/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) b(a(b(b(x1)))) -> a(b(a(a(x1)))) Proof: String Reversal Processor: b(a(b(a(x1)))) -> a(a(b(b(x1)))) a(b(a(b(x1)))) -> b(a(b(a(x1)))) b(b(a(b(x1)))) -> a(a(b(a(x1)))) Matrix Interpretation Processor: dim=1 interpretation: [a](x0) = x0, [b](x0) = 2x0 + 4 orientation: b(a(b(a(x1)))) = 4x1 + 12 >= 4x1 + 12 = a(a(b(b(x1)))) a(b(a(b(x1)))) = 4x1 + 12 >= 4x1 + 12 = b(a(b(a(x1)))) b(b(a(b(x1)))) = 8x1 + 28 >= 2x1 + 4 = a(a(b(a(x1)))) problem: b(a(b(a(x1)))) -> a(a(b(b(x1)))) a(b(a(b(x1)))) -> b(a(b(a(x1)))) String Reversal Processor: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) DP Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> a#(a(x1)) a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) TDG Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> a#(a(x1)) a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) graph: b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(a(x1)) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(x1)) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> b#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> a#(a(x1)) a#(b(a(b(x1)))) -> a#(a(x1)) -> a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(a(x1)) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3} transitions: a{#,0}(5) -> 3* a0(32) -> 33* a0(4) -> 5* f40() -> 4* b0(34) -> 35* b0(33) -> 34* 35 -> 5* 5 -> 32* problem: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Restore Modifier: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) EDG Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) graph: b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> b#(x1) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) a#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(a(x1))) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3} transitions: b{#,0}(6) -> 3* a0(4) -> 5* a0(5) -> 6* b0(31) -> 32* b0(30) -> 31* f100() -> 4* 6 -> 30* 32 -> 5* problem: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Restore Modifier: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) EDG Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) graph: b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(x1)) a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3} transitions: b{#,0}(7) -> 3* a0(4) -> 5* a0(5) -> 6* f120() -> 4* b0(27) -> 28* b0(6) -> 7* 7 -> 27* 28 -> 5* problem: DPs: a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Restore Modifier: DPs: a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) EDG Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) graph: b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(x1)) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) b#(a(b(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1) b#(a(b(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1) a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1) SCC Processor: #sccs: 2 #rules: 3 #arcs: 11/25 DPs: b#(a(b(a(x1)))) -> b#(a(b(x1))) b#(a(b(a(x1)))) -> b#(x1) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) interpretation: [a](x0) = 3x0, [b#](x0) = x0, [b](x0) = 5x0 orientation: b#(a(b(a(x1)))) = 11x1 >= 8x1 = b#(a(b(x1))) b#(a(b(a(x1)))) = 11x1 >= x1 = b#(x1) a(b(a(b(x1)))) = 16x1 >= 16x1 = b(b(a(a(x1)))) b(a(b(a(x1)))) = 16x1 >= 16x1 = a(b(a(b(x1)))) problem: DPs: TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Qed DPs: a#(b(a(b(x1)))) -> a#(x1) TRS: a(b(a(b(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> a(b(a(b(x1)))) Usable Rule Processor: DPs: a#(b(a(b(x1)))) -> a#(x1) TRS: Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [a](x0) = 3x0 + 2, [b](x0) = x0, [a#](x0) = x0 orientation: a#(b(a(b(x1)))) = 3x1 + 2 >= x1 = a#(x1) problem: DPs: TRS: Qed