YES
Time: 0.000326
TRS:
 {  f(x, x) -> a(),
  f(g x, y) -> f(x, y)}
 RUF:
  Strict:
   {f(x, x) -> a()}
  Weak:
   {}
  RUF:
   Strict:
    {}
   Weak:
    {}
   Qed