YES(?,O(1))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(1)).

Strict Trs:
  { first(0(), X) -> nil()
  , first(s(X), cons(Y)) -> cons(Y)
  , from(X) -> cons(X) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(1))

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

 safe(first) = {1}, safe(0) = {}, safe(nil) = {}, safe(s) = {1},
 safe(cons) = {1}, safe(from) = {}

and precedence

 first > from .

Following symbols are considered recursive:

 {}

The recursion depth is 0.

For your convenience, here are the satisfied ordering constraints:

             first(X; 0()) > nil()    
                                      
  first(cons(; Y); s(; X)) > cons(; Y)
                                      
                  from(X;) > cons(; X)
                                      

Hurray, we answered YES(?,O(1))