/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) Proof: DP Processor: DPs: b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> a#(a(b(x1))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) TDG Processor: DPs: b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> a#(a(b(x1))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) graph: a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> b#(a(x1)) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(b(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(a(x1)))) -> a#(a(b(x1))) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(a(x1))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(a(x1)) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> 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#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) Arctic Interpretation Processor: dimension: 1 usable rules: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) interpretation: [b](x0) = 2x0, [a#](x0) = 4x0, [a](x0) = 2x0, [b#](x0) = 4x0 orientation: b#(b(b(a(x1)))) = 10x1 >= 4x1 = b#(x1) b#(b(b(a(x1)))) = 10x1 >= 6x1 = a#(b(x1)) b#(b(b(a(x1)))) = 10x1 >= 8x1 = a#(a(b(x1))) b#(b(b(a(x1)))) = 10x1 >= 10x1 = b#(a(a(b(x1)))) b#(a(b(a(x1)))) = 10x1 >= 4x1 = b#(x1) b#(a(b(a(x1)))) = 10x1 >= 6x1 = a#(b(x1)) b#(a(b(a(x1)))) = 10x1 >= 8x1 = a#(a(b(x1))) b#(a(b(a(x1)))) = 10x1 >= 10x1 = a#(a(a(b(x1)))) a#(a(b(b(x1)))) = 10x1 >= 4x1 = a#(x1) a#(a(b(b(x1)))) = 10x1 >= 6x1 = b#(a(x1)) a#(a(b(b(x1)))) = 10x1 >= 8x1 = b#(b(a(x1))) a#(a(b(b(x1)))) = 10x1 >= 10x1 = b#(b(b(a(x1)))) b(b(b(a(x1)))) = 8x1 >= 8x1 = b(a(a(b(x1)))) b(a(b(a(x1)))) = 8x1 >= 8x1 = a(a(a(b(x1)))) a(a(b(b(x1)))) = 8x1 >= 8x1 = b(b(b(a(x1)))) problem: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) Restore Modifier: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) EDG Processor: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) graph: a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(b(x1)))) -> b#(b(b(a(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [0 1 0] [0] [b](x0) = [0 1 1]x0 + [1] [1 0 0] [0], [a#](x0) = [1 0 0]x0, [0 1 0] [a](x0) = [0 1 1]x0 [1 0 0] , [b#](x0) = [1 0 0]x0 orientation: b#(b(b(a(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = b#(a(a(b(x1)))) b#(a(b(a(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a#(a(a(b(x1)))) a#(a(b(b(x1)))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = b#(b(b(a(x1)))) [1 2 1] [2] [1 2 1] [1] b(b(b(a(x1)))) = [1 3 2]x1 + [3] >= [1 3 2]x1 + [3] = b(a(a(b(x1)))) [1 1 1] [1] [1 1 1] [1] [1 2 1] [1] [1 2 1] [1] b(a(b(a(x1)))) = [1 3 2]x1 + [2] >= [1 3 2]x1 + [2] = a(a(a(b(x1)))) [1 1 1] [1] [1 1 1] [1] [1 2 1] [2] [1 2 1] [2] a(a(b(b(x1)))) = [1 3 2]x1 + [3] >= [1 3 2]x1 + [3] = b(b(b(a(x1)))) [1 1 1] [2] [1 1 1] [1] problem: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) Restore Modifier: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) EDG Processor: DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) graph: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> a#(a(a(b(x1)))) b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [0 0 1] [0] [b](x0) = [1 0 0]x0 + [0] [0 1 1] [1], [0 0 1] [a](x0) = [1 0 0]x0 [0 1 1] , [b#](x0) = [1 0 1]x0 orientation: b#(b(b(a(x1)))) = [2 2 3]x1 + [3] >= [2 2 3]x1 + [2] = b#(a(a(b(x1)))) [1 1 2] [2] [1 1 2] [1] b(b(b(a(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = b(a(a(b(x1)))) [1 2 3] [3] [1 2 3] [3] [1 1 2] [1] [1 1 2] [1] b(a(b(a(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a(a(a(b(x1)))) [1 2 3] [2] [1 2 3] [2] [1 1 2] [2] [1 1 2] [2] a(a(b(b(x1)))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = b(b(b(a(x1)))) [1 2 3] [3] [1 2 3] [3] problem: DPs: TRS: b(b(b(a(x1)))) -> b(a(a(b(x1)))) b(a(b(a(x1)))) -> a(a(a(b(x1)))) a(a(b(b(x1)))) -> b(b(b(a(x1)))) Qed