YES(?,ELEMENTARY) 'epo* (timeout of 60.0 seconds)' -------------------------------- Answer: YES(?,ELEMENTARY) Input Problem: innermost runtime-complexity with respect to Rules: { sum(0()) -> 0() , sum(s(x)) -> +(sum(x), s(x)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, y))} Proof Output: Strict Rules in Predicative Notation: { sum(0();) -> 0() , sum(s(; x);) -> +(s(; x); sum(x;)) , +(0(); x) -> x , +(s(; y); x) -> s(; +(y; x))} Safe Mapping: safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1} Argument Permutation: mu(sum) = [1], mu(+) = [1, 2] Precedence: + ~ +, sum > +, sum ~ sum