/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(f(a(),X,X)) -> mark(f(X,b(),b())) active(b()) -> mark(a()) active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1 0 0] [1 1 0] [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [0] [b] = [0] [0], [1 0 0] [proper](x0) = [0 1 0]x0 [1 0 0] , [0] [a] = [1] [0], [1 0 0] [0] [top](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [0] [active](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [2 1 0] [1] [1 1 0] active(f(a(),X,X)) = [0 0 0]X + [1] >= [0 0 0]X = mark(f(X,b(),b())) [0 0 0] [0] [0 0 0] [0] [0] active(b()) = [1] >= [1] = mark(a()) [0] [0] [1 1 0] [1 0 0] [1 1 0] [0] [1 1 0] [1 0 0] [1 1 0] active(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(X1,active(X2),X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = mark(f(X1,X2,X3)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(proper(X1),proper(X2),proper(X3)) [1 1 0] [1 0 0] [1 1 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] proper(a()) = [1] >= [1] = ok(a()) [0] [0] [0] [0] proper(b()) = [0] >= [0] = ok(b()) [0] [0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = ok(f(X1,X2,X3)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] top(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = top(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] top(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = top(active(X)) [0 0 0] [0] [0 0 0] [0] problem: active(b()) -> mark(a()) active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0 + 4, [f](x0, x1, x2) = 2x0 + x1 + 2x2, [b] = 4, [proper](x0) = x0, [a] = 0, [top](x0) = 2x0 + 1, [ok](x0) = x0, [active](x0) = x0 orientation: active(b()) = 4 >= 4 = mark(a()) active(f(X1,X2,X3)) = 2X1 + X2 + 2X3 >= 2X1 + X2 + 2X3 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = 2X1 + X2 + 2X3 + 4 >= 2X1 + X2 + 2X3 + 4 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 2X1 + X2 + 2X3 >= 2X1 + X2 + 2X3 = f(proper(X1),proper(X2),proper(X3)) proper(a()) = 0 >= 0 = ok(a()) proper(b()) = 4 >= 4 = ok(b()) f(ok(X1),ok(X2),ok(X3)) = 2X1 + X2 + 2X3 >= 2X1 + X2 + 2X3 = ok(f(X1,X2,X3)) top(mark(X)) = 2X + 9 >= 2X + 1 = top(proper(X)) top(ok(X)) = 2X + 1 >= 2X + 1 = top(active(X)) problem: active(b()) -> mark(a()) active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [f](x0, x1, x2) = 4x0 + 4x1 + 5x2 + 4, [b] = 0, [proper](x0) = 4x0 + 1, [a] = 0, [top](x0) = x0 + 2, [ok](x0) = 4x0 + 1, [active](x0) = x0 orientation: active(b()) = 0 >= 0 = mark(a()) active(f(X1,X2,X3)) = 4X1 + 4X2 + 5X3 + 4 >= 4X1 + 4X2 + 5X3 + 4 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = 4X1 + 4X2 + 5X3 + 4 >= 4X1 + 4X2 + 5X3 + 4 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 16X1 + 16X2 + 20X3 + 17 >= 16X1 + 16X2 + 20X3 + 17 = f(proper(X1),proper(X2),proper(X3)) proper(a()) = 1 >= 1 = ok(a()) proper(b()) = 1 >= 1 = ok(b()) f(ok(X1),ok(X2),ok(X3)) = 16X1 + 16X2 + 20X3 + 17 >= 16X1 + 16X2 + 20X3 + 17 = ok(f(X1,X2,X3)) top(ok(X)) = 4X + 3 >= X + 2 = top(active(X)) problem: active(b()) -> mark(a()) active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1 1 0] [0] [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + x2 + [1] [0 0 1] [0 0 1] [0], [0] [b] = [0] [0], [1 0 1] [proper](x0) = [0 1 0]x0 [1 1 0] , [0] [a] = [0] [0], [1 0 0] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [1] [active](x0) = [0 1 0]x0 + [0] [0 0 1] [0] orientation: [1] [0] active(b()) = [0] >= [0] = mark(a()) [0] [0] [1 1 1] [1 1 1] [1 0 1] [1] [1 1 0] [1 1 1] [1] active(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + X3 + [1] = f(X1,active(X2),X3) [0 0 1] [0 0 1] [0 0 1] [0] [0 0 1] [0 0 1] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [1 0 0] [0] f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] = mark(f(X1,X2,X3)) [0 0 1] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1 0 1] [0] [1 1 1] [1 1 1] [1 0 1] [0] proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] = f(proper(X1),proper(X2),proper(X3)) [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] [0] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [0] [0] proper(b()) = [0] >= [0] = ok(b()) [0] [0] [1 1 0] [1 1 0] [1 0 0] [0] [1 1 0] [1 1 0] [1 0 0] [0] f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] = ok(f(X1,X2,X3)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0 + 1, [f](x0, x1, x2) = x0 + x1 + 4x2 + 1, [b] = 4, [proper](x0) = 6x0 + 1, [a] = 4, [ok](x0) = 5x0 + 5, [active](x0) = x0 + 4 orientation: active(f(X1,X2,X3)) = X1 + X2 + 4X3 + 5 >= X1 + X2 + 4X3 + 5 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + X2 + 4X3 + 2 >= X1 + X2 + 4X3 + 2 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 6X1 + 6X2 + 24X3 + 7 >= 6X1 + 6X2 + 24X3 + 7 = f(proper(X1),proper(X2),proper(X3)) proper(a()) = 25 >= 25 = ok(a()) proper(b()) = 25 >= 25 = ok(b()) f(ok(X1),ok(X2),ok(X3)) = 5X1 + 5X2 + 20X3 + 31 >= 5X1 + 5X2 + 20X3 + 10 = ok(f(X1,X2,X3)) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [f](x0, x1, x2) = x0 + 2x1 + x2, [b] = 5, [proper](x0) = 5x0, [a] = 2, [ok](x0) = 2x0 + 6, [active](x0) = x0 orientation: active(f(X1,X2,X3)) = X1 + 2X2 + X3 >= X1 + 2X2 + X3 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + 2X2 + X3 >= X1 + 2X2 + X3 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 5X1 + 10X2 + 5X3 >= 5X1 + 10X2 + 5X3 = f(proper(X1),proper(X2),proper(X3)) proper(a()) = 10 >= 10 = ok(a()) proper(b()) = 25 >= 16 = ok(b()) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(a()) -> ok(a()) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [f](x0, x1, x2) = x0 + x1 + 2x2 + 1, [proper](x0) = 4x0 + 1, [a] = 4, [ok](x0) = 4x0, [active](x0) = x0 orientation: active(f(X1,X2,X3)) = X1 + X2 + 2X3 + 1 >= X1 + X2 + 2X3 + 1 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + X2 + 2X3 + 1 >= X1 + X2 + 2X3 + 1 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 4X1 + 4X2 + 8X3 + 5 >= 4X1 + 4X2 + 8X3 + 5 = f(proper(X1),proper(X2),proper(X3)) proper(a()) = 17 >= 16 = ok(a()) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [f](x0, x1, x2) = x0 + 2x1 + x2 + 1, [proper](x0) = x0, [active](x0) = 4x0 orientation: active(f(X1,X2,X3)) = 4X1 + 8X2 + 4X3 + 4 >= X1 + 8X2 + X3 + 1 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + 2X2 + X3 + 1 >= X1 + 2X2 + X3 + 1 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = X1 + 2X2 + X3 + 1 >= X1 + 2X2 + X3 + 1 = f(proper(X1),proper(X2),proper(X3)) problem: f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 0 1]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 1] [1 0 1] [0] [f](x0, x1, x2) = [0 1 1]x0 + [0 1 0]x1 + [0 1 0]x2 + [1] [0 1 1] [0 0 1] [0 1 0] [0], [1 1 0] [proper](x0) = [0 1 0]x0 [0 0 1] orientation: [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [0] f(X1,mark(X2),X3) = [0 1 1]X1 + [0 0 1]X2 + [0 1 0]X3 + [1] >= [0 1 1]X1 + [0 0 1]X2 + [0 1 0]X3 + [0] = mark(f(X1,X2,X3)) [0 1 1] [0 0 1] [0 1 0] [1] [0 1 1] [0 0 1] [0 1 0] [1] [1 1 1] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 1] [1 1 1] [0] proper(f(X1,X2,X3)) = [0 1 1]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] >= [0 1 1]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] = f(proper(X1),proper(X2),proper(X3)) [0 1 1] [0 0 1] [0 1 0] [0] [0 1 1] [0 0 1] [0 1 0] [0] problem: Qed