YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  g > mark > a__f > h = f