YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = x1
  g_A(x1) = x1 + 2
  g#_A(x1) = 1
  h_A(x1) = 3
  h#_A(x1) = 2

precedence:

  f > h > g