YES

TRS:

  f(x,x) -> a()
  f(g(x),y) -> f(x,y)

max/plus interpretations on N:

  f_A(x1,x2) = max{1, 1 + x1, 1 + x2}
  f#_A(x1,x2) = max{1, 1 + x1, 1 + x2}
  a_A = 0
  a#_A = 0
  g_A(x1) = max{0, x1}
  g#_A(x1) = max{0, x1}

precedence:

  a > f = g