YES

TRS:

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

linear polynomial interpretations on N:

  active_A(x1) = x1
  active#_A(x1) = 4
  f_A(x1) = x1 + 8
  f#_A(x1) = x1
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 2
  c_A(x1) = 5
  c#_A(x1) = 6
  g_A(x1) = 3
  g#_A(x1) = 3
  d_A(x1) = 3
  d#_A(x1) = 3
  h_A(x1) = x1 + 7
  h#_A(x1) = 8

precedence:

  f = h > c > d > mark > active > g