YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{0, -1, -1}
  f#_A(x1,x2) = max{1, -2 + x1, -1}
  a_A = 0
  a#_A = 0
  g_A(x1) = max{4, 4 + x1}
  g#_A(x1) = max{0, 0}

precedence:

  f > a = g