Retracts of contractible simplicial sets

I sent this earlier and it somehow disappeared. Does anyone know if a retract of a contractible augmented simplicial set is contractible? Since I first tried to post this question, John Kennison has provided a counter-example, but I would still like to know if this fact is generally known. There is an obvious attempt and it satisfies all the required simplicial identities except one: tt = s^0t where t is the attempted contraction. I posted this question on MathOverflow and got zero responses. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]