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

max/plus interpretations on N:

  f_A(x1) = max{7, -4 + x1}
  f#_A(x1) = max{2, 3}
  g_A(x1) = max{7, -2 + x1}
  g#_A(x1) = max{3, 3}
  n__h_A(x1) = max{9, -1}
  n__h#_A(x1) = max{0, 0}
  n__f_A(x1) = max{1, -4 + x1}
  n__f#_A(x1) = max{1, 1}
  h_A(x1) = max{9, 8}
  h#_A(x1) = max{1, 1}
  activate_A(x1) = max{7, 1 + x1}
  activate#_A(x1) = max{4, 0}

precedence:

  h > n__h > n__f = activate > f > g