YES

TRS:

  f(f(a())) -> f(g(n__f(a())))
  f(X) -> n__f(X)
  activate(n__f(X)) -> f(X)
  activate(X) -> X

max/plus interpretations on N:

  f_A(x1) = max{3, -4 + x1}
  f#_A(x1) = max{1, 3 + x1}
  a_A = 5
  a#_A = 0
  g_A(x1) = max{2, -2 + x1}
  g#_A(x1) = max{0, 6 + x1}
  n__f_A(x1) = max{1, -11 + x1}
  n__f#_A(x1) = max{3, 0}
  activate_A(x1) = max{0, 7 + x1}
  activate#_A(x1) = max{0, 15 + x1}

precedence:

  activate > f > a = g = n__f