/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(x1))) -> b(b(a(x1))) a(b(a(x1))) -> b(b(a(x1))) b(a(b(x1))) -> a(a(b(x1))) Proof: String Reversal Processor: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) DP Processor: DPs: a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> b#(x1) a#(b(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> b#(a(a(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) TDG Processor: DPs: a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> b#(x1) a#(b(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> b#(a(a(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) graph: b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(x1) b#(a(b(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1) a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(a(x1)) a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(x1) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1)) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(x1) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(x1) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(x1) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(x1) EDG Processor: DPs: a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> b#(x1) a#(b(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> b#(a(a(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) graph: b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(x1) b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(b(x1))) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(x1)) b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1)) a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(x1) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(b(x1)) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(x1) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) SCC Processor: #sccs: 1 #rules: 7 #arcs: 24/81 DPs: b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> b#(x1) b#(a(b(x1))) -> a#(x1) a#(a(a(x1))) -> b#(x1) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) interpretation: [b#](x0) = x0, [a#](x0) = 8x0, [b](x0) = 8x0, [a](x0) = 8x0 orientation: b#(a(b(x1))) = 16x1 >= 16x1 = b#(a(a(x1))) b#(a(b(x1))) = 16x1 >= 16x1 = a#(a(x1)) a#(a(a(x1))) = 24x1 >= 24x1 = a#(b(b(x1))) a#(b(a(x1))) = 24x1 >= 24x1 = a#(b(b(x1))) a#(b(a(x1))) = 24x1 >= x1 = b#(x1) b#(a(b(x1))) = 16x1 >= 8x1 = a#(x1) a#(a(a(x1))) = 24x1 >= x1 = b#(x1) a(a(a(x1))) = 24x1 >= 24x1 = a(b(b(x1))) a(b(a(x1))) = 24x1 >= 24x1 = a(b(b(x1))) b(a(b(x1))) = 24x1 >= 24x1 = b(a(a(x1))) problem: DPs: b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Restore Modifier: DPs: b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) EDG Processor: DPs: b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> a#(a(x1)) a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) graph: b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> b#(a(a(x1))) b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(a(x1)) b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) SCC Processor: #sccs: 2 #rules: 2 #arcs: 5/16 DPs: b#(a(b(x1))) -> b#(a(a(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Matrix Interpretation Processor: dim=3 interpretation: [b#](x0) = [0 1 0]x0 + [1], [0 0 1] [1] [b](x0) = [1 1 0]x0 + [0] [0 0 0] [0], [0 0 1] [0] [a](x0) = [1 0 0]x0 + [0] [0 0 0] [1] orientation: b#(a(b(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(a(x1))) [1] [0] a(a(a(x1))) = [1] >= [1] = a(b(b(x1))) [1] [1] [0] [0] a(b(a(x1))) = [2] >= [1] = a(b(b(x1))) [1] [1] [0 0 0] [2] [0 0 0] [2] b(a(b(x1))) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = b(a(a(x1))) [0 0 0] [0] [0 0 0] [0] problem: DPs: TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Qed DPs: a#(b(a(x1))) -> a#(b(b(x1))) TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4} transitions: a{#,0}(6) -> 4* b0(5) -> 6* b0(2) -> 2* b0(1) -> 2* b0(3) -> 5* a0(2) -> 1* a0(1) -> 1* 1 -> 3* 2 -> 3* problem: DPs: TRS: a(a(a(x1))) -> a(b(b(x1))) a(b(a(x1))) -> a(b(b(x1))) b(a(b(x1))) -> b(a(a(x1))) Qed