/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) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) Proof: DP Processor: DPs: a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(b(a(a(x1)))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) TDG Processor: DPs: a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(b(a(a(x1)))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(c(x1)) -> a#(x1) a#(a(b(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) Arctic Interpretation Processor: dimension: 4 usable rules: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) interpretation: [b#](x0) = [0 0 0 0]x0 + [0], [a#](x0) = [0 -& 0 0 ]x0, [1 0 0 0 ] [1 ] [0 -& 0 0 ] [-&] [c](x0) = [0 -& 0 0 ]x0 + [0 ] [0 0 1 1 ] [1 ], [-& -& 0 -&] [0] [0 0 1 0 ] [0] [b](x0) = [-& -& 0 -&]x0 + [0] [0 -& 0 -&] [0], [0 -& 0 0 ] [0] [0 0 0 0 ] [0] [a](x0) = [-& -& 0 -&]x0 + [0] [0 0 0 0 ] [1] orientation: a#(a(b(x1))) = [0 0 1 0]x1 + [1] >= [0 -& 0 0 ]x1 = a#(x1) a#(a(b(x1))) = [0 0 1 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a#(a(x1)) a#(a(b(x1))) = [0 0 1 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b#(a(a(x1))) a#(a(b(x1))) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 + [1] = b#(b(a(a(x1)))) b#(c(x1)) = [1 0 1 1]x1 + [1] >= [0 -& 0 0 ]x1 = a#(x1) [0 -& 0 0 ] [0] [0 0 0 0 ] [0] a(x1) = [-& -& 0 -&]x1 + [0] >= x1 = x1 [0 0 0 0 ] [1] [0 0 1 0 ] [1] [0 0 1 0 ] [1] [0 0 1 0 ] [1] [-& -& 0 -&] [0] a(a(b(x1))) = [-& -& 0 -&]x1 + [0] >= [-& -& 0 -&]x1 + [0] = c(b(b(a(a(x1))))) [0 0 1 0 ] [1] [0 0 1 0 ] [1] [0 -& 0 0 ] [0] [0 -& 0 0 ] [0] [1 0 1 1 ] [1] [0 0 0 0 ] [0] b(c(x1)) = [0 -& 0 0 ]x1 + [0] >= [-& -& 0 -&]x1 + [0] = a(x1) [1 0 0 0 ] [1] [0 0 0 0 ] [1] problem: DPs: a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(b(a(a(x1)))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(b(a(a(x1)))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) EDG Processor: DPs: a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> b#(b(a(a(x1)))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) SCC Processor: #sccs: 1 #rules: 2 #arcs: 8/16 DPs: a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(x1) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) Arctic Interpretation Processor: dimension: 1 usable rules: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) interpretation: [a#](x0) = x0 + 0, [c](x0) = 7, [b](x0) = 9x0 + 7, [a](x0) = x0 + 11 orientation: a#(a(b(x1))) = 9x1 + 11 >= x1 + 11 = a#(a(x1)) a#(a(b(x1))) = 9x1 + 11 >= x1 + 0 = a#(x1) a(x1) = x1 + 11 >= x1 = x1 a(a(b(x1))) = 9x1 + 11 >= 7 = c(b(b(a(a(x1))))) b(c(x1)) = 16 >= x1 + 11 = a(x1) problem: DPs: a#(a(b(x1))) -> a#(a(x1)) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: a#(a(b(x1))) -> a#(a(x1)) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) EDG Processor: DPs: a#(a(b(x1))) -> a#(a(x1)) TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) graph: a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1)) Arctic Interpretation Processor: dimension: 1 usable rules: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) interpretation: [a#](x0) = 2x0, [c](x0) = 5, [b](x0) = 2x0 + 4, [a](x0) = 2x0 orientation: a#(a(b(x1))) = 6x1 + 8 >= 4x1 = a#(a(x1)) a(x1) = 2x1 >= x1 = x1 a(a(b(x1))) = 6x1 + 8 >= 5 = c(b(b(a(a(x1))))) b(c(x1)) = 7 >= 2x1 = a(x1) problem: DPs: TRS: a(x1) -> x1 a(a(b(x1))) -> c(b(b(a(a(x1))))) b(c(x1)) -> a(x1) Qed