YES(?,PRIMREC)

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

Strict Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , odd(0()) -> false()
  , odd(s(x)) -> not(odd(x))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y))
  , +(s(x), y) -> s(+(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

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

 not > true, not > false, odd > not, odd > true, odd > false,
 0 > not, 0 > true, 0 > false, 0 > odd, 0 > s, s > not, s > true,
 s > false, + > not, + > true, + > false, + > odd, + > s, 0 ~ + .

Hurray, we answered YES(?,PRIMREC)