YES
O(n)
TRS:
 {   f(x, x) -> a(),
  f(g(x), y) -> f(x, y)}
 Natural interpretation:
  Strict:
   {   f(x, x) -> a(),
    f(g(x), y) -> f(x, y)}
  Weak:
   {}
  Interpretation class: stronglylinear
  [g](X0) = + 1*X0 + 1
  [f](X1, X0) = + 1*X0 + 1*X1 + 1
  [a] = + 0
  
  Qed