YES(?,ELEMENTARY)

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

Strict Trs:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,ELEMENTARY)

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

 safe(f) = {}, safe(a) = {}, safe(g) = {1}

and precedence

 empty .

Following symbols are considered recursive:

 {f}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

       f(x,  x;) > a()      
                            
  f(g(; x),  y;) > f(x,  y;)
                            

Hurray, we answered YES(?,ELEMENTARY)