YES(?,POLY)

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

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

The input was oriented with the instance of 'Polynomial Path Order'
as induced by the safe mapping

 safe(and) = {}, safe(tt) = {}, safe(activate) = {},
 safe(plus) = {1}, safe(0) = {}, safe(s) = {1}

and precedence

 and > plus, activate > plus, and ~ activate .

Following symbols are considered recursive:

 {and, activate, plus}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

   and(tt(),  X;) > activate(X;)   
                                   
     activate(X;) > X              
                                   
     plus(0(); N) > N              
                                   
  plus(s(; M); N) > s(; plus(M; N))
                                   

Hurray, we answered YES(?,POLY)