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