YES

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

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

  f_A(x1) = x1 + 2
  g_A(x1) = x1 + 1

weights

  w0 = 1
  w(f) = 3
  w(g) = 1

and precedence:

g > f
)