/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(f(g(X),Y)) -> mark(f(X,f(g(X),Y))) mark(f(X1,X2)) -> active(f(mark(X1),X2)) mark(g(X)) -> active(g(mark(X))) f(mark(X1),X2) -> f(X1,X2) f(X1,mark(X2)) -> f(X1,X2) f(active(X1),X2) -> f(X1,X2) f(X1,active(X2)) -> f(X1,X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 0 0] [f](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [mark](x0) = [0 0 0]x0 [0 0 1] , [1 1 0] [0] [g](x0) = [1 1 0]x0 + [0] [1 1 1] [1], [1 1 0] [active](x0) = [0 0 0]x0 [0 0 1] orientation: [3 3 1] [1 0 0] [1] [3 3 1] [1 0 0] active(f(g(X),Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y = mark(f(X,f(g(X),Y))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] mark(f(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(f(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 2 0] [0] [2 2 0] [0] mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(g(mark(X))) [1 1 1] [1] [1 1 1] [1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] f(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] f(X1,mark(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] f(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] f(X1,active(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] g(mark(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = g(X) [1 1 1] [1] [1 1 1] [1] [1 1 0] [0] [1 1 0] [0] g(active(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = g(X) [1 1 1] [1] [1 1 1] [1] problem: mark(f(X1,X2)) -> active(f(mark(X1),X2)) mark(g(X)) -> active(g(mark(X))) f(mark(X1),X2) -> f(X1,X2) f(X1,mark(X2)) -> f(X1,X2) f(active(X1),X2) -> f(X1,X2) f(X1,active(X2)) -> f(X1,X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [f](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [1], [1 0 1] [mark](x0) = [1 0 1]x0 [1 0 1] , [1 0 0] [1] [g](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [active](x0) = [1 0 0]x0 [0 0 1] orientation: [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [0] mark(f(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [1] >= [1 0 1]X1 + [1 0 0]X2 + [0] = active(f(mark(X1),X2)) [1 0 1] [1 0 0] [1] [1 0 1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] mark(g(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(g(mark(X))) [1 0 1] [1] [1 0 1] [0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] f(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 + [0] = f(X1,X2) [1 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] f(X1,mark(X2)) = [1 0 0]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 + [0] = f(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] f(active(X1),X2) = [1 0 0]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 + [0] = f(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] f(X1,active(X2)) = [1 0 0]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 + [0] = f(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 1] [1] [1 0 0] [1] g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(X) [1 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] g(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(X) [0 0 1] [0] [0 0 1] [0] problem: mark(g(X)) -> active(g(mark(X))) f(mark(X1),X2) -> f(X1,X2) f(X1,mark(X2)) -> f(X1,X2) f(active(X1),X2) -> f(X1,X2) f(X1,active(X2)) -> f(X1,X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 1 1] [1], [1 0 0] [1] [g](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 0] [1] [1 0 0] [1] mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(g(mark(X))) [0 0 1] [1] [0 0 0] [1] [1 1 1] [1 0 0] [1] [1 0 1] [1 0 0] f(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = f(X1,X2) [1 0 0] [0 0 0] [0] [1 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] f(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = f(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] f(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = f(X1,X2) [1 0 0] [0 0 0] [0] [1 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] f(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = f(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] g(mark(X)) = [0 1 1]X + [1] >= [0 0 1]X + [0] = g(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] g(active(X)) = [0 0 1]X + [1] >= [0 0 1]X + [0] = g(X) [0 0 0] [0] [0 0 0] [0] problem: mark(g(X)) -> active(g(mark(X))) f(X1,mark(X2)) -> f(X1,X2) f(X1,active(X2)) -> f(X1,X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 1 0] [0] [f](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1] [0 0 0] [0 0 0] [1], [1 0 0] [mark](x0) = [0 1 1]x0 [1 0 0] , [1 0 0] [1] [g](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [active](x0) = [0 1 0]x0 + [1] [1 0 0] [0] orientation: [1 0 0] [1] [1 0 0] [1] mark(g(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = active(g(mark(X))) [1 0 0] [1] [1 0 0] [1] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 0] [0] f(X1,mark(X2)) = [0 0 0]X1 + [1 0 0]X2 + [1] >= [0 0 0]X1 + [1 0 0]X2 + [1] = f(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [0] f(X1,active(X2)) = [0 0 0]X1 + [1 0 0]X2 + [1] >= [0 0 0]X1 + [1 0 0]X2 + [1] = f(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] g(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = g(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] g(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = g(X) [0 0 0] [1] [0 0 0] [1] problem: mark(g(X)) -> active(g(mark(X))) f(X1,mark(X2)) -> f(X1,X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 1 0] [1] [mark](x0) = [1 1 0]x0 + [0] [0 0 0] [0], [1 0 0] [g](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 1]x0 [0 0 0] orientation: [1 1 0] [1] [1 1 0] [1] mark(g(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = active(g(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [0] f(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = f(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1] [1 0 0] g(mark(X)) = [1 1 0]X + [0] >= [0 1 0]X = g(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] g(active(X)) = [0 1 1]X >= [0 1 0]X = g(X) [0 0 0] [0 0 0] problem: mark(g(X)) -> active(g(mark(X))) g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [0] [g](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [active](x0) = [0 1 1]x0 [0 0 0] orientation: [1 1 0] [1] [1 1 0] [0] mark(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(g(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] g(active(X)) = [0 1 1]X + [1] >= [0 1 0]X + [1] = g(X) [0 0 0] [0] [0 0 0] [0] problem: g(active(X)) -> g(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [g](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [1] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [1 0 0] [1] [1 0 0] g(active(X)) = [1 0 0]X + [1] >= [1 0 0]X = g(X) [0 0 0] [0] [0 0 0] problem: Qed