/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a(a(a(a(x1)))) -> b(a(b(b(x1)))) b(b(a(a(x1)))) -> a(a(b(b(x1)))) b(a(b(b(x1)))) -> a(a(b(b(x1)))) Proof: String Reversal Processor: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) DP Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) TDG Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(a(a(x1))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(x1) EDG Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) b#(b(a(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(a(a(x1))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(a(a(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) SCC Processor: #sccs: 1 #rules: 8 #arcs: 48/144 DPs: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(b(a(a(x1)))) b#(b(a(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) interpretation: [b](x0) = 4x0 + 14, [b#](x0) = 2x0 + 0, [a](x0) = 4x0 + 14, [a#](x0) = 6x0 orientation: b#(b(a(b(x1)))) = 14x1 + 24 >= 14x1 + 24 = b#(b(a(a(x1)))) b#(b(a(b(x1)))) = 14x1 + 24 >= 10x1 + 20 = a#(a(x1)) a#(a(b(b(x1)))) = 18x1 + 28 >= 14x1 + 24 = b#(b(a(a(x1)))) b#(b(a(b(x1)))) = 14x1 + 24 >= 6x1 = a#(x1) a#(a(b(b(x1)))) = 18x1 + 28 >= 10x1 + 20 = a#(a(x1)) a#(a(b(b(x1)))) = 18x1 + 28 >= 6x1 = a#(x1) a#(a(a(a(x1)))) = 18x1 + 28 >= 14x1 + 24 = b#(b(a(b(x1)))) a#(a(a(a(x1)))) = 18x1 + 28 >= 2x1 + 0 = b#(x1) a(a(a(a(x1)))) = 16x1 + 26 >= 16x1 + 26 = b(b(a(b(x1)))) a(a(b(b(x1)))) = 16x1 + 26 >= 16x1 + 26 = b(b(a(a(x1)))) b(b(a(b(x1)))) = 16x1 + 26 >= 16x1 + 26 = b(b(a(a(x1)))) problem: DPs: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) Restore Modifier: DPs: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) EDG Processor: DPs: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) graph: b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(b(a(a(x1)))) Bounds Processor: bound: 1 enrichment: match-dp automaton: final states: {1} transitions: b{#,0}(5) -> 1* a0(16) -> 17* a0(12) -> 13* a0(3) -> 4* a0(2) -> 3* a1(34) -> 35* a1(21) -> 22* a1(20) -> 21* b1(22) -> 23* b1(30) -> 31* b{#,1}(23) -> 24* f40() -> 2* b0(13) -> 14* b0(4) -> 5* b0(14) -> 15* b0(11) -> 12* 24 -> 1* 17 -> 12* 35 -> 21* 30 -> 34* 14 -> 20* 11 -> 16* 2 -> 11* 31 -> 15,17,3,4,13,12,22 15 -> 17,13,3,4 23 -> 30* problem: DPs: TRS: a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(a(b(b(x1)))) -> b(b(a(a(x1)))) b(b(a(b(x1)))) -> b(b(a(a(x1)))) Qed