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