YES

TRS:

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

max/plus interpretations on N:

  active_A(x1) = max{0, x1}
  active#_A(x1) = max{8, 4 + x1}
  f_A(x1) = max{9, 6 + x1}
  f#_A(x1) = max{0, 3}
  mark_A(x1) = max{0, 1 + x1}
  mark#_A(x1) = max{7, 6 + x1}
  g_A(x1) = max{2, -2}
  g#_A(x1) = max{8, 1}
  h_A(x1) = max{3, x1}
  h#_A(x1) = max{9, 7}

precedence:

  g > mark > active = f > h