/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(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) Proof: DP Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(a(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) TDG Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(a(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) graph: b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> b#(a(a(a(x1)))) -> b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) EDG Processor: DPs: a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(x1) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> b#(a(a(a(x1)))) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) graph: b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(b(x1)))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(x1))) -> b#(a(a(a(x1)))) SCC Processor: #sccs: 1 #rules: 6 #arcs: 24/64 DPs: b#(b(b(x1))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(b(b(x1))) b#(b(b(x1))) -> a#(a(x1)) a#(a(b(a(x1)))) -> b#(b(x1)) b#(b(b(x1))) -> a#(x1) a#(a(b(a(x1)))) -> b#(x1) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) Arctic Interpretation Processor: dimension: 3 usable rules: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) interpretation: [b#](x0) = [-& -& 0 ]x0 + [0], [a#](x0) = [0 0 -&]x0 + [0], [0 0 1 ] [0] [b](x0) = [0 0 0 ]x0 + [0] [-& 0 0 ] [1], [-& 0 0 ] [0] [a](x0) = [0 0 0 ]x0 + [0] [0 0 0 ] [1] orientation: b#(b(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a#(a(a(x1))) a#(a(b(a(x1)))) = [1 1 1]x1 + [2] >= [0 0 0]x1 + [1] = b#(b(b(x1))) b#(b(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a#(a(x1)) a#(a(b(a(x1)))) = [1 1 1]x1 + [2] >= [-& 0 0 ]x1 + [1] = b#(b(x1)) b#(b(b(x1))) = [0 0 0]x1 + [1] >= [0 0 -&]x1 + [0] = a#(x1) a#(a(b(a(x1)))) = [1 1 1]x1 + [2] >= [-& -& 0 ]x1 + [0] = b#(x1) [1 1 1] [2] [0 1 1] [2] a(a(b(a(x1)))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = a(b(b(b(x1)))) [1 1 1] [2] [1 1 1] [2] [1 1 1] [2] [1 1 1] [2] b(b(b(x1))) = [0 1 1]x1 + [2] >= [0 0 0]x1 + [1] = b(a(a(a(x1)))) [0 0 1] [1] [0 0 0] [1] problem: DPs: b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) Restore Modifier: DPs: b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) EDG Processor: DPs: b#(b(b(x1))) -> a#(a(a(x1))) b#(b(b(x1))) -> a#(a(x1)) b#(b(b(x1))) -> a#(x1) TRS: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/9