YES O(n^2) TRS: {g(h(x), y) -> h(g(x, y)), g(h(x), y) -> h(f(x, y)), f(x, y) -> g(x, y)} Natural interpretation: Strict: {g(h(x), y) -> h(g(x, y)), g(h(x), y) -> h(f(x, y)), f(x, y) -> g(x, y)} Weak: {} Interpretation class: deltarestricted [h](delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta [f](delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 2*X0*delta + 2*X1*delta + 2*delta [g](delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 2*X0*delta + 2*X1*delta + 0*delta h_tau_1(delta) = delta/(1 + 0 * delta) f_tau_1(delta) = delta/(1 + 2 * delta)f_tau_2(delta) = delta/(0 + 2 * delta) g_tau_1(delta) = delta/(1 + 2 * delta)g_tau_2(delta) = delta/(0 + 2 * delta) Qed