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