/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: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> 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)))) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> 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)))) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 graph: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(b(b(a(a(x1))))) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> b#(b(a(a(x1)))) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> b#(a(a(x1))) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(a(x1)) a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(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#(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))) -> a#(b(b(a(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) SCC Processor: #sccs: 1 #rules: 3 #arcs: 15/25 DPs: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) a#(a(b(x1))) -> a#(x1) a#(a(b(x1))) -> a#(a(x1)) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 interpretation: [a#](x0) = [-& -& 0 ]x0 + [0], [0 0 0 ] [1 ] [c](x0) = [-& -& -&]x0 + [-&] [-& -& -&] [1 ], [0 0 1] [0 ] [b](x0) = [0 1 1]x0 + [-&] [0 0 0] [1 ], [0 0 1 ] [-&] [a](x0) = [-& 0 0 ]x0 + [-&] [-& 0 0 ] [0 ] orientation: a#(a(b(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a#(b(b(a(a(x1))))) a#(a(b(x1))) = [0 1 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(x1) a#(a(b(x1))) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = a#(a(x1)) [0 0 1 ] [-&] a(x1) = [-& 0 0 ]x1 + [-&] >= x1 = x1 [-& 0 0 ] [0 ] [1 2 2] [2] [1 2 2 ] [2 ] a(a(b(x1))) = [0 1 1]x1 + [1] >= [-& -& -&]x1 + [-&] = c(a(b(b(a(a(x1)))))) [0 1 1] [1] [-& -& -&] [1 ] [0 0 0] [2] b(c(x1)) = [0 0 0]x1 + [2] >= x1 = x1 [0 0 0] [1] problem: DPs: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 Restore Modifier: DPs: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 EDG Processor: DPs: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 graph: a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(b(b(a(a(x1))))) Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 interpretation: [a#](x0) = [0 0 1]x0 + [0], [0 0 -&] [1] [c](x0) = [0 0 0 ]x0 + [0] [1 0 0 ] [0], [0 -& -&] [1] [b](x0) = [0 -& -&]x0 + [1] [0 0 -&] [0], [0 -& -&] [1 ] [a](x0) = [0 0 0 ]x0 + [-&] [0 1 0 ] [0 ] orientation: a#(a(b(x1))) = [2 1 -&]x1 + [3] >= [1 -& -&]x1 + [2] = a#(b(b(a(a(x1))))) [0 -& -&] [1 ] a(x1) = [0 0 0 ]x1 + [-&] >= x1 = x1 [0 1 0 ] [0 ] [0 -& -&] [1] [0 -& -&] [1] a(a(b(x1))) = [1 0 -&]x1 + [2] >= [1 -& -&]x1 + [2] = c(a(b(b(a(a(x1)))))) [1 1 -&] [2] [1 -& -&] [2] [0 0 -&] [1] b(c(x1)) = [0 0 -&]x1 + [1] >= x1 = x1 [0 0 0 ] [1] problem: DPs: TRS: a(x1) -> x1 a(a(b(x1))) -> c(a(b(b(a(a(x1)))))) b(c(x1)) -> x1 Qed