#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a34#(x1) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) -> a23#(a56(x1)) -> a56#(a23(x1)) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) -> a23#(a56(x1)) -> a23#(x1) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) -> a23#(a45(x1)) -> a45#(a23(x1)) a25#(x1) -> a23#(a34(a45(a34(a23(x1))))) -> a23#(a45(x1)) -> a23#(x1) a25#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a56#(a23(x1)) a25#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a23#(x1) a25#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a45#(a23(x1)) a25#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a23#(x1) a24#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a56#(a34(x1)) a24#(x1) -> a34#(a23(x1)) -> a34#(a56(x1)) -> a34#(x1) a24#(x1) -> a23#(a34(a23(x1))) -> a23#(a56(x1)) -> a56#(a23(x1)) a24#(x1) -> a23#(a34(a23(x1))) -> a23#(a56(x1)) -> a23#(x1) a24#(x1) -> a23#(a34(a23(x1))) -> a23#(a45(x1)) -> a45#(a23(x1)) a24#(x1) -> a23#(a34(a23(x1))) -> a23#(a45(x1)) -> a23#(x1) a24#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a56#(a23(x1)) a24#(x1) -> a23#(x1) -> a23#(a56(x1)) -> a23#(x1) a24#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a45#(a23(x1)) a24#(x1) -> a23#(x1) -> a23#(a45(x1)) -> a23#(x1) a23#(a56(x1)) -> a23#(x1) -> a23#(a56(x1)) -> a56#(a23(x1)) a23#(a56(x1)) -> a23#(x1) -> a23#(a56(x1)) -> a23#(x1) a23#(a56(x1)) -> a23#(x1) -> a23#(a45(x1)) -> a45#(a23(x1)) a23#(a56(x1)) -> a23#(x1) -> a23#(a45(x1)) -> a23#(x1) a23#(a45(x1)) -> a23#(x1) -> a23#(a56(x1)) -> a56#(a23(x1)) a23#(a45(x1)) -> a23#(x1) -> a23#(a56(x1)) -> a23#(x1) a23#(a45(x1)) -> a23#(x1) -> a23#(a45(x1)) -> a45#(a23(x1)) a23#(a45(x1)) -> a23#(x1) -> a23#(a45(x1)) -> a23#(x1) a16#(x1) -> a34#(a45(a56(a45(a34(a23(a12(x1))))))) -> a34#(a56(x1)) -> a56#(a34(x1)) a16#(x1) -> a34#(a45(a56(a45(a34(a23(a12(x1))))))) -> a34#(a56(x1)) -> a34#(x1) a16#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a56#(a34(x1)) a16#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a34#(x1) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) -> a23#(a56(x1)) -> a56#(a23(x1)) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) -> a23#(a56(x1)) -> a23#(x1) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) -> a23#(a45(x1)) -> a45#(a23(x1)) a16#(x1) -> a23#(a34(a45(a56(a45(a34(a23(a12(x1)))))))) -> a23#(a45(x1)) -> a23#(x1) a16#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a56#(a23(x1)) a16#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a23#(x1) a16#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a45#(a23(x1)) a16#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a23#(x1) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a56(x1)) -> a56#(a12(x1)) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a56(x1)) -> a12#(x1) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a45(x1)) -> a45#(a12(x1)) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a45(x1)) -> a12#(x1) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a34(x1)) -> a34#(a12(x1)) a16#(x1) -> a12#(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) -> a12#(a34(x1)) -> a12#(x1) a16#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a16#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a16#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a16#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a16#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a16#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a15#(x1) -> a34#(a45(a34(a23(a12(x1))))) -> a34#(a56(x1)) -> a56#(a34(x1)) a15#(x1) -> a34#(a45(a34(a23(a12(x1))))) -> a34#(a56(x1)) -> a34#(x1) a15#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a56#(a34(x1)) a15#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a34#(x1) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) -> a23#(a56(x1)) -> a56#(a23(x1)) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) -> a23#(a56(x1)) -> a23#(x1) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) -> a23#(a45(x1)) -> a45#(a23(x1)) a15#(x1) -> a23#(a34(a45(a34(a23(a12(x1)))))) -> a23#(a45(x1)) -> a23#(x1) a15#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a56#(a23(x1)) a15#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a23#(x1) a15#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a45#(a23(x1)) a15#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a23#(x1) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a56(x1)) -> a56#(a12(x1)) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a56(x1)) -> a12#(x1) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a45(x1)) -> a45#(a12(x1)) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a45(x1)) -> a12#(x1) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a34(x1)) -> a34#(a12(x1)) a15#(x1) -> a12#(a23(a34(a45(a34(a23(a12(x1))))))) -> a12#(a34(x1)) -> a12#(x1) a15#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a15#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a15#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a15#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a15#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a15#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a14#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a56#(a34(x1)) a14#(x1) -> a34#(a23(a12(x1))) -> a34#(a56(x1)) -> a34#(x1) a14#(x1) -> a23#(a34(a23(a12(x1)))) -> a23#(a56(x1)) -> a56#(a23(x1)) a14#(x1) -> a23#(a34(a23(a12(x1)))) -> a23#(a56(x1)) -> a23#(x1) a14#(x1) -> a23#(a34(a23(a12(x1)))) -> a23#(a45(x1)) -> a45#(a23(x1)) a14#(x1) -> a23#(a34(a23(a12(x1)))) -> a23#(a45(x1)) -> a23#(x1) a14#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a56#(a23(x1)) a14#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a23#(x1) a14#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a45#(a23(x1)) a14#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a23#(x1) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a56(x1)) -> a56#(a12(x1)) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a56(x1)) -> a12#(x1) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a45(x1)) -> a45#(a12(x1)) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a45(x1)) -> a12#(x1) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a34(x1)) -> a34#(a12(x1)) a14#(x1) -> a12#(a23(a34(a23(a12(x1))))) -> a12#(a34(x1)) -> a12#(x1) a14#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a14#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a14#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a14#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a14#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a14#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a13#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a56#(a23(x1)) a13#(x1) -> a23#(a12(x1)) -> a23#(a56(x1)) -> a23#(x1) a13#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a45#(a23(x1)) a13#(x1) -> a23#(a12(x1)) -> a23#(a45(x1)) -> a23#(x1) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a56(x1)) -> a56#(a12(x1)) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a56(x1)) -> a12#(x1) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a45(x1)) -> a45#(a12(x1)) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a45(x1)) -> a12#(x1) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a34(x1)) -> a34#(a12(x1)) a13#(x1) -> a12#(a23(a12(x1))) -> a12#(a34(x1)) -> a12#(x1) a13#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a13#(x1) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a13#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a13#(x1) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a13#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a13#(x1) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a12#(a56(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a12#(a56(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a12#(a56(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a12#(a56(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a12#(a56(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a12#(a56(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a12#(a45(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a12#(a45(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a12#(a45(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a12#(a45(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a12#(a45(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a12#(a45(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) a12#(a34(x1)) -> a34#(a12(x1)) -> a34#(a56(x1)) -> a56#(a34(x1)) a12#(a34(x1)) -> a34#(a12(x1)) -> a34#(a56(x1)) -> a34#(x1) a12#(a34(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a56#(a12(x1)) a12#(a34(x1)) -> a12#(x1) -> a12#(a56(x1)) -> a12#(x1) a12#(a34(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a45#(a12(x1)) a12#(a34(x1)) -> a12#(x1) -> a12#(a45(x1)) -> a12#(x1) a12#(a34(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a34#(a12(x1)) a12#(a34(x1)) -> a12#(x1) -> a12#(a34(x1)) -> a12#(x1) SCC Processor: #sccs: 3 #rules: 6 #arcs: 158/3844 DPs: a12#(a34(x1)) -> a12#(x1) a12#(a45(x1)) -> a12#(x1) a12#(a56(x1)) -> a12#(x1) TRS: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Usable Rule Processor: DPs: a12#(a34(x1)) -> a12#(x1) a12#(a45(x1)) -> a12#(x1) a12#(a56(x1)) -> a12#(x1) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [a12#](x0) = x0 + 1, [a56](x0) = x0 + 1, [a45](x0) = x0, [a34](x0) = x0 + 1 orientation: a12#(a34(x1)) = x1 + 2 >= x1 + 1 = a12#(x1) a12#(a45(x1)) = x1 + 1 >= x1 + 1 = a12#(x1) a12#(a56(x1)) = x1 + 2 >= x1 + 1 = a12#(x1) problem: DPs: a12#(a45(x1)) -> a12#(x1) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [a12#](x0) = x0, [a45](x0) = x0 + 1 orientation: a12#(a45(x1)) = x1 + 1 >= x1 = a12#(x1) problem: DPs: TRS: Qed DPs: a23#(a45(x1)) -> a23#(x1) a23#(a56(x1)) -> a23#(x1) TRS: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Usable Rule Processor: DPs: a23#(a45(x1)) -> a23#(x1) a23#(a56(x1)) -> a23#(x1) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [a23#](x0) = x0 + 1, [a56](x0) = x0 + 1, [a45](x0) = x0 orientation: a23#(a45(x1)) = x1 + 1 >= x1 + 1 = a23#(x1) a23#(a56(x1)) = x1 + 2 >= x1 + 1 = a23#(x1) problem: DPs: a23#(a45(x1)) -> a23#(x1) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [a23#](x0) = x0, [a45](x0) = x0 + 1 orientation: a23#(a45(x1)) = x1 + 1 >= x1 = a23#(x1) problem: DPs: TRS: Qed DPs: a34#(a56(x1)) -> a34#(x1) TRS: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Usable Rule Processor: DPs: a34#(a56(x1)) -> a34#(x1) TRS: Polynomial Interpretation Processor: dimension: 1 interpretation: [a34#](x0) = x0, [a56](x0) = x0 + 1 orientation: a34#(a56(x1)) = x1 + 1 >= x1 = a34#(x1) problem: DPs: TRS: Qed