/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) Proof: DP Processor: DPs: a#(d(x1)) -> b#(x1) a#(d(x1)) -> d#(b(x1)) a#(x1) -> b#(x1) a#(x1) -> b#(b(x1)) a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> d#(x1) b#(d(b(x1))) -> a#(d(x1)) b#(c(x1)) -> d#(x1) b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(c(d(x1))) a#(c(x1)) -> b#(b(c(d(x1)))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) TDG Processor: DPs: a#(d(x1)) -> b#(x1) a#(d(x1)) -> d#(b(x1)) a#(x1) -> b#(x1) a#(x1) -> b#(b(x1)) a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> d#(x1) b#(d(b(x1))) -> a#(d(x1)) b#(c(x1)) -> d#(x1) b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(c(d(x1))) a#(c(x1)) -> b#(b(c(d(x1)))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) graph: b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> b#(b(c(d(x1)))) b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> b#(c(d(x1))) b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> d#(x1) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(x1)) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(x1) b#(d(b(x1))) -> a#(d(x1)) -> a#(d(x1)) -> d#(b(x1)) b#(d(b(x1))) -> a#(d(x1)) -> a#(d(x1)) -> b#(x1) a#(c(x1)) -> b#(c(d(x1))) -> b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> b#(c(d(x1))) -> b#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(c(d(x1))) -> b#(d(b(x1))) -> a#(d(x1)) a#(c(x1)) -> b#(c(d(x1))) -> b#(d(b(x1))) -> d#(x1) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(d(b(x1))) -> a#(d(x1)) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(d(b(x1))) -> d#(x1) a#(d(x1)) -> b#(x1) -> b#(c(x1)) -> d#(d(x1)) a#(d(x1)) -> b#(x1) -> b#(c(x1)) -> d#(x1) a#(d(x1)) -> b#(x1) -> b#(d(b(x1))) -> a#(d(x1)) a#(d(x1)) -> b#(x1) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(b(b(x1))) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(b(b(x1))) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(b(x1)) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(b(x1)) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(b(x1)) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(x1)) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(x1) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(x1) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(x1) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(x1) -> b#(d(b(x1))) -> d#(x1) EDG Processor: DPs: a#(d(x1)) -> b#(x1) a#(d(x1)) -> d#(b(x1)) a#(x1) -> b#(x1) a#(x1) -> b#(b(x1)) a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> d#(x1) b#(d(b(x1))) -> a#(d(x1)) b#(c(x1)) -> d#(x1) b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(c(d(x1))) a#(c(x1)) -> b#(b(c(d(x1)))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) graph: b#(d(b(x1))) -> a#(d(x1)) -> a#(d(x1)) -> b#(x1) b#(d(b(x1))) -> a#(d(x1)) -> a#(d(x1)) -> d#(b(x1)) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(x1) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(x1)) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> d#(x1) b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> b#(c(d(x1))) b#(d(b(x1))) -> a#(d(x1)) -> a#(c(x1)) -> b#(b(c(d(x1)))) a#(c(x1)) -> b#(c(d(x1))) -> b#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(c(d(x1))) -> b#(c(x1)) -> d#(d(x1)) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(c(x1)) -> d#(x1) a#(c(x1)) -> b#(b(c(d(x1)))) -> b#(c(x1)) -> d#(d(x1)) a#(d(x1)) -> b#(x1) -> b#(d(b(x1))) -> d#(x1) a#(d(x1)) -> b#(x1) -> b#(d(b(x1))) -> a#(d(x1)) a#(d(x1)) -> b#(x1) -> b#(c(x1)) -> d#(x1) a#(d(x1)) -> b#(x1) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(b(b(x1))) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(b(x1)) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(b(x1)) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(x1)) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(b(x1)) -> b#(c(x1)) -> d#(d(x1)) a#(x1) -> b#(x1) -> b#(d(b(x1))) -> d#(x1) a#(x1) -> b#(x1) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(x1) -> b#(c(x1)) -> d#(x1) a#(x1) -> b#(x1) -> b#(c(x1)) -> d#(d(x1)) SCC Processor: #sccs: 1 #rules: 5 #arcs: 28/144 DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) a#(x1) -> b#(b(x1)) a#(x1) -> b#(x1) a#(d(x1)) -> b#(x1) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) interpretation: [b#](x0) = 1x0, [a#](x0) = 1x0 + 0, [c](x0) = 0, [b](x0) = x0, [a](x0) = x0 + 0, [d](x0) = 8x0 + 9 orientation: b#(d(b(x1))) = 9x1 + 10 >= 9x1 + 10 = a#(d(x1)) a#(x1) = 1x1 + 0 >= 1x1 = b#(b(b(x1))) a#(x1) = 1x1 + 0 >= 1x1 = b#(b(x1)) a#(x1) = 1x1 + 0 >= 1x1 = b#(x1) a#(d(x1)) = 9x1 + 10 >= 1x1 = b#(x1) a(d(x1)) = 8x1 + 9 >= 8x1 + 9 = d(b(x1)) a(x1) = x1 + 0 >= x1 = b(b(b(x1))) d(x1) = 8x1 + 9 >= x1 = x1 a(x1) = x1 + 0 >= x1 = x1 b(d(b(x1))) = 8x1 + 9 >= 8x1 + 9 = a(d(x1)) b(c(x1)) = 0 >= 0 = c(d(d(x1))) a(c(x1)) = 0 >= 0 = b(b(c(d(x1)))) problem: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) a#(x1) -> b#(b(x1)) a#(x1) -> b#(x1) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) Restore Modifier: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) a#(x1) -> b#(b(x1)) a#(x1) -> b#(x1) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) EDG Processor: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) a#(x1) -> b#(b(x1)) a#(x1) -> b#(x1) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) graph: b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(b(x1))) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(x1)) b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(x1) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(x1)) -> b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(x1) -> b#(d(b(x1))) -> a#(d(x1)) Matrix Interpretation Processor: dim=1 interpretation: [b#](x0) = 8x0, [a#](x0) = 8x0 + 16, [c](x0) = 13, [b](x0) = x0 + 1, [a](x0) = x0 + 3, [d](x0) = 2x0 orientation: b#(d(b(x1))) = 16x1 + 16 >= 16x1 + 16 = a#(d(x1)) a#(x1) = 8x1 + 16 >= 8x1 + 16 = b#(b(b(x1))) a#(x1) = 8x1 + 16 >= 8x1 + 8 = b#(b(x1)) a#(x1) = 8x1 + 16 >= 8x1 = b#(x1) a(d(x1)) = 2x1 + 3 >= 2x1 + 2 = d(b(x1)) a(x1) = x1 + 3 >= x1 + 3 = b(b(b(x1))) d(x1) = 2x1 >= x1 = x1 a(x1) = x1 + 3 >= x1 = x1 b(d(b(x1))) = 2x1 + 3 >= 2x1 + 3 = a(d(x1)) b(c(x1)) = 14 >= 13 = c(d(d(x1))) a(c(x1)) = 16 >= 15 = b(b(c(d(x1)))) problem: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) Restore Modifier: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) EDG Processor: DPs: b#(d(b(x1))) -> a#(d(x1)) a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) graph: b#(d(b(x1))) -> a#(d(x1)) -> a#(x1) -> b#(b(b(x1))) a#(x1) -> b#(b(b(x1))) -> b#(d(b(x1))) -> a#(d(x1)) Matrix Interpretation Processor: dim=3 interpretation: [b#](x0) = [0 0 1]x0, [a#](x0) = [0 1 0]x0, [0] [c](x0) = [0] [0], [0 1 0] [0] [b](x0) = [0 0 1]x0 + [1] [1 0 0] [0], [1] [a](x0) = x0 + [1] [1], [1 1 1] [d](x0) = [1 1 1]x0 [1 1 1] orientation: b#(d(b(x1))) = [1 1 1]x1 + [1] >= [1 1 1]x1 = a#(d(x1)) a#(x1) = [0 1 0]x1 >= [0 1 0]x1 = b#(b(b(x1))) [1 1 1] [1] [1 1 1] [1] a(d(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = d(b(x1)) [1 1 1] [1] [1 1 1] [1] [1] [1] a(x1) = x1 + [1] >= x1 + [1] = b(b(b(x1))) [1] [1] [1 1 1] d(x1) = [1 1 1]x1 >= x1 = x1 [1 1 1] [1] a(x1) = x1 + [1] >= x1 = x1 [1] [1 1 1] [1] [1 1 1] [1] b(d(b(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = a(d(x1)) [1 1 1] [1] [1 1 1] [1] [0] [0] b(c(x1)) = [1] >= [0] = c(d(d(x1))) [0] [0] [1] [1] a(c(x1)) = [1] >= [1] = b(b(c(d(x1)))) [1] [0] problem: DPs: a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) Restore Modifier: DPs: a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) EDG Processor: DPs: a#(x1) -> b#(b(b(x1))) TRS: a(d(x1)) -> d(b(x1)) a(x1) -> b(b(b(x1))) d(x1) -> x1 a(x1) -> x1 b(d(b(x1))) -> a(d(x1)) b(c(x1)) -> c(d(d(x1))) a(c(x1)) -> b(b(c(d(x1)))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1