YES

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

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

  f_A(x1,x2) = 45405
  nil_A = 24867
  g_A(x1,x2) = x1 + x2 + 45406
  cdr_A(x1) = 45407
  cons_A(x1,x2) = x1 + x2 + 1
  f#_A(x1,x2) = x2
  nil#_A = 0
  cons#_A(x1,x2) = x2

and precedence:

g > cdr > cons > f > nil
)