YES(?,O(n^3))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).

Strict Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , after(s(N), cons(X, XS)) -> after(N, activate(XS))
  , after(0(), XS) -> XS
  , activate(X) -> X
  , activate(n__from(X)) -> from(X) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^3))

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

 safe(from) = {1}, safe(cons) = {1, 2}, safe(n__from) = {1},
 safe(s) = {1}, safe(after) = {2}, safe(0) = {},
 safe(activate) = {1}

and precedence

 after > from, after > activate, activate > from .

Following symbols are considered recursive:

 {from, after, activate}

The recursion depth is 3.

For your convenience, here are the satisfied ordering constraints:

                      from(; X) > cons(; X,  n__from(; s(; X)))
                                                               
                      from(; X) > n__from(; X)                 
                                                               
  after(s(; N); cons(; X,  XS)) > after(N; activate(; XS))     
                                                               
                 after(0(); XS) > XS                           
                                                               
                  activate(; X) > X                            
                                                               
       activate(; n__from(; X)) > from(; X)                    
                                                               

Hurray, we answered YES(?,O(n^3))