YES

TRS:

  f(f(a())) -> c(n__f(n__g(n__f(n__a()))))
  f(X) -> n__f(X)
  g(X) -> n__g(X)
  a() -> n__a()
  activate(n__f(X)) -> f(activate(X))
  activate(n__g(X)) -> g(activate(X))
  activate(n__a()) -> a()
  activate(X) -> X

max/plus interpretations on N:

  f_A(x1) = max{19, 5 + x1}
  f#_A(x1) = max{19, 5 + x1}
  a_A = 16
  a#_A = 16
  c_A(x1) = max{26, x1}
  c#_A(x1) = max{26, x1}
  n__f_A(x1) = max{15, 5 + x1}
  n__f#_A(x1) = max{15, 5 + x1}
  n__g_A(x1) = max{21, 6 + x1}
  n__g#_A(x1) = max{21, 6 + x1}
  n__a_A = 4
  n__a#_A = 4
  g_A(x1) = max{22, 6 + x1}
  g#_A(x1) = max{22, 6 + x1}
  activate_A(x1) = max{17, 13 + x1}
  activate#_A(x1) = max{17, 13 + x1}

precedence:

  a > activate > g > f = n__g > c = n__f = n__a