/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(x1) -> x1 a(a(x1)) -> b(a(b(c(c(b(x1)))))) c(b(x1)) -> a(x1) Proof: String Reversal Processor: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) DP Processor: DPs: a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) a#(a(x1)) -> b#(c(c(b(a(b(x1)))))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) TDG Processor: DPs: a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) a#(a(x1)) -> b#(c(c(b(a(b(x1)))))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(c(b(a(b(x1)))))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) a#(a(x1)) -> b#(c(c(b(a(b(x1)))))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(c(b(a(b(x1)))))) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {10} transitions: a0(40) -> 41* a0(67) -> 68* a0(12) -> 13* a0(83) -> 84* a0(115) -> 116* c0(70) -> 71* c0(15) -> 16* c0(69) -> 70* c0(14) -> 15* f50() -> 11* b{#,0}(16) -> 10* a{#,0}(23) -> 24* b0(11) -> 12* b0(68) -> 69* b0(13) -> 14* 11 -> 40* 12 -> 41,116,13 14 -> 67* 15 -> 23* 24 -> 10* 40 -> 41* 41 -> 12,13 67 -> 68* 69 -> 115* 70 -> 83* 71 -> 11* 83 -> 84,12,67 84 -> 12,14,67,13 115 -> 116,67,69 116 -> 69,14 problem: DPs: a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) EDG Processor: DPs: a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> b#(a(b(x1))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(x1))) a#(a(x1)) -> b#(a(b(x1))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(x1))) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) interpretation: [b#](x0) = [-& 0 ]x0 + [0], [a#](x0) = [-& 1 ]x0 + [0], [-& -&] [3] [c](x0) = [3 3 ]x0 + [3], [-& 0 ] [0] [b](x0) = [-& -3]x0 + [0], [3 3] [3] [a](x0) = [0 0]x0 + [0] orientation: a#(a(x1)) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1) a#(a(x1)) = [1 1]x1 + [1] >= [-& -2]x1 + [1] = a#(b(x1)) a#(a(x1)) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(a(b(x1))) b#(c(x1)) = [3 3]x1 + [3] >= [-& 1 ]x1 + [0] = a#(x1) [3 3] [3] a(x1) = [0 0]x1 + [0] >= x1 = x1 [6 6] [6] [-& 6 ] [6] a(a(x1)) = [3 3]x1 + [3] >= [-& 3 ]x1 + [3] = b(c(c(b(a(b(x1)))))) [3 3] [3] [3 3] [3] b(c(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(x1) problem: DPs: a#(a(x1)) -> a#(b(x1)) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: a#(a(x1)) -> a#(b(x1)) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) EDG Processor: DPs: a#(a(x1)) -> a#(b(x1)) TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) graph: a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) interpretation: [a#](x0) = [0 0 0]x0 + [0], [0 0 0] [0] [c](x0) = [0 0 0]x0 + [0] [1 1 1] [1], [0 -& -&] [0 ] [b](x0) = [0 -& 0 ]x0 + [0 ] [0 -& -&] [-&], [0 0 -&] [0 ] [a](x0) = [1 1 1 ]x0 + [1 ] [0 0 0 ] [-&] orientation: a#(a(x1)) = [1 1 1]x1 + [1] >= [0 -& 0 ]x1 + [0] = a#(b(x1)) [0 0 -&] [0 ] a(x1) = [1 1 1 ]x1 + [1 ] >= x1 = x1 [0 0 0 ] [-&] [1 1 1] [1] [1 -& 1 ] [1] a(a(x1)) = [2 2 2]x1 + [2] >= [2 -& 2 ]x1 + [2] = b(c(c(b(a(b(x1)))))) [1 1 1] [1] [1 -& 1 ] [1] [0 0 0] [0] [0 0 -&] [0 ] b(c(x1)) = [1 1 1]x1 + [1] >= [1 1 1 ]x1 + [1 ] = a(x1) [0 0 0] [0] [0 0 0 ] [-&] problem: DPs: TRS: a(x1) -> x1 a(a(x1)) -> b(c(c(b(a(b(x1)))))) b(c(x1)) -> a(x1) Qed