YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{21, 15 + x1}
  f#_A(x1) = max{0, -13 + x1}
  g_A(x1) = max{31, 10 + x1}
  g#_A(x1) = max{1, -22 + x1}

precedence:

  f > g