YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{0, 1}
  f#_A(x1) = max{8, 9}
  h_A(x1) = max{1, -2 + x1}
  h#_A(x1) = max{7, -1}
  i_A(x1) = max{3, -1 + x1}
  i#_A(x1) = max{1, -2}
  g_A(x1) = max{0, 0}
  g#_A(x1) = max{6, 4 + x1}
  a_A = 1
  a#_A = 1
  b_A = 1
  b#_A = 0

precedence:

  g > f = h > i = a > b