YES(?,PRIMREC)

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

Strict Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

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

 and > plus, and > s, tt > plus, tt > s, activate > plus,
 activate > s, plus > s, 0 > plus, 0 > s, x > plus, x > s, and ~ tt,
 and ~ activate, and ~ 0, and ~ x, tt ~ activate, tt ~ 0, tt ~ x,
 activate ~ 0, activate ~ x, 0 ~ x .

Hurray, we answered YES(?,PRIMREC)