YES
O(n^4)
TRS:
 {   f(x, x) -> a(),
  f(g(x), y) -> f(x, y)}
 DUP: We consider a non-duplicating system.
  Trs:
   {   f(x, x) -> a(),
    f(g(x), y) -> f(x, y)}
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [g]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [1]
   
       [X7]  [X3]    [1 0 0 1][X7]   [1 0 0 0][X3]   [1]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [f]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [a] = [0]
         [0]
   
   
   Qed