YES
O(n^4)
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
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [g]([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]
   
       [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 1][X3]   [0]
       [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]   [1]
   
   
   Qed