YES

TRS:

  f(h(x)) -> f(i(x))
  g(i(x)) -> g(h(x))
  h(a()) -> b()
  i(a()) -> b()

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = x1 + 1
  h_A(x1) = x1 + 2
  h#_A(x1) = 1
  i_A(x1) = x1 + 1
  i#_A(x1) = 2
  g_A(x1) = 0
  g#_A(x1) = 3
  a_A = 1
  a#_A = 1
  b_A = 0
  b#_A = 0

precedence:

  f > i > g > h = a > b