YES O(n^2) TRS: { +(0(), y) -> y, +(s(x), y) -> +(x, s(y)), +(s(x), y) -> s(+(x, y))} Natural interpretation: Strict: { +(0(), y) -> y, +(s(x), y) -> +(x, s(y)), +(s(x), y) -> s(+(x, y))} Weak: {} Interpretation class: deltarestricted [s](delta, X0) = + 1*X0 + 1 + 0*X0*delta + 0*delta [0](delta) = + 1 + 0*delta [+](delta, X1, X0) = + 1*X0 + 1*X1 + 1 + 0*X0*delta + 1*X1*delta + 0*delta s_tau_1(delta) = delta/(1 + 0 * delta) +_tau_1(delta) = delta/(1 + 1 * delta)+_tau_2(delta) = delta/(1 + 0 * delta) Qed