Problem: f(X,g(X)) -> f(1(),g(X)) g(1()) -> g(0()) Proof: Matrix Interpretation Processor: dim=3 interpretation: [0] [0] = [0] [0], [0] [1] = [0] [1], [1 1 0] [1 1 1] [f](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [1 0 0] [0 0 0] , [1 1 1] [0] [g](x0) = [1 0 1]x0 + [1] [0 0 1] [1] orientation: [3 2 3] [2] [2 1 3] [2] f(X,g(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = f(1(),g(X)) [1 0 0] [0] [0 0 0] [0] [1] [0] g(1()) = [2] >= [1] = g(0()) [2] [1] problem: f(X,g(X)) -> f(1(),g(X)) Unfolding Processor: loop length: 1 terms: f(1(),g(1())) context: [] substitution: Qed