YES

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

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

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

and precedence:

a > g > f
)