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