/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(a(b(x1)))) -> b(b(a(a(x1)))) a(a(a(b(x1)))) -> a(a(b(a(x1)))) b(b(a(b(x1)))) -> b(a(b(b(x1)))) Proof: String Reversal Processor: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) DP Processor: DPs: b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) EDG Processor: DPs: b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) graph: b#(a(a(a(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) SCC Processor: #sccs: 2 #rules: 5 #arcs: 21/25 DPs: b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) KBO Processor: argument filtering: pi(b) = [0] pi(a) = 0 pi(b#) = 0 usable rules: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) weight function: w0 = 1 w(a) = w(b) = 1 w(b#) = 0 precedence: b# > a > b problem: DPs: b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) Restore Modifier: DPs: b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) EDG Processor: DPs: b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) graph: b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(x1)) KBO Processor: argument filtering: pi(b) = 0 pi(a) = [0] pi(b#) = 0 usable rules: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) weight function: w0 = 1 w(b#) = w(a) = 1 w(b) = 0 precedence: b > a > b# problem: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) graph: b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) Matrix Interpretation Processor: dim=4 interpretation: [0 0 0 0] [0 0 0 0] [a](x0) = [0 0 0 0]x0 [1 0 0 0] , [0 1 0 1] [0] [0 0 0 0] [1] [b](x0) = [0 0 0 0]x0 + [0] [0 0 0 0] [0], [b#](x0) = [0 0 0 1]x0 orientation: b#(a(b(b(x1)))) = [1] >= [0] = b#(b(a(b(x1)))) [1 0 0 0] [0] [0] [0 0 0 0] [1] [0] b(a(b(a(x1)))) = [0 0 0 0]x1 + [0] >= [0] = a(a(b(b(x1)))) [0 0 0 0] [0] [0] [0] [0] [1] [0] b(a(a(a(x1)))) = [0] >= [0] = a(b(a(a(x1)))) [0] [0] [1] [1] [1] [1] b(a(b(b(x1)))) = [0] >= [0] = b(b(a(b(x1)))) [0] [0] problem: DPs: TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) Qed DPs: b#(a(a(a(x1)))) -> b#(a(a(x1))) TRS: b(a(b(a(x1)))) -> a(a(b(b(x1)))) b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(a(b(b(x1)))) -> b(b(a(b(x1)))) Usable Rule Processor: DPs: b#(a(a(a(x1)))) -> b#(a(a(x1))) TRS: Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [a](x0) = 9x0 + 13, [b#](x0) = x0 + 0 orientation: b#(a(a(a(x1)))) = 27x1 + 31 >= 18x1 + 22 = b#(a(a(x1))) problem: DPs: TRS: Qed