YES
Input TRS:
      1: a__f(f(a())) -> c(f(g(f(a()))))
      2: mark(f(X)) -> a__f(mark(X))
      3: mark(a()) -> a()
      4: mark(c(X)) -> c(X)
      5: mark(g(X)) -> g(mark(X))
      6: a__f(X) -> f(X)
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      a 	w: 2438
      a__f	w: 2 * x1 + 35431
      c 	w: x1 + 1
      f 	w: 2 * x1 + 17717
      mark	w: 2 * x1 + 2
      g 	w: x1 + 8856
Number of strict rules: 0