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

precedence:

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