YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = x1 + 3
  f#_A(x1) = x1 + 3
  g_A(x1) = x1 + 2
  g#_A(x1) = x1 + 2

precedence:

  f > g