/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: active(f(b(),X,c())) -> mark(f(X,c(),X)) active(c()) -> mark(b()) 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(b()) -> ok(b()) proper(c()) -> ok(c()) 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=2 interpretation: [1 1] [mark](x0) = [0 0]x0, [2] [c] = [0], [1 0] [active](x0) = [0 0]x0, [proper](x0) = x0, [1] [b] = [1], [2 0] [1] [top](x0) = [3 0]x0 + [0], [ok](x0) = x0, [2 3] [3 3] [1 0] [f](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2 orientation: [3 3] [7] [3 3] [6] active(f(b(),X,c())) = [0 0]X + [0] >= [0 0]X + [0] = mark(f(X,c(),X)) [2] [2] active(c()) = [0] >= [0] = mark(b()) [2 3] [3 3] [1 0] [2 3] [3 0] [1 0] active(f(X1,X2,X3)) = [0 0]X1 + [0 0]X2 + [0 0]X3 >= [0 0]X1 + [0 0]X2 + [0 0]X3 = f(X1,active(X2),X3) [2 3] [3 3] [1 0] [2 3] [3 3] [1 0] f(X1,mark(X2),X3) = [0 0]X1 + [0 0]X2 + [0 0]X3 >= [0 0]X1 + [0 0]X2 + [0 0]X3 = mark(f(X1,X2,X3)) [2 3] [3 3] [1 0] [2 3] [3 3] [1 0] proper(f(X1,X2,X3)) = [0 0]X1 + [0 0]X2 + [0 0]X3 >= [0 0]X1 + [0 0]X2 + [0 0]X3 = f(proper(X1),proper(X2),proper(X3)) [1] [1] proper(b()) = [1] >= [1] = ok(b()) [2] [2] proper(c()) = [0] >= [0] = ok(c()) [2 3] [3 3] [1 0] [2 3] [3 3] [1 0] f(ok(X1),ok(X2),ok(X3)) = [0 0]X1 + [0 0]X2 + [0 0]X3 >= [0 0]X1 + [0 0]X2 + [0 0]X3 = ok(f(X1,X2,X3)) [2 2] [1] [2 0] [1] top(mark(X)) = [3 3]X + [0] >= [3 0]X + [0] = top(proper(X)) [2 0] [1] [2 0] [1] top(ok(X)) = [3 0]X + [0] >= [3 0]X + [0] = top(active(X)) problem: active(c()) -> mark(b()) 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(b()) -> ok(b()) proper(c()) -> ok(c()) 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=3 interpretation: [1 1 0] [mark](x0) = [0 1 0]x0 [0 0 1] , [1] [c] = [0] [0], [1 0 0] [active](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [proper](x0) = [0 0 0]x0 [0 0 0] , [0] [b] = [0] [0], [1 0 1] [1] [top](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [ok](x0) = x0 , [1 0 1] [1 0 0] [1 0 0] [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 1 1] [0 1 1] orientation: [1] [0] active(c()) = [0] >= [0] = mark(b()) [0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] active(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(X1,active(X2),X3) [0 0 0] [0 1 1] [0 1 1] [0 0 0] [0 0 1] [0 1 1] [1 0 1] [1 1 0] [1 0 0] [1 0 1] [1 0 0] [1 0 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 1 1] [0 1 1] [0 0 0] [0 1 1] [0 1 1] [1 0 1] [1 1 1] [1 1 1] [1 0 1] [1 0 1] [1 0 1] 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)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] proper(b()) = [0] >= [0] = ok(b()) [0] [0] [1] [1] proper(c()) = [0] >= [0] = ok(c()) [0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 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 1 1] [0 1 1] [0 0 0] [0 1 1] [0 1 1] [1 1 1] [1] [1 0 1] [1] top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X)) [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(b()) -> ok(b()) proper(c()) -> ok(c()) 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 + 2, [c] = 0, [active](x0) = x0, [proper](x0) = x0, [b] = 0, [top](x0) = x0, [ok](x0) = x0, [f](x0, x1, x2) = x0 + 6x1 + 2x2 orientation: active(f(X1,X2,X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + 6X2 + 2X3 + 12 >= X1 + 6X2 + 2X3 + 2 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = f(proper(X1),proper(X2),proper(X3)) proper(b()) = 0 >= 0 = ok(b()) proper(c()) = 0 >= 0 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = ok(f(X1,X2,X3)) top(mark(X)) = X + 2 >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [c] = [0] [0], [0] [active](x0) = x0 + [1] [0], [1 0 1] [proper](x0) = [0 0 1]x0 [0 1 0] , [0] [b] = [1] [1], [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [ok](x0) = x0 , [1 0 0] [1 0 1] [1] [f](x0, x1, x2) = [0 1 1]x0 + x1 + [0 0 1]x2 + [0] [0 1 1] [0 1 0] [0] orientation: [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1] active(f(X1,X2,X3)) = [0 1 1]X1 + X2 + [0 0 1]X3 + [1] >= [0 1 1]X1 + X2 + [0 0 1]X3 + [1] = f(X1,active(X2),X3) [0 1 1] [0 1 0] [0] [0 1 1] [0 1 0] [0] [1 1 1] [1 0 1] [1 1 1] [1] [1 0 1] [1 0 1] [1 1 1] [1] proper(f(X1,X2,X3)) = [0 1 1]X1 + [0 0 1]X2 + [0 1 0]X3 + [0] >= [0 1 1]X1 + [0 0 1]X2 + [0 1 0]X3 + [0] = f(proper(X1),proper(X2),proper(X3)) [0 1 1] [0 1 0] [0 0 1] [0] [0 1 1] [0 1 0] [0 0 1] [0] [1] [0] proper(b()) = [1] >= [1] = ok(b()) [1] [1] [0] [0] proper(c()) = [0] >= [0] = ok(c()) [0] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1] f(ok(X1),ok(X2),ok(X3)) = [0 1 1]X1 + X2 + [0 0 1]X3 + [0] >= [0 1 1]X1 + X2 + [0 0 1]X3 + [0] = ok(f(X1,X2,X3)) [0 1 1] [0 1 0] [0] [0 1 1] [0 1 0] [0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [c] = 1, [active](x0) = 2x0, [proper](x0) = 4x0, [top](x0) = 4x0 + 4, [ok](x0) = 3x0 + 1, [f](x0, x1, x2) = 6x0 + 2x1 + 4x2 orientation: active(f(X1,X2,X3)) = 12X1 + 4X2 + 8X3 >= 6X1 + 4X2 + 4X3 = f(X1,active(X2),X3) proper(f(X1,X2,X3)) = 24X1 + 8X2 + 16X3 >= 24X1 + 8X2 + 16X3 = f(proper(X1),proper(X2),proper(X3)) proper(c()) = 4 >= 4 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = 18X1 + 6X2 + 12X3 + 12 >= 18X1 + 6X2 + 12X3 + 1 = ok(f(X1,X2,X3)) top(ok(X)) = 12X + 8 >= 8X + 4 = top(active(X)) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(c()) -> ok(c()) Matrix Interpretation Processor: dim=1 interpretation: [c] = 5, [active](x0) = x0 + 1, [proper](x0) = 5x0 + 4, [ok](x0) = x0 + 7, [f](x0, x1, x2) = x0 + x1 + x2 + 2 orientation: active(f(X1,X2,X3)) = X1 + X2 + X3 + 3 >= X1 + X2 + X3 + 3 = f(X1,active(X2),X3) proper(f(X1,X2,X3)) = 5X1 + 5X2 + 5X3 + 14 >= 5X1 + 5X2 + 5X3 + 14 = f(proper(X1),proper(X2),proper(X3)) proper(c()) = 29 >= 12 = ok(c()) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) Matrix Interpretation Processor: dim=1 interpretation: [active](x0) = x0, [proper](x0) = 5x0 + 1, [f](x0, x1, x2) = 4x0 + 2x1 + 2x2 + 2 orientation: active(f(X1,X2,X3)) = 4X1 + 2X2 + 2X3 + 2 >= 4X1 + 2X2 + 2X3 + 2 = f(X1,active(X2),X3) proper(f(X1,X2,X3)) = 20X1 + 10X2 + 10X3 + 11 >= 20X1 + 10X2 + 10X3 + 10 = f(proper(X1),proper(X2),proper(X3)) problem: active(f(X1,X2,X3)) -> f(X1,active(X2),X3) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [active](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [0] [f](x0, x1, x2) = [0 0 0]x0 + x1 + [0 0 0]x2 + [1] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 1 0] [1 0 0] [1] [1 0 0] [1 1 0] [1 0 0] [0] active(f(X1,X2,X3)) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] = f(X1,active(X2),X3) [0 0 0] [0 0 1] [0 0 1] [1] [0 0 0] [0 0 1] [0 0 1] [1] problem: Qed