YES(?,ELEMENTARY)

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

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(?,ELEMENTARY)

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

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

and precedence

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

Following symbols are considered recursive:

 {and, activate, plus}

The recursion depth is 3.

For your convenience, here are the satisfied ordering constraints:

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

Hurray, we answered YES(?,ELEMENTARY)