YES(?,O(n^1))

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

Strict Trs:
  { app(nil(), xs) -> nil()
  , app(cons(x, xs), ys) -> cons(x, app(xs, ys)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

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

 safe(app) = {}, safe(nil) = {}, safe(cons) = {1, 2}

and precedence

 empty .

Following symbols are considered recursive:

 {app}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

           app(nil(),  xs;) > nil()                    
                                                       
  app(cons(; x,  xs),  ys;) > cons(; x,  app(xs,  ys;))
                                                       

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