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

max/plus interpretations on N:

  f_A(x1) = max{2, 9 + x1}
  f#_A(x1) = max{2, 9 + x1}
  c_A(x1) = max{18, 15 + x1}
  c#_A(x1) = max{18, 15 + x1}
  n__f_A(x1) = max{1, x1}
  n__f#_A(x1) = max{1, x1}
  g_A(x1) = max{3, 2 + x1}
  g#_A(x1) = max{3, 2 + x1}
  d_A(x1) = max{18, 4 + x1}
  d#_A(x1) = max{18, 4 + x1}
  activate_A(x1) = max{14, 10 + x1}
  activate#_A(x1) = max{14, 10 + x1}
  h_A(x1) = max{32, 16 + x1}
  h#_A(x1) = max{32, 16 + x1}
  n__d_A(x1) = max{17, x1}
  n__d#_A(x1) = max{17, x1}

precedence:

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