TRS: { sum(0()) -> 0(), sum(s(x)) -> +(sum(x), s(x)), +(x, 0()) -> x, +(x, s(y)) -> s(+(x, y))} LMPO: Quasi-Precedence: sum > + empty Normal: pi(+) = [2], pi(sum) = [1] Safe: pi(+) = [1] Predicative System: { sum(0();) -> 0(), sum(s(x;);) -> +(s(x;);sum(x;)), +(0();x) -> x, +(s(y;);x) -> s(+(y;x);)} Qed