YES

TRS:

  active(f(f(a()))) -> mark(f(g(f(a()))))
  mark(f(X)) -> active(f(mark(X)))
  mark(a()) -> active(a())
  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) = x1
  active#_A(x1) = 1
  f_A(x1) = x1 + 3
  f#_A(x1) = x1 + 2
  a_A = 1
  a#_A = 0
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 1
  g_A(x1) = 1
  g#_A(x1) = 3

precedence:

  active > g > f > mark > a