YES
O(n^4)
TRS:
 {
                    f(x, x, y) -> x,
                    f(x, y, y) -> y,
                 f(x, y, g(y)) -> x,
  f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v)),
                 f(g(x), x, y) -> y
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                      f(x, x, y) -> x,
                      f(x, y, y) -> y,
                   f(x, y, g(y)) -> x,
    f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v)),
                   f(g(x), x, y) -> 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 0][X0]   [0]
   
       [X11]  [X7]  [X3]    [1 0 0 0][X11]   [1 0 0 0][X7]   [1 0 0 0][X3]   [1]
       [X10]  [X6]  [X2]    [0 1 0 0][X10]   [0 0 0 0][X6]   [0 1 0 0][X2]   [0]
   [f]([ X9], [X5], [X1]) = [0 0 1 0][X9] + [0 0 0 0][X5] + [0 0 1 0][X1] + [0]
       [ X8]  [X4]  [X0]    [0 0 0 1][X8]   [0 0 0 0][X4]   [0 0 0 1][X0]   [0]
   
   
   Qed