YES(?,PRIMREC)

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

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

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

 f > 0, f > s, f > *, + > 0, + > s, + > *, f ~ +, 0 ~ s, 0 ~ * .

Hurray, we answered YES(?,PRIMREC)