YES
Input TRS:
      1: a__f(f(a())) -> a__f(g(f(a())))
      2: mark(f(X)) -> a__f(mark(X))
      3: mark(a()) -> a()
      4: mark(g(X)) -> g(X)
      5: a__f(X) -> f(X)
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 3 5
      a 	w: 1
      a__f	w: x1 + 564
      f 	w: x1 + 282
      mark	w: 2 * x1 + 1
      g 	w: x1
Number of strict rules: 2
Direct POLO(bPol) ... removes: 2
      a 	w: 15922
      a__f	w: x1 + 79
      f 	w: x1 + 79
      mark	w: 2 * x1 + 486
      g 	w: x1
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying a__f
      1: a__f^1_f(a()) -> a__f^1_g(f(a()))
      6: a__f(g(_1)) ->= a__f^1_g(_1)
      7: a__f(f(_1)) ->= a__f^1_f(_1)
Number of strict rules: 1
Direct POLO(bPol) ... removes: 1 7 6
      a 	w: 1
      a__f	w: 2 * x1 + 2439
      f 	w: x1 + 1
      a__f^1_g	w: 2 * x1
      mark	w: x1
      a__f^1_f	w: 2 * x1 + 3
      g 	w: 2 * x1 + 1
Number of strict rules: 0