YES O(n^2) TRS: { h(x, y) -> g(x, f(y)), g(f(x), y) -> f(h(x, y))} Natural interpretation: Strict: { h(x, y) -> g(x, f(y)), g(f(x), y) -> f(h(x, y))} Weak: {} Interpretation class: deltarestricted [g](delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 1*X0*delta + 2*X1*delta + 0*delta [h](delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 1*X0*delta + 2*X1*delta + 3*delta [f](delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta g_tau_1(delta) = delta/(1 + 2 * delta)g_tau_2(delta) = delta/(0 + 1 * delta) h_tau_1(delta) = delta/(1 + 2 * delta)h_tau_2(delta) = delta/(0 + 1 * delta) f_tau_1(delta) = delta/(1 + 0 * delta) Qed