YES

TRS:

  f(X) -> g(n__h(n__f(X)))
  h(X) -> n__h(X)
  f(X) -> n__f(X)
  activate(n__h(X)) -> h(activate(X))
  activate(n__f(X)) -> f(activate(X))
  activate(X) -> X

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 1
  g_A(x1) = x1
  g#_A(x1) = x1
  n__h_A(x1) = x1
  n__h#_A(x1) = x1
  n__f_A(x1) = x1 + 1
  n__f#_A(x1) = x1 + 1
  h_A(x1) = x1
  h#_A(x1) = x1
  activate_A(x1) = x1 + 2
  activate#_A(x1) = x1 + 2

precedence:

  activate > f = h > g = n__h = n__f