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)

linear polynomial interpretations on N:

  active_A(x1) = x1
  active#_A(x1) = x1 + 1
  f_A(x1) = x1 + 5
  f#_A(x1) = x1 + 7
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 4
  g_A(x1) = 1
  g#_A(x1) = x1
  h_A(x1) = x1
  h#_A(x1) = x1

precedence:

  f = mark > active > g = h