YES

TRS:

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

linear polynomial interpretations on N:

  active_A(x1) = 1
  active#_A(x1) = x1 + 1
  c_A = 5
  c#_A = 8
  mark_A(x1) = 1
  mark#_A(x1) = x1 + 2
  f_A(x1) = 3
  f#_A(x1) = x1
  g_A(x1) = 1
  g#_A(x1) = 5

precedence:

  active > mark > c = f > g