YES
Input TRS:
      1: f(f(X)) -> c(n__f(g(n__f(X))))
      2: c(X) -> d(activate(X))
      3: h(X) -> c(n__d(X))
      4: f(X) -> n__f(X)
      5: d(X) -> n__d(X)
      6: activate(n__f(X)) -> f(X)
      7: activate(n__d(X)) -> d(X)
      8: activate(X) -> X
Number of strict rules: 8
Direct POLO(bPol) ... removes: 4 8 1 3 5 7 6 2
      h 	w: 2 * x1 + 15
      d 	w: x1 + 2
      activate	w: 2 * x1 + 9
      c 	w: 2 * x1 + 12
      f 	w: 2 * x1 + 41084
      n__f	w: x1 + 20538
      n__d	w: x1 + 1
      g 	w: x1
Number of strict rules: 0