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)

max/plus interpretations on N:

  active_A(x1) = max{12, x1}
  active#_A(x1) = max{0, 2}
  g_A(x1) = max{4, 8 + x1}
  g#_A(x1) = max{7, 6 + x1}
  mark_A(x1) = max{12, 3 + x1}
  mark#_A(x1) = max{1, 4}
  h_A(x1) = max{6, 1}
  h#_A(x1) = max{3, 5 + x1}
  c_A = 1
  c#_A = 9
  d_A = 4
  d#_A = 8

precedence:

  h > g = c > mark > active > d