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{0, 8 + x1}
  f#_A(x1) = max{5, 1 + x1}
  c_A(x1) = max{16, 9}
  c#_A(x1) = max{8, 6 + x1}
  n__f_A(x1) = max{0, x1}
  n__f#_A(x1) = max{2, 0}
  g_A(x1) = max{1, -6 + x1}
  g#_A(x1) = max{0, 0}
  d_A(x1) = max{10, 10}
  d#_A(x1) = max{5, 3}
  activate_A(x1) = max{7, 8 + x1}
  activate#_A(x1) = max{7, 2 + x1}
  h_A(x1) = max{16, 8}
  h#_A(x1) = max{8, 8}
  n__d_A(x1) = max{2, 2}
  n__d#_A(x1) = max{2, 2}

precedence:

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