YES

TRS:

  f(f(a())) -> c(n__f(g(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{16, 12 + x1}
  f#_A(x1) = max{16, 12 + x1}
  a_A = 0
  a#_A = 0
  c_A(x1) = max{17, 2 + x1}
  c#_A(x1) = max{17, 2 + x1}
  n__f_A(x1) = max{11, x1}
  n__f#_A(x1) = max{11, x1}
  g_A(x1) = max{13, 5 + x1}
  g#_A(x1) = max{13, 5 + x1}
  activate_A(x1) = max{17, 17 + x1}
  activate#_A(x1) = max{17, 17 + x1}

precedence:

  a = activate > f > c = n__f = g