YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{15, 5 + x1}
  f#_A(x1) = max{4, 2 + x1}
  n__f_A(x1) = max{6, -2 + x1}
  n__f#_A(x1) = max{1, -1}
  n__a_A = 6
  n__a#_A = 0
  n__g_A(x1) = max{3, -15 + x1}
  n__g#_A(x1) = max{8, 3}
  a_A = 6
  a#_A = 1
  g_A(x1) = max{3, 1 + x1}
  g#_A(x1) = max{27, 9}
  activate_A(x1) = max{0, 16 + x1}
  activate#_A(x1) = max{3, 25 + x1}

precedence:

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