YES

(VAR x0 x)
(RULES
  f(x0) -> x0
  g(g(x)) -> x
  g(a()) -> a()
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  f_A(x1) = x1
  g_A(x1) = x1
  a_A = 0
  a#_A = 0

weights

  w0 = 1
  w(f) = 1
  w(g) = 1
  w(a) = 1

and precedence:

f > g > a
)