YES

TRS:

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

linear polynomial interpretations on N:

  active_A(x1) = x1
  active#_A(x1) = x1 + 7
  f_A(x1) = x1 + 3
  f#_A(x1) = x1 + 6
  a_A = 1
  a#_A = 11
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 9
  c_A(x1) = 2
  c#_A(x1) = x1
  g_A(x1) = x1 + 2
  g#_A(x1) = x1 + 9

precedence:

  a > active = f > mark = g > c