YES(?,O(n^1))

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

Strict Trs:
  { f(S(x), x2) -> f(x2, x)
  , f(0(), x2) -> 0() }
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(f) = {}, safe(S) = {1}, safe(0) = {}

and precedence

 empty .

Following symbols are considered recursive:

 {f}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

  f(S(; x),  x2;) > f(x2,  x;)
                              
     f(0(),  x2;) > 0()       
                              

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