/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: b(a(b(x1))) -> b(a(a(a(b(x1))))) b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1) b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) b(a(a(b(b(x1))))) -> b(x1) b(b(a(a(b(x1))))) -> b(x1) b(a(a(a(b(a(b(x1))))))) -> b(x1) b(a(b(a(a(a(b(x1))))))) -> b(x1) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [a](x0) = [0 0 0]x0 [0 1 0] , [1 0 1] [0] [b](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 1] [1] [1 0 1] [0] b(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(a(b(x1))))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(a(a(a(b(a(a(a(b(x1))))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(a(a(a(b(b(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(a(a(b(x1))))))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(a(a(b(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(b(a(a(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [0] b(a(a(a(b(a(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [0] b(a(b(a(a(a(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] problem: b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1) b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) b(a(a(b(b(x1))))) -> b(x1) b(b(a(a(b(x1))))) -> b(x1) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [a](x0) = [0 0 1]x0 [0 1 0] , [1 0 1] [0] [b](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 1] [1] [1 0 1] [1] b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [2] [1 0 1] [0] b(a(a(a(b(a(a(a(b(x1))))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] b(a(a(a(b(b(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(a(a(b(x1))))))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(a(a(b(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] b(b(a(a(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] problem: b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) b(a(a(b(b(x1))))) -> b(x1) b(b(a(a(b(x1))))) -> b(x1) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [a](x0) = [0 0 1]x0 [1 0 0] , [1 0 0] [0] [b](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [2 0 0] [3] [2 0 0] [3] b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) [0 0 0] [0] [0 0 0] [0] [2 0 0] [1] [2 0 0] [1] b(a(a(a(b(b(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(a(a(b(x1))))))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [0] b(a(a(b(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [0] b(b(a(a(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) [0 0 0] [0] [0 0 0] [0] problem: b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) String Reversal Processor: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) DP Processor: DPs: b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(a(b(a(a(b(a(a(b(x1))))))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) -> b#(a(a(a(b(b(b(x1))))))) TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) EDG Processor: DPs: b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(a(b(a(a(b(a(a(b(x1))))))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) -> b#(a(a(a(b(b(b(x1))))))) TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) graph: b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(a(b(a(a(b(a(a(b(x1))))))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(a(b(a(a(b(a(a(b(x1))))))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) -> b#(a(a(b(a(a(a(b(x1)))))))) -> b#(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) -> b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) -> b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) -> b#(b(b(a(a(a(b(x1))))))) -> b#(a(a(a(b(b(b(x1))))))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) -> b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) -> b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) -> b#(b(b(a(a(a(b(x1))))))) -> b#(a(a(a(b(b(b(x1))))))) SCC Processor: #sccs: 2 #rules: 4 #arcs: 14/49 DPs: b#(b(b(a(a(a(b(x1))))))) -> b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) -> b#(b(x1)) TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [0 0 0 1]x0, [0 0 0 0] [1] [0 0 1 0] [0] [a](x0) = [1 1 0 1]x0 + [0] [0 1 0 0] [0], [0 0 0 0] [0 0 0 0] [b](x0) = [0 0 0 0]x0 [0 1 0 1] orientation: b#(b(b(a(a(a(b(x1))))))) = [0 1 0 1]x1 + [1] >= [0 1 0 1]x1 = b#(b(b(x1))) b#(b(b(a(a(a(b(x1))))))) = [0 1 0 1]x1 + [1] >= [0 1 0 1]x1 = b#(b(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(a(a(b(a(a(a(b(x1)))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) [0 1 0 1] [1] [0 1 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(b(b(a(a(a(b(x1))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(a(a(b(b(b(x1))))))) [0 1 0 1] [1] [0 1 0 1] [1] problem: DPs: TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) Qed DPs: b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) -> b#(a(a(b(x1)))) TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [1 0 0 0]x0, [0 1 0 0] [0 0 0 1] [a](x0) = [0 0 0 0]x0 [1 0 1 0] , [0 0 0 0] [0] [0 0 0 0] [0] [b](x0) = [0 0 0 0]x0 + [1] [1 0 0 1] [0] orientation: b#(a(a(b(a(a(a(b(x1)))))))) = [1 0 0 1]x1 + [1] >= [1 0 0 1]x1 = b#(a(a(b(a(a(b(x1))))))) b#(a(a(b(a(a(a(b(x1)))))))) = [1 0 0 1]x1 + [1] >= [1 0 0 1]x1 = b#(a(a(b(x1)))) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(a(a(b(a(a(a(b(x1)))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) [1 0 0 1] [1] [1 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(b(b(a(a(a(b(x1))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(a(a(b(b(b(x1))))))) [1 0 0 1] [1] [1 0 0 1] [1] problem: DPs: TRS: b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) Qed