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

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 2
  n__f_A(x1) = x1 + 1
  n__f#_A(x1) = 1
  n__a_A = 1
  n__a#_A = 0
  n__g_A(x1) = 1
  n__g#_A(x1) = 2
  a_A = 1
  a#_A = 1
  g_A(x1) = 1
  g#_A(x1) = 3
  activate_A(x1) = x1
  activate#_A(x1) = x1 + 3

precedence:

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