YES

TRS:

  f(g(x)) -> g(f(f(x)))
  f(h(x)) -> h(g(x))
  f'(s(x),y,y) -> f'(y,x,s(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) = 2
  h#_A(x1) = 1
  f'_A(x1,x2,x3) = 0
  f'#_A(x1,x2,x3) = x1 + x2
  s_A(x1) = x1 + 1
  s#_A(x1) = 0

precedence:

  f > g = h = f' > s