YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{3, 16 + x1}
  f#_A(x1) = max{30, 28 + x1}
  c_A(x1) = max{32, 10 + x1}
  c#_A(x1) = max{30, 22 + x1}
  n__f_A(x1) = max{10, 16 + x1}
  n__f#_A(x1) = max{30, 27 + x1}
  n__g_A(x1) = max{2, -11 + x1}
  n__g#_A(x1) = max{0, 0}
  d_A(x1) = max{12, 11}
  d#_A(x1) = max{10, 12}
  activate_A(x1) = max{1, 1 + x1}
  activate#_A(x1) = max{30, 13 + x1}
  h_A(x1) = max{22, 32}
  h#_A(x1) = max{34, 34}
  n__d_A(x1) = max{0, 12}
  n__d#_A(x1) = max{11, 12}
  g_A(x1) = max{3, -10 + x1}
  g#_A(x1) = max{16, 1}

precedence:

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