/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: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Proof: String Reversal Processor: f(f(active(X))) -> f(g(f(c(mark(X))))) c(active(X)) -> d(mark(X)) h(active(X)) -> d(c(mark(X))) f(mark(X)) -> mark(f(active(X))) c(mark(X)) -> c(active(X)) g(mark(X)) -> g(active(X)) d(mark(X)) -> d(active(X)) h(mark(X)) -> mark(h(active(X))) mark(f(X)) -> f(X) active(f(X)) -> f(X) mark(c(X)) -> c(X) active(c(X)) -> c(X) mark(g(X)) -> g(X) active(g(X)) -> g(X) mark(d(X)) -> d(X) active(d(X)) -> d(X) mark(h(X)) -> h(X) active(h(X)) -> h(X) Matrix Interpretation Processor: dim=1 interpretation: [h](x0) = 2x0 + 2, [d](x0) = x0, [mark](x0) = x0, [c](x0) = x0, [g](x0) = x0, [active](x0) = x0, [f](x0) = 4x0 orientation: f(f(active(X))) = 16X >= 16X = f(g(f(c(mark(X))))) c(active(X)) = X >= X = d(mark(X)) h(active(X)) = 2X + 2 >= X = d(c(mark(X))) f(mark(X)) = 4X >= 4X = mark(f(active(X))) c(mark(X)) = X >= X = c(active(X)) g(mark(X)) = X >= X = g(active(X)) d(mark(X)) = X >= X = d(active(X)) h(mark(X)) = 2X + 2 >= 2X + 2 = mark(h(active(X))) mark(f(X)) = 4X >= 4X = f(X) active(f(X)) = 4X >= 4X = f(X) mark(c(X)) = X >= X = c(X) active(c(X)) = X >= X = c(X) mark(g(X)) = X >= X = g(X) active(g(X)) = X >= X = g(X) mark(d(X)) = X >= X = d(X) active(d(X)) = X >= X = d(X) mark(h(X)) = 2X + 2 >= 2X + 2 = h(X) active(h(X)) = 2X + 2 >= 2X + 2 = h(X) problem: f(f(active(X))) -> f(g(f(c(mark(X))))) c(active(X)) -> d(mark(X)) f(mark(X)) -> mark(f(active(X))) c(mark(X)) -> c(active(X)) g(mark(X)) -> g(active(X)) d(mark(X)) -> d(active(X)) h(mark(X)) -> mark(h(active(X))) mark(f(X)) -> f(X) active(f(X)) -> f(X) mark(c(X)) -> c(X) active(c(X)) -> c(X) mark(g(X)) -> g(X) active(g(X)) -> g(X) mark(d(X)) -> d(X) active(d(X)) -> d(X) mark(h(X)) -> h(X) active(h(X)) -> h(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [h](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [d](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [c](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 0 1] f(f(active(X))) = [0 0 0]X >= [0 0 0]X = f(g(f(c(mark(X))))) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] c(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = d(mark(X)) [0 0 0] [1] [0 0 0] [1 0 1] [1 0 1] f(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(f(active(X))) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] c(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = c(active(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] g(mark(X)) = [0 0 0]X >= [0 0 0]X = g(active(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] d(mark(X)) = [0 0 0]X >= [0 0 0]X = d(active(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] h(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(h(active(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(f(X)) = [0 0 0]X >= [0 0 0]X = f(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(f(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [0] mark(c(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = c(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] active(c(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = c(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] mark(g(X)) = [0 0 0]X >= [0 0 0]X = g(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(g(X)) = [0 0 0]X + [0] >= [0 0 0]X = g(X) [0 0 0] [1] [0 0 0] [1 0 0] [1 0 0] mark(d(X)) = [0 0 0]X >= [0 0 0]X = d(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(d(X)) = [0 0 0]X + [0] >= [0 0 0]X = d(X) [0 0 0] [1] [0 0 0] [1 0 0] [1 0 0] mark(h(X)) = [0 0 0]X >= [0 0 0]X = h(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(h(X)) = [0 0 0]X + [0] >= [0 0 0]X = h(X) [0 0 0] [1] [0 0 0] problem: f(f(active(X))) -> f(g(f(c(mark(X))))) c(active(X)) -> d(mark(X)) f(mark(X)) -> mark(f(active(X))) c(mark(X)) -> c(active(X)) g(mark(X)) -> g(active(X)) d(mark(X)) -> d(active(X)) h(mark(X)) -> mark(h(active(X))) mark(f(X)) -> f(X) active(f(X)) -> f(X) mark(g(X)) -> g(X) active(g(X)) -> g(X) mark(d(X)) -> d(X) active(d(X)) -> d(X) mark(h(X)) -> h(X) active(h(X)) -> h(X) String Reversal Processor: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(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) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [h](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [d](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1] [mark](x0) = [1 0 1]x0 + [0] [0 0 1] [0], [1 0 0] [0] [c](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [active](x0) = [1 0 0]x0 [0 0 1] , [1 0 1] [0] [f](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 2] [1] [1 0 1] [1] active(f(f(X))) = [1 0 2]X + [1] >= [1 0 1]X + [0] = mark(c(f(g(f(X))))) [0 0 1] [2] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] active(c(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = mark(d(X)) [0 0 0] [0] [0 0 0] [0] [1 0 2] [2] [1 0 2] [1] mark(f(X)) = [1 0 2]X + [1] >= [1 0 2]X + [1] = active(f(mark(X))) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1] [1 0 0] [1] mark(c(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = active(c(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] mark(g(X)) = [1 0 0]X + [0] >= [1 0 0]X = active(g(X)) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] mark(d(X)) = [1 0 0]X + [0] >= [1 0 0]X = active(d(X)) [0 0 0] [0] [0 0 0] [1 0 1] [2] [1 0 1] [1] mark(h(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(h(mark(X))) [0 0 1] [1] [0 0 1] [1] [1 0 2] [1] [1 0 1] [0] f(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(X) [0 0 1] [1] [0 0 1] [1] [1 1 1] [0] [1 0 1] [0] f(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(X) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1] [1 0 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 0 0] g(active(X)) = [0 0 0]X >= [0 0 0]X = g(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] d(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = d(X) [0 0 0] [0] [0 0 0] [1 1 0] [1 0 0] d(active(X)) = [0 0 0]X >= [0 0 0]X = d(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [0] h(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = h(X) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 0 0] [0] h(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = h(X) [0 0 1] [1] [0 0 1] [1] problem: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) mark(c(X)) -> active(c(X)) f(active(X)) -> f(X) g(active(X)) -> g(X) d(active(X)) -> d(X) h(active(X)) -> h(X) Bounds Processor: bound: 2 enrichment: match automaton: final states: {12,8,11,3,9,7,1} transitions: f70() -> 2* mark0(6) -> 1* mark0(8) -> 7* c0(5) -> 6* c0(2) -> 10* f0(2) -> 3* f0(4) -> 5* g0(2) -> 11* g0(3) -> 4* d0(2) -> 8* active0(10) -> 9* h0(2) -> 12* active1(20) -> 21* c1(19) -> 20* mark1(17) -> 18* d1(16) -> 17* mark2(29) -> 30* d2(28) -> 29* 2 -> 16* 5 -> 19* 18 -> 9* 19 -> 28* 21 -> 1* 30 -> 21,1 problem: Qed