YES

TRS:

  active(g(X)) -> mark(h(X))
  active(c()) -> mark(d())
  active(h(d())) -> mark(g(c()))
  mark(g(X)) -> active(g(X))
  mark(h(X)) -> active(h(X))
  mark(c()) -> active(c())
  mark(d()) -> active(d())
  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) = 1
  active#_A(x1) = x1 + 3
  g_A(x1) = 1
  g#_A(x1) = x1 + 3
  mark_A(x1) = 1
  mark#_A(x1) = x1 + 3
  h_A(x1) = 0
  h#_A(x1) = x1
  c_A = 2
  c#_A = 2
  d_A = 1
  d#_A = 5

precedence:

  mark > active > d > c > h > g