YES
O(n^2)
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
       [X1]    [1 0][X1]   [0]
   [g]([X0]) = [0 0][X0] + [0]
   
       [X5]  [X3]  [X1]    [1 0][X5]   [1 0][X3]   [1 0][X1]   [1]
   [f]([X4], [X2], [X0]) = [0 1][X4] + [0 0][X2] + [0 1][X0] + [0]
   
   
   Qed