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

Strict Trs:
  { duplicate(Cons(x, xs)) -> Cons(x, Cons(x, duplicate(xs)))
  , duplicate(Nil()) -> Nil()
  , goal(x) -> duplicate(x) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS,1-bounded)' as induced by the safe mapping

 safe(duplicate) = {}, safe(Cons) = {1, 2}, safe(Nil) = {},
 safe(goal) = {}

and precedence

 goal > duplicate .

Following symbols are considered recursive:

 {duplicate}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

  duplicate(Cons(; x,  xs);) > Cons(; x,  Cons(; x,  duplicate(xs;)))
                                                                     
           duplicate(Nil();) > Nil()                                 
                                                                     
                    goal(x;) > duplicate(x;)                         
                                                                     

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