YES

(VAR x0 x1 x)
(RULES
  f(x0,x1) -> x0
  g(g(x)) -> x
)

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

  f_A(x1,x2) = x1
  g_A(x1) = x1
  f#_A(x1,x2) = x1 + x2
  g#_A(x1) = x1

and precedence:

g > f
)