YES

TRS:

  f(g(X)) -> g(f(f(X)))
  f(h(X)) -> h(g(X))

max/plus interpretations on N:

  f_A(x1) = max{0, x1}
  f#_A(x1) = max{5, 4 + x1}
  g_A(x1) = max{2, 3 + x1}
  g#_A(x1) = max{5, 2}
  h_A(x1) = max{2, -1}
  h#_A(x1) = max{0, 1}

precedence:

  g > h > f