Problem: f(h(x)) -> f(i(x)) f(i(x)) -> a() i(x) -> h(x) Proof: Matrix Interpretation Processor: dim=3 interpretation: [0] [a] = [0] [0], [1 0 0] [0] [i](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [f](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [h](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1] [1 0 0] [1] f(h(x)) = [1 0 0]x + [0] >= [1 0 0]x + [0] = f(i(x)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [0] f(i(x)) = [1 0 0]x + [0] >= [0] = a() [0 0 0] [0] [0] [1 0 0] [0] [1 0 0] i(x) = [0 0 0]x + [0] >= [0 0 0]x = h(x) [0 0 0] [1] [0 0 0] problem: f(h(x)) -> f(i(x)) i(x) -> h(x) Unfolding Processor: loop length: 2 terms: f(h(x4)) f(i(x4)) context: [] substitution: x4 -> x4 Qed