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{3, -1 + x1}
  f#_A(x1) = max{6, 1}
  a_A = 8
  a#_A = 2
  c_A(x1) = max{4, 5 + x1}
  c#_A(x1) = max{0, -1 + x1}
  n__f_A(x1) = max{1, -2 + x1}
  n__f#_A(x1) = max{6, 0}
  g_A(x1) = max{1, 1}
  g#_A(x1) = max{6, -1 + x1}
  activate_A(x1) = max{3, 1 + x1}
  activate#_A(x1) = max{7, 4 + x1}

precedence:

  activate > f > a = c = n__f = g