/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: b(b(a(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(b(a(b(x1)))) a(b(a(a(x1)))) -> a(a(a(b(x1)))) Proof: String Reversal Processor: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) DP Processor: DPs: b#(a(b(b(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) TDG Processor: DPs: b#(a(b(b(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) graph: a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(b(x1))) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(a(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(a(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(a(x1)) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(b(x1)) b#(a(b(b(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(x1) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) EDG Processor: DPs: b#(a(b(b(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) graph: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> a#(b(b(x1))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) b#(a(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> a#(b(x1)) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> a#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) SCC Processor: #sccs: 1 #rules: 7 #arcs: 29/100 DPs: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) b#(a(b(b(x1)))) -> a#(a(b(x1))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) a#(a(b(a(x1)))) -> a#(a(a(x1))) a#(a(b(a(x1)))) -> a#(a(x1)) a#(a(a(a(x1)))) -> b#(x1) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) interpretation: [a](x0) = 1x0, [a#](x0) = x0, [b](x0) = 1x0, [b#](x0) = x0 orientation: a#(a(a(a(x1)))) = 3x1 >= 3x1 = b#(a(b(b(x1)))) b#(a(b(b(x1)))) = 3x1 >= 3x1 = b#(a(a(b(x1)))) b#(a(b(b(x1)))) = 3x1 >= 2x1 = a#(a(b(x1))) a#(a(b(a(x1)))) = 3x1 >= 3x1 = b#(a(a(a(x1)))) a#(a(b(a(x1)))) = 3x1 >= 2x1 = a#(a(a(x1))) a#(a(b(a(x1)))) = 3x1 >= 1x1 = a#(a(x1)) a#(a(a(a(x1)))) = 3x1 >= x1 = b#(x1) b(a(b(b(x1)))) = 4x1 >= 4x1 = b(a(a(b(x1)))) a(a(a(a(x1)))) = 4x1 >= 4x1 = b(a(b(b(x1)))) a(a(b(a(x1)))) = 4x1 >= 4x1 = b(a(a(a(x1)))) problem: DPs: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) Restore Modifier: DPs: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) EDG Processor: DPs: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) graph: a#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 3/9 DPs: b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4} transitions: b0(3) -> 5* b0(2) -> 1* b0(1) -> 1* b{#,0}(7) -> 4* a0(1) -> 2* a0(6) -> 7* a0(2) -> 2* a0(5) -> 6* 2 -> 3* 1 -> 7,2,3 problem: DPs: TRS: b(a(b(b(x1)))) -> b(a(a(b(x1)))) a(a(a(a(x1)))) -> b(a(b(b(x1)))) a(a(b(a(x1)))) -> b(a(a(a(x1)))) Qed