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

Strict Trs:
  { append(Cons(x, xs), ys) -> Cons(x, append(xs, ys))
  , append(Nil(), ys) -> ys
  , goal(x, y) -> append(x, y) }
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(append) = {2}, safe(Cons) = {1, 2}, safe(Nil) = {},
 safe(goal) = {}

and precedence

 goal > append .

Following symbols are considered recursive:

 {append}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

  append(Cons(; x,  xs); ys) > Cons(; x,  append(xs; ys))
                                                         
           append(Nil(); ys) > ys                        
                                                         
                goal(x,  y;) > append(x; y)              
                                                         

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