YES Problem: minus(minus(x)) -> x minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y)))) minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y)))) f(minus(x)) -> minus(minus(minus(f(x)))) Proof: Matrix Interpretation Processor: dim=2 interpretation: [2 0] [2 0] [+](x0, x1) = [0 0]x0 + [0 0]x1, [1 1] [2] [f](x0) = [0 3]x0 + [2], [0] [minus](x0) = x0 + [1], [2 0] [2 0] [*](x0, x1) = [0 0]x0 + [0 0]x1 orientation: [0] minus(minus(x)) = x + [2] >= x = x [2 0] [2 0] [0] [2 0] [2 0] minus(+(x,y)) = [0 0]x + [0 0]y + [1] >= [0 0]x + [0 0]y = *(minus(minus(minus(x))),minus(minus(minus(y)))) [2 0] [2 0] [0] [2 0] [2 0] minus(*(x,y)) = [0 0]x + [0 0]y + [1] >= [0 0]x + [0 0]y = +(minus(minus(minus(x))),minus(minus(minus(y)))) [1 1] [3] [1 1] [2] f(minus(x)) = [0 3]x + [5] >= [0 3]x + [5] = minus(minus(minus(f(x)))) problem: minus(minus(x)) -> x minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y)))) minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y)))) Matrix Interpretation Processor: dim=2 interpretation: [1 0] [1 0] [1] [+](x0, x1) = [0 3]x0 + [0 3]x1 + [1], [1 2] [minus](x0) = [0 1]x0, [1 0] [1 0] [0] [*](x0, x1) = [0 3]x0 + [0 3]x1 + [1] orientation: [1 4] minus(minus(x)) = [0 1]x >= x = x [1 6] [1 6] [3] [1 6] [1 6] [0] minus(+(x,y)) = [0 3]x + [0 3]y + [1] >= [0 3]x + [0 3]y + [1] = *(minus(minus(minus(x))),minus(minus(minus(y)))) [1 6] [1 6] [2] [1 6] [1 6] [1] minus(*(x,y)) = [0 3]x + [0 3]y + [1] >= [0 3]x + [0 3]y + [1] = +(minus(minus(minus(x))),minus(minus(minus(y)))) problem: minus(minus(x)) -> x Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [minus](x0) = [0 0 1]x0 + [0] [0 1 0] [1] orientation: [1 1 1] [1] minus(minus(x)) = [0 1 0]x + [1] >= x = x [0 0 1] [1] problem: Qed