/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: p(0(x1)) -> s(s(0(s(s(p(x1)))))) p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Proof: Matrix Interpretation Processor: dim=4 interpretation: [1 1 0 1] [0] [0 1 0 0] [0] [g](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [1 0 0 0] [0 0 0 0] [q](x0) = [0 0 1 1]x0 [0 0 0 0] , [1 0 0 0] [0] [0 0 1 0] [1] [i](x0) = [0 0 1 1]x0 + [1] [0 1 1 0] [1], [1 0 0 0] [0] [0 0 0 0] [0] [f](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [1 0 0 0] [0 0 1 0] [s](x0) = [0 0 0 0]x0 [0 0 0 0] , [1 0 0 1] [1 0 0 0] [p](x0) = [1 0 0 0]x0 [0 1 0 0] , [1 0 0 1] [1] [0 0 0 0] [0] [0](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [1] orientation: [1 0 0 1] [2] [1 0 0 1] [1] [1 0 0 1] [1] [0 0 0 0] [0] p(0(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [0] = s(s(0(s(s(p(x1)))))) [0 0 0 0] [0] [0 0 0 0] [0] [1 0 0 1] [1] [1 0 0 1] [1] [1 0 0 1] [1] [0 0 0 0] [0] p(s(0(x1))) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = 0(x1) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 0 0] [1 0 0 0] [1 0 0 0] [1 0 0 0] p(s(s(x1))) = [1 0 0 0]x1 >= [0 0 0 0]x1 = s(p(s(x1))) [0 0 0 0] [0 0 0 0] [1 0 0 0] [0] [1 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] f(s(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = g(q(i(x1))) [0 0 0 0] [0] [0 0 0 0] [0] [1 1 0 1] [0] [1 1 0 1] [0] [0 1 0 0] [0] [0 0 0 0] [0] g(x1) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = f(p(p(x1))) [0 0 0 0] [0] [0 0 0 0] [0] [1 0 0 0] [0] [1 0 0 0] [0 0 0 0] [0] [0 0 0 0] q(i(x1)) = [0 1 2 1]x1 + [2] >= [0 0 0 0]x1 = q(s(x1)) [0 0 0 0] [0] [0 0 0 0] [1 0 0 0] [1 0 0 0] [0 0 0 0] [0 0 0 0] q(s(x1)) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(s(x1)) [0 0 0 0] [0 0 0 0] [1 0 0 0] [0] [1 0 0 0] [0 0 1 0] [1] [0 0 1 0] i(x1) = [0 0 1 1]x1 + [1] >= [0 0 0 0]x1 = s(x1) [0 1 1 0] [1] [0 0 0 0] problem: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) DP Processor: DPs: p#(s(s(x1))) -> p#(s(x1)) f#(s(x1)) -> i#(x1) f#(s(x1)) -> q#(i(x1)) f#(s(x1)) -> g#(q(i(x1))) g#(x1) -> p#(x1) g#(x1) -> p#(p(x1)) g#(x1) -> f#(p(p(x1))) q#(i(x1)) -> q#(s(x1)) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) TDG Processor: DPs: p#(s(s(x1))) -> p#(s(x1)) f#(s(x1)) -> i#(x1) f#(s(x1)) -> q#(i(x1)) f#(s(x1)) -> g#(q(i(x1))) g#(x1) -> p#(x1) g#(x1) -> p#(p(x1)) g#(x1) -> f#(p(p(x1))) q#(i(x1)) -> q#(s(x1)) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) graph: g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> g#(q(i(x1))) g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> q#(i(x1)) g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> i#(x1) g#(x1) -> p#(p(x1)) -> p#(s(s(x1))) -> p#(s(x1)) g#(x1) -> p#(x1) -> p#(s(s(x1))) -> p#(s(x1)) q#(i(x1)) -> q#(s(x1)) -> q#(i(x1)) -> q#(s(x1)) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> f#(p(p(x1))) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> p#(p(x1)) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> p#(x1) f#(s(x1)) -> q#(i(x1)) -> q#(i(x1)) -> q#(s(x1)) p#(s(s(x1))) -> p#(s(x1)) -> p#(s(s(x1))) -> p#(s(x1)) EDG Processor: DPs: p#(s(s(x1))) -> p#(s(x1)) f#(s(x1)) -> i#(x1) f#(s(x1)) -> q#(i(x1)) f#(s(x1)) -> g#(q(i(x1))) g#(x1) -> p#(x1) g#(x1) -> p#(p(x1)) g#(x1) -> f#(p(p(x1))) q#(i(x1)) -> q#(s(x1)) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) graph: g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> i#(x1) g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> q#(i(x1)) g#(x1) -> f#(p(p(x1))) -> f#(s(x1)) -> g#(q(i(x1))) g#(x1) -> p#(p(x1)) -> p#(s(s(x1))) -> p#(s(x1)) g#(x1) -> p#(x1) -> p#(s(s(x1))) -> p#(s(x1)) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> p#(x1) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> p#(p(x1)) f#(s(x1)) -> g#(q(i(x1))) -> g#(x1) -> f#(p(p(x1))) f#(s(x1)) -> q#(i(x1)) -> q#(i(x1)) -> q#(s(x1)) p#(s(s(x1))) -> p#(s(x1)) -> p#(s(s(x1))) -> p#(s(x1)) SCC Processor: #sccs: 2 #rules: 3 #arcs: 10/64 DPs: g#(x1) -> f#(p(p(x1))) f#(s(x1)) -> g#(q(i(x1))) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Usable Rule Processor: DPs: g#(x1) -> f#(p(p(x1))) f#(s(x1)) -> g#(q(i(x1))) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) i(x1) -> s(x1) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) Matrix Interpretation Processor: dim=4 interpretation: [g#](x0) = [1 0 0 1]x0 + [1], [f#](x0) = [0 1 1 0]x0, [0 0 0 1] [0] [0 0 1 1] [1] [q](x0) = [1 0 0 1]x0 + [1] [0 0 1 0] [0], [0 0 0 1] [0] [0 1 1 1] [1] [i](x0) = [0 1 0 0]x0 + [0] [0 0 1 0] [0], [0 0 0 1] [0] [0 0 1 1] [1] [s](x0) = [0 1 0 0]x0 + [0] [0 0 1 0] [0], [0 0 1 0] [0 0 1 0] [p](x0) = [0 0 0 1]x0 [1 0 0 0] , [0 0 0 1] [0] [0 0 0 1] [1] [0](x0) = [0 0 1 0]x0 + [0] [0 0 0 0] [0] orientation: g#(x1) = [1 0 0 1]x1 + [1] >= [1 0 0 1]x1 = f#(p(p(x1))) f#(s(x1)) = [0 1 1 1]x1 + [1] >= [0 1 1 0]x1 + [1] = g#(q(i(x1))) [0 0 0 1] [1] [0 0 0 1] [0] [0 0 0 1] [1] [0 0 0 1] [1] p(s(0(x1))) = [0 0 1 0]x1 + [0] >= [0 0 1 0]x1 + [0] = 0(x1) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 1 1] [1] [0 0 0 1] [0] [0 0 1 1] [1] [0 0 1 1] [1] p(s(s(x1))) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = s(p(s(x1))) [0 0 1 0] [0] [0 0 1 0] [0] [0 0 0 1] [0] [0 0 0 1] [0] [0 1 1 1] [1] [0 0 1 1] [1] i(x1) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = s(x1) [0 0 1 0] [0] [0 0 1 0] [0] [0 0 1 0] [0] [0 0 1 0] [0] [0 1 1 0] [1] [0 1 1 0] [1] q(i(x1)) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = q(s(x1)) [0 1 0 0] [0] [0 1 0 0] [0] [0 0 1 0] [0] [0 0 1 0] [0] [0 1 1 0] [1] [0 1 1 0] [1] q(s(x1)) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = s(s(x1)) [0 1 0 0] [0] [0 1 0 0] [0] problem: DPs: f#(s(x1)) -> g#(q(i(x1))) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) i(x1) -> s(x1) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) Restore Modifier: DPs: f#(s(x1)) -> g#(q(i(x1))) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) EDG Processor: DPs: f#(s(x1)) -> g#(q(i(x1))) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1 DPs: p#(s(s(x1))) -> p#(s(x1)) TRS: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Usable Rule Processor: DPs: p#(s(s(x1))) -> p#(s(x1)) TRS: Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [p#](x0) = 3x0 + 0, [s](x0) = 1x0 + 3 orientation: p#(s(s(x1))) = 5x1 + 7 >= 4x1 + 6 = p#(s(x1)) problem: DPs: TRS: Qed