/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: b(b(b(x1))) -> a(a(b(x1))) b(a(a(x1))) -> a(a(b(x1))) a(a(x1)) -> b(a(b(x1))) Proof: String Reversal Processor: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) DP Processor: DPs: b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) TDG Processor: DPs: b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(b(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) EDG Processor: DPs: b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(b(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) SCC Processor: #sccs: 1 #rules: 8 #arcs: 36/81 DPs: a#(a(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(a(b(x1))) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) Arctic Interpretation Processor: dimension: 2 usable rules: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) interpretation: [a#](x0) = [1 1]x0 + [0], [b#](x0) = [0 1]x0 + [0], [0 0 ] [1] [a](x0) = [0 -&]x0 + [0], [-& -&] [0] [b](x0) = [0 0 ]x0 + [1] orientation: a#(a(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a#(a(x1)) a#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = b#(a(b(x1))) b#(b(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b#(a(a(x1))) b#(b(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a#(a(x1)) a#(a(x1)) = [1 1]x1 + [2] >= [0 1]x1 + [0] = b#(x1) b#(b(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [0] = a#(x1) a#(a(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b#(a(a(x1))) a#(a(b(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [0] = a#(x1) [-& -&] [0] [-& -&] [0] b(b(b(x1))) = [0 0 ]x1 + [1] >= [0 0 ]x1 + [1] = b(a(a(x1))) [0 0] [1] [-& -&] [0] a(a(b(x1))) = [0 0]x1 + [1] >= [0 0 ]x1 + [1] = b(a(a(x1))) [0 0] [1] [-& -&] [0] a(a(x1)) = [0 0]x1 + [1] >= [0 0 ]x1 + [1] = b(a(b(x1))) problem: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) Restore Modifier: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) EDG Processor: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(a(x1))) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(x1) Arctic Interpretation Processor: dimension: 2 usable rules: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) interpretation: [a#](x0) = [0 0]x0 + [3], [b#](x0) = [-& 0 ]x0 + [0], [0 2] [2] [a](x0) = [2 0]x0 + [1], [-& 0 ] [0] [b](x0) = [0 2 ]x0 + [2] orientation: a#(a(b(x1))) = [2 4]x1 + [4] >= [2 2]x1 + [3] = a#(a(x1)) b#(b(b(x1))) = [2 4]x1 + [4] >= [2 4]x1 + [4] = b#(a(a(x1))) b#(b(b(x1))) = [2 4]x1 + [4] >= [2 2]x1 + [3] = a#(a(x1)) a#(a(x1)) = [2 2]x1 + [3] >= [-& 0 ]x1 + [0] = b#(x1) b#(b(b(x1))) = [2 4]x1 + [4] >= [0 0]x1 + [3] = a#(x1) a#(a(b(x1))) = [2 4]x1 + [4] >= [2 4]x1 + [4] = b#(a(a(x1))) a#(a(b(x1))) = [2 4]x1 + [4] >= [0 0]x1 + [3] = a#(x1) [2 4] [4] [2 4] [4] b(b(b(x1))) = [4 6]x1 + [6] >= [4 6]x1 + [6] = b(a(a(x1))) [2 4] [4] [2 4] [4] a(a(b(x1))) = [4 6]x1 + [6] >= [4 6]x1 + [6] = b(a(a(x1))) [4 2] [3] [0 2] [2] a(a(x1)) = [2 4]x1 + [4] >= [2 4]x1 + [4] = b(a(b(x1))) problem: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) Restore Modifier: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) EDG Processor: DPs: a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) Matrix Interpretation Processor: dim=3 interpretation: [a#](x0) = [0 1 0]x0, [b#](x0) = [0 0 1]x0, [0 0 0] [0] [a](x0) = [0 0 1]x0 + [1] [0 1 0] [0], [0 0 0] [0] [b](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: a#(a(b(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = a#(a(x1)) b#(b(b(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(a(x1))) b#(b(b(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = a#(a(x1)) a#(a(b(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(a(x1))) [0 0 0] [0] [0 0 0] [0] b(b(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(a(x1))) [0 0 1] [3] [0 0 1] [2] [0 0 0] [0] [0 0 0] [0] a(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(a(a(x1))) [0 0 1] [2] [0 0 1] [2] [0 0 0] [0] [0] a(a(x1)) = [0 1 0]x1 + [1] >= [0] = b(a(b(x1))) [0 0 1] [1] [1] problem: DPs: TRS: b(b(b(x1))) -> b(a(a(x1))) a(a(b(x1))) -> b(a(a(x1))) a(a(x1)) -> b(a(b(x1))) Qed