YES
O(n)
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
 }
 Natural interpretation:
  Strict:
   {
                      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
   }
  Weak:
   {}
  Interpretation class: stronglylinear
  [g](X0) = + 1*X0 + 0
  [f](X2, X1, X0) = + 1*X0 + 1*X1 + 1*X2 + 1
  
  Qed