MAYBE 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: RT Transformation Processor: strict: 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)))) weak: Matrix Interpretation Processor: dimension: 1 interpretation: [f](x0) = x0 + 3, [*](x0, x1) = x0 + x1 + 2, [+](x0, x1) = x0 + x1, [minus](x0) = x0 orientation: minus(minus(x)) = x >= x = x minus(+(x,y)) = x + y >= x + y + 2 = *(minus(minus(minus(x))),minus(minus(minus(y)))) minus(*(x,y)) = x + y + 2 >= x + y = +(minus(minus(minus(x))),minus(minus(minus(y)))) f(minus(x)) = x + 3 >= x + 3 = minus(minus(minus(f(x)))) problem: strict: minus(minus(x)) -> x minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y)))) f(minus(x)) -> minus(minus(minus(f(x)))) weak: minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y)))) Matrix Interpretation Processor: dimension: 1 interpretation: [f](x0) = x0 + 16, [*](x0, x1) = x0 + x1 + 30, [+](x0, x1) = x0 + x1 + 20, [minus](x0) = x0 + 2 orientation: minus(minus(x)) = x + 4 >= x = x minus(+(x,y)) = x + y + 22 >= x + y + 42 = *(minus(minus(minus(x))),minus(minus(minus(y)))) f(minus(x)) = x + 18 >= x + 22 = minus(minus(minus(f(x)))) minus(*(x,y)) = x + y + 32 >= x + y + 32 = +(minus(minus(minus(x))),minus(minus(minus(y)))) problem: strict: minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y)))) f(minus(x)) -> minus(minus(minus(f(x)))) weak: minus(minus(x)) -> x minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y)))) Open