/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(g(X)) -> mark(h(X)) active(c()) -> mark(d()) active(h(d())) -> mark(g(c())) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [proper](x0) = [0 0 1]x0 [0 1 0] , [0] [d] = [0] [1], [0] [c] = [0] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [h](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [0] [g](x0) = [0 0 0]x0 + [1] [0 0 0] [1] orientation: [1 1 1] [1] [1 1 1] active(g(X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(h(X)) [0 0 0] [0] [0 0 0] [0] [0] active(c()) = [0] >= [0] = mark(d()) [0] [0] [1] [1] active(h(d())) = [0] >= [0] = mark(g(c())) [0] [0] [1 1 1] [0] [1 1 1] [0] proper(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = g(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 1] proper(h(X)) = [0 0 0]X >= [0 0 0]X = h(proper(X)) [0 0 0] [0 0 0] [0] [0] proper(c()) = [0] >= [0] = ok(c()) [0] [0] [0] [0] proper(d()) = [1] >= [1] = ok(d()) [0] [0] [1 1 1] [0] [1 1 1] [0] g(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(g(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 1] h(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(h(X)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(c()) -> mark(d()) active(h(d())) -> mark(g(c())) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = 3x0 + 1, [proper](x0) = 4x0 + 1, [d] = 0, [c] = 0, [mark](x0) = 4x0 + 1, [h](x0) = 4x0 + 1, [active](x0) = 2x0 + 1, [g](x0) = x0 orientation: active(c()) = 1 >= 1 = mark(d()) active(h(d())) = 3 >= 1 = mark(g(c())) proper(g(X)) = 4X + 1 >= 4X + 1 = g(proper(X)) proper(h(X)) = 16X + 5 >= 16X + 5 = h(proper(X)) proper(c()) = 1 >= 1 = ok(c()) proper(d()) = 1 >= 1 = ok(d()) g(ok(X)) = 3X + 1 >= 3X + 1 = ok(g(X)) h(ok(X)) = 12X + 5 >= 12X + 4 = ok(h(X)) top(mark(X)) = 8X + 2 >= 8X + 2 = top(proper(X)) top(ok(X)) = 6X + 2 >= 4X + 2 = top(active(X)) problem: active(c()) -> mark(d()) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = 5x0 + 4, [proper](x0) = 5x0 + 4, [d] = 0, [c] = 2, [mark](x0) = 5x0 + 4, [h](x0) = x0, [active](x0) = 5x0 + 4, [g](x0) = 3x0 + 2 orientation: active(c()) = 14 >= 4 = mark(d()) proper(g(X)) = 15X + 14 >= 15X + 14 = g(proper(X)) proper(h(X)) = 5X + 4 >= 5X + 4 = h(proper(X)) proper(c()) = 14 >= 14 = ok(c()) proper(d()) = 4 >= 4 = ok(d()) g(ok(X)) = 15X + 14 >= 15X + 14 = ok(g(X)) top(mark(X)) = 10X + 8 >= 10X + 8 = top(proper(X)) top(ok(X)) = 10X + 8 >= 10X + 8 = top(active(X)) problem: proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [1] [ok](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 0] [proper](x0) = [0 1 0]x0 [1 1 0] , [0] [d] = [1] [0], [0] [c] = [1] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [h](x0) = [0 1 0]x0 + [0] [0 1 0] [1], [1 0 0] [1] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [g](x0) = [0 1 0]x0 + [1] [1 0 0] [0] orientation: [1 1 0] [1] [1 1 0] [0] proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X)) [1 1 0] [1] [1 1 0] [0] [1 1 0] [1] [1 1 0] [1] proper(h(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = h(proper(X)) [1 1 0] [1] [0 1 0] [1] [1] [1] proper(c()) = [1] >= [0] = ok(c()) [1] [0] [1] [1] proper(d()) = [1] >= [0] = ok(d()) [1] [0] [1 0 0] [1] [1 0 0] [1] g(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = ok(g(X)) [1 0 0] [1] [0 0 0] [0] [1 1 0] [1 1 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [1 1 0] [1 1 0] [1 0 0] [1] [1 0 0] [1] top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X)) [1 0 0] [1] [1 0 0] [1] problem: proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [d] = 2, [c] = 4, [mark](x0) = x0 + 1, [h](x0) = x0 + 4, [active](x0) = x0, [g](x0) = x0 + 7 orientation: proper(h(X)) = X + 5 >= X + 5 = h(proper(X)) proper(c()) = 5 >= 5 = ok(c()) proper(d()) = 3 >= 3 = ok(d()) g(ok(X)) = X + 8 >= X + 8 = ok(g(X)) top(mark(X)) = X + 3 >= X + 3 = top(proper(X)) top(ok(X)) = X + 3 >= X + 2 = top(active(X)) problem: proper(h(X)) -> h(proper(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [1 0 0]x0 [0 0 0] , [1 1 1] [proper](x0) = [0 1 1]x0 [0 1 1] , [0] [d] = [0] [0], [0] [c] = [1] [0], [1 1 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [h](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [1] [g](x0) = [0 1 0]x0 + [1] [0 0 0] [0] orientation: [1 1 1] [1] [1 1 1] [0] proper(h(X)) = [0 1 1]X + [1] >= [0 1 1]X + [0] = h(proper(X)) [0 1 1] [1] [0 1 1] [1] [1] [0] proper(c()) = [1] >= [0] = ok(c()) [1] [0] [0] [0] proper(d()) = [0] >= [0] = ok(d()) [0] [0] [1 0 0] [1] [1 0 0] [1] g(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = ok(g(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 1 1] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] problem: proper(d()) -> ok(d()) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [top](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [proper](x0) = [0 1 1]x0 [0 0 0] , [0] [d] = [1] [0], [1 0 0] [0] [mark](x0) = [0 1 1]x0 + [0] [0 1 0] [1], [1 1 0] [1] [g](x0) = [0 1 0]x0 + [0] [0 0 0] [0] orientation: [1] [0] proper(d()) = [1] >= [1] = ok(d()) [0] [0] [1 1 0] [1] [1 1 0] [1] g(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(g(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] top(mark(X)) = [0 1 1]X + [0] >= [0 1 1]X = top(proper(X)) [0 1 0] [1] [0 0 0] problem: g(ok(X)) -> ok(g(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [ok](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 1] [g](x0) = [0 0 0]x0 [0 0 1] orientation: [1 0 1] [1] [1 0 1] [0] g(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(g(X)) [0 0 1] [1] [0 0 1] [1] problem: Qed