YES
Input TRS:
      1: f(n__f(n__a())) -> f(n__g(n__f(n__a())))
      2: f(X) -> n__f(X)
      3: a() -> n__a()
      4: g(X) -> n__g(X)
      5: activate(n__f(X)) -> f(X)
      6: activate(n__a()) -> a()
      7: activate(n__g(X)) -> g(activate(X))
      8: activate(X) -> X
Number of strict rules: 8
Direct POLO(bPol) ... removes: 8 3 5 6 2
      a 	w: 1144
      n__a	w: 1143
      activate	w: x1 + 283
      f 	w: x1 + 2
      n__f	w: x1 + 1
      n__g	w: x1
      g 	w: x1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying f
      1: f^1_n__f(n__a()) -> f^1_n__g(n__f(n__a()))
      4: g(X) -> n__g(X)
      7: activate(n__g(X)) -> g(activate(X))
      9: f(n__f(_1)) ->= f^1_n__f(_1)
      10: f(n__g(_1)) ->= f^1_n__g(_1)
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4 1 10 7 9
      a 	w: 0
      n__a	w: 1
      activate	w: 2 * x1 + 1
      f 	w: 2 * x1 + 21242
      f^1_n__f	w: 2 * x1 + 5
      n__f	w: 2 * x1 + 1
      n__g	w: 2 * x1 + 7722
      f^1_n__g	w: 2 * x1
      g 	w: 2 * x1 + 15442
Number of strict rules: 0