/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: b(b(a(b(x1)))) -> a(b(b(b(x1)))) a(a(a(b(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> a(a(a(b(x1)))) Proof: String Reversal Processor: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) DP Processor: DPs: b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) graph: b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(a(a(a(x1)))) -> b#(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)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(x1)) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) interpretation: [a](x0) = 2x0, [b](x0) = 2x0, [b#](x0) = 1x0 orientation: b#(a(b(b(x1)))) = 7x1 >= 3x1 = b#(a(x1)) b#(a(b(b(x1)))) = 7x1 >= 5x1 = b#(b(a(x1))) b#(a(b(b(x1)))) = 7x1 >= 7x1 = b#(b(b(a(x1)))) b#(a(a(a(x1)))) = 7x1 >= 3x1 = b#(a(x1)) b#(a(a(a(x1)))) = 7x1 >= 5x1 = b#(b(a(x1))) b#(a(a(b(x1)))) = 7x1 >= 7x1 = b#(a(a(a(x1)))) b(a(b(b(x1)))) = 8x1 >= 8x1 = b(b(b(a(x1)))) b(a(a(a(x1)))) = 8x1 >= 8x1 = a(b(b(a(x1)))) b(a(a(b(x1)))) = 8x1 >= 8x1 = b(a(a(a(x1)))) problem: DPs: b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) graph: b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) Matrix Interpretation Processor: dim=4 interpretation: [0 0 0 0] [0] [1 0 0 0] [1] [a](x0) = [0 0 0 0]x0 + [0] [0 1 0 0] [0], [1 0 1 0] [0 0 0 1] [b](x0) = [0 0 0 0]x0 [0 0 0 0] , [b#](x0) = [0 1 0 0]x0 orientation: b#(a(b(b(x1)))) = [1 0 1 0]x1 + [1] >= [0] = b#(b(b(a(x1)))) [0] [0] [0] [0] b(a(b(b(x1)))) = [0] >= [0] = b(b(b(a(x1)))) [0] [0] [0] [0] [1] [1] b(a(a(a(x1)))) = [0] >= [0] = a(b(b(a(x1)))) [0] [0] [0 0 0 0] [0] [0] [1 0 1 0] [1] [1] b(a(a(b(x1)))) = [0 0 0 0]x1 + [0] >= [0] = b(a(a(a(x1)))) [0 0 0 0] [0] [0] problem: DPs: TRS: b(a(b(b(x1)))) -> b(b(b(a(x1)))) b(a(a(a(x1)))) -> a(b(b(a(x1)))) b(a(a(b(x1)))) -> b(a(a(a(x1)))) Qed