/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(a(b(x1)))) -> b(a(b(a(a(a(x1)))))) b(a(x1)) -> x1 Proof: String Reversal Processor: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 DP Processor: DPs: b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> a#(a(b(a(b(x1))))) b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1)))))) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 TDG Processor: DPs: b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> a#(a(b(a(b(x1))))) b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1)))))) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 graph: b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1)))))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(a(b(a(b(x1))))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(a(b(a(b(x1)))))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(b(a(b(x1))))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(a(b(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) SCC Processor: #sccs: 1 #rules: 2 #arcs: 12/36 DPs: b#(a(a(a(x1)))) -> b#(a(b(x1))) b#(a(a(a(x1)))) -> b#(x1) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 Arctic Interpretation Processor: dimension: 3 usable rules: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 interpretation: [b#](x0) = [0 0 0]x0 + [0], [-& -& 0 ] [0] [a](x0) = [1 -& 0 ]x0 + [1] [0 0 -&] [0], [-& -& 0 ] [0 ] [b](x0) = [-& -& 0 ]x0 + [0 ] [0 0 1 ] [-&] orientation: b#(a(a(a(x1)))) = [1 1 1]x1 + [1] >= [0 0 1]x1 + [1] = b#(a(b(x1))) b#(a(a(a(x1)))) = [1 1 1]x1 + [1] >= [0 0 0]x1 + [0] = b#(x1) [0 0 1] [1] [0 0 1] [1] b(a(a(a(x1)))) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(a(a(b(a(b(x1)))))) [1 1 2] [2] [1 1 2] [2] [0 0 1 ] [0] a(b(x1)) = [0 0 1 ]x1 + [1] >= x1 = x1 [-& -& 0 ] [0] problem: DPs: b#(a(a(a(x1)))) -> b#(a(b(x1))) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 Restore Modifier: DPs: b#(a(a(a(x1)))) -> b#(a(b(x1))) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 EDG Processor: DPs: b#(a(a(a(x1)))) -> b#(a(b(x1))) TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 graph: b#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(a(a(x1)))) -> b#(a(b(x1))) Arctic Interpretation Processor: dimension: 3 usable rules: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 interpretation: [b#](x0) = [0 0 1]x0 + [0], [-& 1 0 ] [0] [a](x0) = [-& -& 0 ]x0 + [0] [0 0 -&] [0], [-& -& 0 ] [0 ] [b](x0) = [-& -& 0 ]x0 + [-&] [0 0 1 ] [0 ] orientation: b#(a(a(a(x1)))) = [1 1 2]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(b(x1))) [0 0 1] [1] [0 0 1] [1] b(a(a(a(x1)))) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(a(a(b(a(b(x1)))))) [1 1 2] [2] [1 1 2] [2] [0 0 1 ] [0] a(b(x1)) = [0 0 1 ]x1 + [0] >= x1 = x1 [-& -& 0 ] [0] problem: DPs: TRS: b(a(a(a(x1)))) -> a(a(a(b(a(b(x1)))))) a(b(x1)) -> x1 Qed