YES

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

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

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

weights

  w0 = 1
  w(f) = 0
  w(g) = 1

and precedence:

f > g
)