/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(b(b(x1)))) -> b(b(a(b(x1)))) a(b(a(a(x1)))) -> b(a(b(a(x1)))) b(b(a(a(x1)))) -> b(a(a(a(x1)))) a(b(b(b(x1)))) -> a(b(a(a(x1)))) Proof: Matrix Interpretation Processor: dim=4 interpretation: [1 0 0 0] [0] [0 0 0 0] [1] [a](x0) = [0 1 0 0]x0 + [0] [0 0 0 0] [0], [1 0 0 1] [0 0 0 0] [b](x0) = [0 0 1 0]x0 [0 0 1 0] orientation: [1 0 2 1] [0] [1 0 0 1] [0 0 0 0] [1] [0 0 0 0] a(b(b(b(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = b(b(a(b(x1)))) [0 0 0 0] [0] [0 0 0 0] [1 0 0 0] [0] [1 0 0 0] [0 0 0 0] [1] [0 0 0 0] a(b(a(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = b(a(b(a(x1)))) [0 0 0 0] [0] [0 0 0 0] [1 0 0 0] [1] [1 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(b(a(a(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(a(a(x1)))) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 2 1] [0] [1 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] a(b(b(b(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(b(a(a(x1)))) [0 0 0 0] [0] [0 0 0 0] [0] problem: a(b(b(b(x1)))) -> b(b(a(b(x1)))) a(b(a(a(x1)))) -> b(a(b(a(x1)))) a(b(b(b(x1)))) -> a(b(a(a(x1)))) String Reversal Processor: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) DP Processor: DPs: b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) TDG Processor: DPs: b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(b(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) EDG Processor: DPs: b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) a#(a(b(a(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(x1)) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(a(b(x1))) b#(b(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> b#(b(x1)) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> b#(x1) -> b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) SCC Processor: #sccs: 1 #rules: 8 #arcs: 38/100 DPs: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(a(b(a(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(x1) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) b#(b(b(a(x1)))) -> a#(b(a(x1))) b#(b(b(a(x1)))) -> a#(b(b(x1))) b#(b(b(a(x1)))) -> b#(b(x1)) b#(b(b(a(x1)))) -> b#(x1) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) interpretation: [a](x0) = 1x0 + 12, [a#](x0) = x0 + 0, [b](x0) = 1x0 + 9, [b#](x0) = x0 + 0 orientation: a#(a(b(a(x1)))) = 3x1 + 14 >= 3x1 + 13 = a#(b(a(b(x1)))) a#(a(b(a(x1)))) = 3x1 + 14 >= 1x1 + 9 = a#(b(x1)) a#(a(b(a(x1)))) = 3x1 + 14 >= x1 + 0 = b#(x1) b#(b(b(a(x1)))) = 3x1 + 14 >= 3x1 + 14 = a#(a(b(a(x1)))) b#(b(b(a(x1)))) = 3x1 + 14 >= 2x1 + 13 = a#(b(a(x1))) b#(b(b(a(x1)))) = 3x1 + 14 >= 2x1 + 10 = a#(b(b(x1))) b#(b(b(a(x1)))) = 3x1 + 14 >= 1x1 + 9 = b#(b(x1)) b#(b(b(a(x1)))) = 3x1 + 14 >= x1 + 0 = b#(x1) b(b(b(a(x1)))) = 4x1 + 15 >= 4x1 + 13 = b(a(b(b(x1)))) a(a(b(a(x1)))) = 4x1 + 15 >= 4x1 + 14 = a(b(a(b(x1)))) b(b(b(a(x1)))) = 4x1 + 15 >= 4x1 + 15 = a(a(b(a(x1)))) problem: DPs: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) Restore Modifier: DPs: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) EDG Processor: DPs: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) graph: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(b(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: a#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4} transitions: b0(3) -> 5* b0(2) -> 1* b0(6) -> 7* b0(1) -> 1* a{#,0}(7) -> 4* a0(1) -> 2* a0(2) -> 2* a0(5) -> 6* 2 -> 5,1,3 1 -> 3* problem: DPs: TRS: b(b(b(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> a(b(a(b(x1)))) b(b(b(a(x1)))) -> a(a(b(a(x1)))) Qed