/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: b(a(b(b(x1)))) -> b(b(a(a(x1)))) a(a(b(b(x1)))) -> a(b(a(a(x1)))) b(b(b(b(x1)))) -> b(a(a(a(x1)))) a(b(a(a(x1)))) -> a(b(b(a(x1)))) Proof: String Reversal Processor: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) DP Processor: DPs: b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) TDG Processor: DPs: b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) EDG Processor: DPs: b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(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)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) SCC Processor: #sccs: 1 #rules: 10 #arcs: 31/121 DPs: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(a(x1)))) -> a#(b(a(x1))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(a(b(x1)))) -> a#(b(b(x1))) b#(b(a(b(x1)))) -> b#(b(x1)) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(b(b(x1)))) -> a#(a(b(x1))) b#(b(b(b(x1)))) -> a#(b(x1)) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) interpretation: [a](x0) = 2x0 + 14, [a#](x0) = x0 + 15, [b](x0) = 2x0 + 14, [b#](x0) = x0 + 0 orientation: a#(a(b(a(x1)))) = 6x1 + 18 >= 6x1 + 18 = a#(b(b(a(x1)))) a#(a(b(a(x1)))) = 6x1 + 18 >= 4x1 + 16 = b#(b(a(x1))) b#(b(a(a(x1)))) = 6x1 + 18 >= 6x1 + 18 = a#(a(b(a(x1)))) b#(b(a(a(x1)))) = 6x1 + 18 >= 4x1 + 16 = a#(b(a(x1))) b#(b(a(b(x1)))) = 6x1 + 18 >= 6x1 + 18 = a#(a(b(b(x1)))) b#(b(a(b(x1)))) = 6x1 + 18 >= 4x1 + 16 = a#(b(b(x1))) b#(b(a(b(x1)))) = 6x1 + 18 >= 2x1 + 14 = b#(b(x1)) b#(b(b(b(x1)))) = 6x1 + 18 >= 6x1 + 18 = a#(a(a(b(x1)))) b#(b(b(b(x1)))) = 6x1 + 18 >= 4x1 + 16 = a#(a(b(x1))) b#(b(b(b(x1)))) = 6x1 + 18 >= 2x1 + 15 = a#(b(x1)) b(b(a(b(x1)))) = 8x1 + 20 >= 8x1 + 20 = a(a(b(b(x1)))) b(b(a(a(x1)))) = 8x1 + 20 >= 8x1 + 20 = a(a(b(a(x1)))) b(b(b(b(x1)))) = 8x1 + 20 >= 8x1 + 20 = a(a(a(b(x1)))) a(a(b(a(x1)))) = 8x1 + 20 >= 8x1 + 20 = a(b(b(a(x1)))) problem: DPs: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) Restore Modifier: DPs: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) EDG Processor: DPs: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 4/16 DPs: a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) Matrix Interpretation Processor: dim=4 interpretation: [0 0 0 0] [1] [0 0 0 0] [0] [a](x0) = [0 0 0 0]x0 + [0] [0 0 1 0] [0], [a#](x0) = [0 0 0 1]x0, [0 1 0 0] [0] [0 0 0 0] [1] [b](x0) = [1 0 0 0]x0 + [0] [0 0 0 0] [0] orientation: a#(a(b(a(x1)))) = [1] >= [0] = a#(b(b(a(x1)))) [1] [1] [1] [0] b(b(a(b(x1)))) = [0] >= [0] = a(a(b(b(x1)))) [0] [0] [1] [1] [1] [0] b(b(a(a(x1)))) = [0] >= [0] = a(a(b(a(x1)))) [0] [0] [1] [1] [1] [0] b(b(b(b(x1)))) = [1] >= [0] = a(a(a(b(x1)))) [0] [0] [1] [1] [0] [0] a(a(b(a(x1)))) = [0] >= [0] = a(b(b(a(x1)))) [0] [0] problem: DPs: TRS: b(b(a(b(x1)))) -> a(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(a(x1)))) b(b(b(b(x1)))) -> a(a(a(b(x1)))) a(a(b(a(x1)))) -> a(b(b(a(x1)))) Qed