YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{1, 3 + x1, 3 + x2}
  f#_A(x1,x2) = max{1, 3 + x1, 3 + x2}
  g_A(x1,x2) = max{0, 2 + x1, 1 + x2}
  g#_A(x1,x2) = max{0, 2 + x1, 1 + x2}

precedence:

  g > f