/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: a(x1) -> x1 a(a(b(x1))) -> c(a(a(a(x1)))) c(a(x1)) -> b(b(x1)) Proof: String Reversal Processor: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) DP Processor: DPs: b#(a(a(x1))) -> a#(c(x1)) b#(a(a(x1))) -> a#(a(c(x1))) b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) TDG Processor: DPs: b#(a(a(x1))) -> a#(c(x1)) b#(a(a(x1))) -> a#(a(c(x1))) b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) graph: b#(a(a(x1))) -> a#(c(x1)) -> a#(c(x1)) -> b#(b(x1)) b#(a(a(x1))) -> a#(c(x1)) -> a#(c(x1)) -> b#(x1) b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(b(x1)) b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(x1) b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(b(x1)) b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(c(x1))) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(c(x1)) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(x1))) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(x1)) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) interpretation: [b#](x0) = [0 -&]x0 + [1], [a#](x0) = [-& 0 ]x0 + [0], [0 -&] [-&] [c](x0) = [0 -&]x0 + [1 ], [0 -&] [1] [b](x0) = [1 -&]x0 + [0], [0 0] [2] [a](x0) = [1 0]x0 + [3] orientation: b#(a(a(x1))) = [1 0]x1 + [3] >= [0 -&]x1 + [1] = a#(c(x1)) b#(a(a(x1))) = [1 0]x1 + [3] >= [1 -&]x1 + [3] = a#(a(c(x1))) b#(a(a(x1))) = [1 0]x1 + [3] >= [1 -&]x1 + [3] = a#(a(a(c(x1)))) a#(c(x1)) = [0 -&]x1 + [1] >= [0 -&]x1 + [1] = b#(x1) a#(c(x1)) = [0 -&]x1 + [1] >= [0 -&]x1 + [1] = b#(b(x1)) [0 0] [2] a(x1) = [1 0]x1 + [3] >= x1 = x1 [1 0] [3] [1 -&] [3] b(a(a(x1))) = [2 1]x1 + [4] >= [2 -&]x1 + [4] = a(a(a(c(x1)))) [0 -&] [2] [0 -&] [1] a(c(x1)) = [1 -&]x1 + [3] >= [1 -&]x1 + [2] = b(b(x1)) problem: DPs: b#(a(a(x1))) -> a#(a(c(x1))) b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) Restore Modifier: DPs: b#(a(a(x1))) -> a#(a(c(x1))) b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) EDG Processor: DPs: b#(a(a(x1))) -> a#(a(c(x1))) b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) graph: b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(x1) b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(b(x1)) b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(x1) b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(c(x1))) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(x1))) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) interpretation: [b#](x0) = [0 1 0]x0 + [0], [a#](x0) = [-& 1 0 ]x0 + [0], [-& 0 0 ] [0 ] [c](x0) = [0 0 0 ]x0 + [0 ] [-& -& -&] [-&], [-& -& 0 ] [0 ] [b](x0) = [0 0 0 ]x0 + [0 ] [-& 0 0 ] [-&], [0 -& -&] [0] [a](x0) = [0 0 1 ]x0 + [0] [0 0 0 ] [0] orientation: b#(a(a(x1))) = [2 2 2]x1 + [2] >= [1 1 1]x1 + [1] = a#(a(c(x1))) b#(a(a(x1))) = [2 2 2]x1 + [2] >= [2 2 2]x1 + [2] = a#(a(a(c(x1)))) a#(c(x1)) = [1 1 1]x1 + [1] >= [0 1 0]x1 + [0] = b#(x1) a#(c(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = b#(b(x1)) [0 -& -&] [0] a(x1) = [0 0 1 ]x1 + [0] >= x1 = x1 [0 0 0 ] [0] [0 0 1] [0] [-& 0 0 ] [0] b(a(a(x1))) = [1 1 1]x1 + [1] >= [1 1 1 ]x1 + [1] = a(a(a(c(x1)))) [1 1 1] [1] [1 1 1 ] [1] [-& 0 0 ] [0] [-& 0 0 ] [0] a(c(x1)) = [0 0 0 ]x1 + [0] >= [0 0 0 ]x1 + [0] = b(b(x1)) [0 0 0 ] [0] [0 0 0 ] [0] problem: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) Restore Modifier: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) EDG Processor: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) graph: b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(b(x1)) b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(x1)))) Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) interpretation: [b#](x0) = [0 -& -&]x0 + [0], [a#](x0) = [-& -& 1 ]x0 + [1], [0 -& -&] [c](x0) = [-& -& -&]x0 [0 -& -&] , [0 -& -&] [-&] [b](x0) = [1 -& 0 ]x0 + [0 ] [0 -& -&] [0 ], [0 1 0] [-&] [a](x0) = [1 0 0]x0 + [0 ] [0 0 0] [0 ] orientation: b#(a(a(x1))) = [2 1 1]x1 + [1] >= [2 -& -&]x1 + [1] = a#(a(a(c(x1)))) a#(c(x1)) = [1 -& -&]x1 + [1] >= [0 -& -&]x1 + [0] = b#(x1) a#(c(x1)) = [1 -& -&]x1 + [1] >= [0 -& -&]x1 + [0] = b#(b(x1)) [0 1 0] [-&] a(x1) = [1 0 0]x1 + [0 ] >= x1 = x1 [0 0 0] [0 ] [2 1 1] [1] [2 -& -&] [1] b(a(a(x1))) = [3 2 2]x1 + [2] >= [3 -& -&]x1 + [2] = a(a(a(c(x1)))) [2 1 1] [1] [2 -& -&] [1] [0 -& -&] [-&] [0 -& -&] [-&] a(c(x1)) = [1 -& -&]x1 + [0 ] >= [1 -& -&]x1 + [0 ] = b(b(x1)) [0 -& -&] [0 ] [0 -& -&] [0 ] problem: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) Restore Modifier: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) EDG Processor: DPs: b#(a(a(x1))) -> a#(a(a(c(x1)))) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(a(c(x1)))) a(c(x1)) -> b(b(x1)) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1