YES

TRS:

  f(f(x)) -> g(f(x))
  g(g(x)) -> f(x)

max/plus interpretations on N:

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

precedence:

  g > f