YES
O(n^2)
TRS:
 {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]  [X1]    [1 0][X3]   [1 0][X1]   [0]
   [g]([X2], [X0]) = [0 0][X2] + [0 0][X0] + [0]
   
       [X3]  [X1]    [1 0][X3]   [1 1][X1]   [0]
   [f]([X2], [X0]) = [0 0][X2] + [0 0][X0] + [1]
   
   
   Qed