/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 1 0] [g](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [h](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [0] [f](x0) = [0 1 0]x0 + [1] [0 0 0] [0] orientation: [1 0 0] [0] [1 0 0] [0] active(f(X)) = [0 1 0]X + [1] >= [0 0 0]X + [1] = mark(g(h(f(X)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] mark(f(X)) = [0 1 0]X + [2] >= [0 1 0]X + [2] = active(f(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] mark(g(X)) = [0 0 0]X + [1] >= [0 0 0]X = active(g(X)) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] mark(h(X)) = [0 0 0]X + [1] >= [0 0 0]X = active(h(mark(X))) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] f(mark(X)) = [0 1 0]X + [2] >= [0 1 0]X + [1] = f(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] f(active(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = f(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = g(X) [0 0 0] [0] [0 0 0] [1 1 0] [1 1 0] g(active(X)) = [0 0 0]X >= [0 0 0]X = g(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] h(mark(X)) = [0 0 0]X >= [0 0 0]X = h(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] h(active(X)) = [0 0 0]X >= [0 0 0]X = h(X) [0 0 0] [0 0 0] problem: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) String Reversal Processor: f(active(X)) -> f(h(g(mark(X)))) f(mark(X)) -> mark(f(active(X))) g(mark(X)) -> g(active(X)) h(mark(X)) -> mark(h(active(X))) mark(f(X)) -> f(X) active(f(X)) -> f(X) active(g(X)) -> g(X) mark(h(X)) -> h(X) active(h(X)) -> h(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 1] [1], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [h](x0) = [0 0 1]x0 [0 1 0] , [active](x0) = x0 , [1 1 1] [0] [f](x0) = [0 1 0]x0 + [1] [0 0 1] [1] orientation: [1 1 1] [0] [1 1 1] [0] f(active(X)) = [0 1 0]X + [1] >= [0 0 0]X + [1] = f(h(g(mark(X)))) [0 0 1] [1] [0 0 0] [1] [1 2 2] [2] [1 2 2] [2] f(mark(X)) = [0 1 0]X + [2] >= [0 1 0]X + [2] = mark(f(active(X))) [0 0 1] [2] [0 0 1] [2] [1 1 1] [1 0 0] g(mark(X)) = [0 0 0]X >= [0 0 0]X = g(active(X)) [0 0 0] [0 0 0] [1 1 1] [0] [1 1 1] [0] h(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = mark(h(active(X))) [0 1 0] [1] [0 1 0] [1] [1 2 2] [2] [1 1 1] [0] mark(f(X)) = [0 1 0]X + [2] >= [0 1 0]X + [1] = f(X) [0 0 1] [2] [0 0 1] [1] [1 1 1] [0] [1 1 1] [0] active(f(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = f(X) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] active(g(X)) = [0 0 0]X >= [0 0 0]X = g(X) [0 0 0] [0 0 0] [1 1 1] [0] [1 0 0] mark(h(X)) = [0 0 1]X + [1] >= [0 0 1]X = h(X) [0 1 0] [1] [0 1 0] [1 0 0] [1 0 0] active(h(X)) = [0 0 1]X >= [0 0 1]X = h(X) [0 1 0] [0 1 0] problem: f(active(X)) -> f(h(g(mark(X)))) f(mark(X)) -> mark(f(active(X))) g(mark(X)) -> g(active(X)) h(mark(X)) -> mark(h(active(X))) active(f(X)) -> f(X) active(g(X)) -> g(X) mark(h(X)) -> h(X) active(h(X)) -> h(X) String Reversal Processor: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(active(X)) -> f(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Bounds Processor: bound: 2 enrichment: match automaton: final states: {13,10,3,11,9,6,1} transitions: h1(50) -> 51* h1(30) -> 31* h1(15) -> 16* h1(52) -> 53* h1(74) -> 75* h1(64) -> 65* h1(58) -> 59* active1(28) -> 29* g1(27) -> 28* g1(16) -> 17* mark1(17) -> 18* f1(62) -> 63* f1(14) -> 15* f1(46) -> 47* f1(68) -> 69* active2(38) -> 39* g2(37) -> 38* f50() -> 2* f2(40) -> 41* mark0(5) -> 1* mark0(2) -> 7* g0(2) -> 10* g0(4) -> 5* h0(7) -> 12* h0(2) -> 13* h0(3) -> 4* f0(7) -> 8* f0(2) -> 3* active0(10) -> 9* active0(12) -> 11* active0(8) -> 6* 2 -> 30* 4 -> 27* 6 -> 7,14 7 -> 14* 8 -> 58,46 9 -> 7,14 10 -> 64,62 11 -> 7,14 12 -> 74,68 16 -> 37* 17 -> 50* 18 -> 6* 29 -> 1* 31 -> 12* 38 -> 52,40 39 -> 18,6 41 -> 8,15 47 -> 8,15 51 -> 12* 53 -> 12* 59 -> 12* 63 -> 8,15 65 -> 12* 69 -> 8,15 75 -> 12,68 problem: Qed