YES

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

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

  f_A(x1) = x1 + 1
  g_A(x1) = x1 + 3
  f#_A(x1) = x1
  g#_A(x1) = x1

and precedence:

g > f
)