YES O(n^2) TRS: {f(s(x)) -> s(s(g(x))), f(0()) -> s(0()), g(s(x)) -> f(x), g(0()) -> 0()} Natural interpretation: Strict: {f(s(x)) -> s(s(g(x))), f(0()) -> s(0()), g(s(x)) -> f(x), g(0()) -> 0()} Weak: {} Interpretation class: deltarestricted [0](delta) = + 0 + 0*delta [s](delta, X0) = + 1*X0 + 1 + 0*X0*delta + 0*delta [g](delta, X0) = + 1*X0 + 0 + 1*X0*delta + 1*delta [f](delta, X0) = + 1*X0 + 1 + 1*X0*delta + 1*delta s_tau_1(delta) = delta/(1 + 0 * delta) g_tau_1(delta) = delta/(1 + 1 * delta) f_tau_1(delta) = delta/(1 + 1 * delta) Qed