/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(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: [2 0] [2] [top](x0) = [1 1]x0 + [0], [ok](x0) = x0, [proper](x0) = x0, [1 1] [mark](x0) = [0 0]x0, [1 0] [active](x0) = [0 0]x0, [1 2] [3 2] [2 0] [f](x0, x1, x2) = [0 0]x0 + [0 1]x1 + [0 0]x2, [1] [c] = [0], [0] [b] = [1] orientation: [3 2] [4] [3 2] [3] active(f(b(),X,c())) = [0 0]X + [0] >= [0 0]X + [0] = mark(f(X,c(),X)) [1] [1] active(c()) = [0] >= [0] = mark(b()) [1 2] [3 2] [2 0] [1 2] [3 0] [2 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) [1 2] [3 3] [2 0] [1 2] [3 3] [2 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)) [1 2] [3 2] [2 0] [1 2] [3 2] [2 0] proper(f(X1,X2,X3)) = [0 0]X1 + [0 1]X2 + [0 0]X3 >= [0 0]X1 + [0 1]X2 + [0 0]X3 = f(proper(X1),proper(X2),proper(X3)) [0] [0] proper(b()) = [1] >= [1] = ok(b()) [1] [1] proper(c()) = [0] >= [0] = ok(c()) [1 2] [3 2] [2 0] [1 2] [3 2] [2 0] f(ok(X1),ok(X2),ok(X3)) = [0 0]X1 + [0 1]X2 + [0 0]X3 >= [0 0]X1 + [0 1]X2 + [0 0]X3 = ok(f(X1,X2,X3)) [2 2] [2] [2 0] [2] top(mark(X)) = [1 1]X + [0] >= [1 1]X + [0] = top(proper(X)) [2 0] [2] [2 0] [2] top(ok(X)) = [1 1]X + [0] >= [1 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=1 interpretation: [top](x0) = x0 + 2, [ok](x0) = x0, [proper](x0) = x0, [mark](x0) = x0 + 1, [active](x0) = x0, [f](x0, x1, x2) = x0 + x1 + x2, [c] = 3, [b] = 2 orientation: active(c()) = 3 >= 3 = mark(b()) active(f(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = f(proper(X1),proper(X2),proper(X3)) proper(b()) = 2 >= 2 = ok(b()) proper(c()) = 3 >= 3 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(f(X1,X2,X3)) top(mark(X)) = X + 3 >= X + 2 = top(proper(X)) top(ok(X)) = X + 2 >= X + 2 = 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(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0 + 5, [ok](x0) = x0, [proper](x0) = 2x0, [mark](x0) = x0 + 1, [active](x0) = x0, [f](x0, x1, x2) = x0 + 2x1 + 2x2, [c] = 2, [b] = 1 orientation: active(c()) = 2 >= 2 = mark(b()) active(f(X1,X2,X3)) = X1 + 2X2 + 2X3 >= X1 + 2X2 + 2X3 = f(X1,active(X2),X3) f(X1,mark(X2),X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 1 = mark(f(X1,X2,X3)) proper(f(X1,X2,X3)) = 2X1 + 4X2 + 4X3 >= 2X1 + 4X2 + 4X3 = f(proper(X1),proper(X2),proper(X3)) proper(b()) = 2 >= 1 = ok(b()) proper(c()) = 4 >= 2 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = X1 + 2X2 + 2X3 >= X1 + 2X2 + 2X3 = ok(f(X1,X2,X3)) top(ok(X)) = 2X + 5 >= 2X + 5 = top(active(X)) problem: active(c()) -> mark(b()) active(f(X1,X2,X3)) -> f(X1,active(X2),X3) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [ok](x0) = 6x0 + 4, [proper](x0) = 2x0, [mark](x0) = x0 + 4, [active](x0) = 4x0, [f](x0, x1, x2) = 2x0 + 2x1 + 2x2, [c] = 4, [b] = 2 orientation: active(c()) = 16 >= 6 = mark(b()) active(f(X1,X2,X3)) = 8X1 + 8X2 + 8X3 >= 2X1 + 8X2 + 2X3 = f(X1,active(X2),X3) proper(f(X1,X2,X3)) = 4X1 + 4X2 + 4X3 >= 4X1 + 4X2 + 4X3 = f(proper(X1),proper(X2),proper(X3)) f(ok(X1),ok(X2),ok(X3)) = 12X1 + 12X2 + 12X3 + 24 >= 12X1 + 12X2 + 12X3 + 4 = ok(f(X1,X2,X3)) top(ok(X)) = 6X + 6 >= 4X + 2 = 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)) Matrix Interpretation Processor: dim=1 interpretation: [proper](x0) = 7x0 + 1, [active](x0) = 2x0, [f](x0, x1, x2) = x0 + 2x1 + 4x2 + 1 orientation: active(f(X1,X2,X3)) = 2X1 + 4X2 + 8X3 + 2 >= X1 + 4X2 + 4X3 + 1 = f(X1,active(X2),X3) proper(f(X1,X2,X3)) = 7X1 + 14X2 + 28X3 + 8 >= 7X1 + 14X2 + 28X3 + 8 = f(proper(X1),proper(X2),proper(X3)) problem: proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [proper](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 1 0] [1 1 0] [0] [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0] [0 0 1] [0 0 1] [0 0 1] [1] orientation: [1 0 1] [1 1 1] [1 1 1] [1] [1 0 1] [1 0 1] [1 0 1] [0] proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] = f(proper(X1),proper(X2),proper(X3)) [0 0 1] [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [0 0 1] [1] problem: Qed