YES(?,PRIMREC)

We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).

Strict Trs:
  { sum(0()) -> 0()
  , sum(s(x)) -> +(sum(x), s(x))
  , sum1(0()) -> 0()
  , sum1(s(x)) -> s(+(sum1(x), +(x, x))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

The input was oriented with the instance of'multiset path order' as
induced by the precedence

 sum > s, sum > +, 0 > s, 0 > +, s > +, sum1 > s, sum1 > +, sum ~ 0,
 sum ~ sum1, 0 ~ sum1 .

Hurray, we answered YES(?,PRIMREC)