YES

TRS:

  f(f(X)) -> c(n__f(g(n__f(X))))
  c(X) -> d(activate(X))
  h(X) -> c(n__d(X))
  f(X) -> n__f(X)
  d(X) -> n__d(X)
  activate(n__f(X)) -> f(X)
  activate(n__d(X)) -> d(X)
  activate(X) -> X

linear polynomial interpretations on N:

  f_A(x1) = x1 + 4
  f#_A(x1) = x1 + 4
  c_A(x1) = x1 + 4
  c#_A(x1) = x1 + 5
  n__f_A(x1) = x1 + 1
  n__f#_A(x1) = 3
  g_A(x1) = 1
  g#_A(x1) = x1 + 2
  d_A(x1) = x1 + 1
  d#_A(x1) = x1 + 1
  activate_A(x1) = x1 + 3
  activate#_A(x1) = x1 + 4
  h_A(x1) = x1 + 5
  h#_A(x1) = x1 + 7
  n__d_A(x1) = x1 + 1
  n__d#_A(x1) = x1

precedence:

  n__f > f = h > c = g > activate > d > n__d