YES

TRS:

  f(a()) -> f(b())
  g(b()) -> g(a())

max/plus interpretations on N:

  f_A(x1) = max{0, 1}
  f#_A(x1) = max{2, 4}
  a_A = 1
  a#_A = 3
  b_A = 6
  b#_A = 1
  g_A(x1) = max{0, x1}
  g#_A(x1) = max{0, -2 + x1}

precedence:

  g > a > f > b