Kinnim 1:3 - 1:4

בחובה ובנדבה – that the couple of sacrificial birds of obligatory offering that some of them are sin-offerings and some of them were burnt-offerings were mixed up with the couple of sacrificial birds for free-will offering – all of which are burnt offerings.

אבל בחובה שנתערבה זו בזו – from the couple of birds concerning which it not been decided if it for the woman who just experienced childbirth or for a woman who experiences a flow of menstrual-type on three consecutive days during a time of the month in which she is not due to experience menstrual bleeding that became mixed up with a couple of sacrificial birds of a woman who experiences childbirth or that of another woman who experiences a flow of menstrual-type on three consecutive days during a time of the month in which she is not due to experience menstrual bleeding.

מחצה כשר ומחצה פסול – and he (i.e., the priest) offers up only two from the four that are mixed up, one for a burnt offering and one for a sin-offering, and nothing additional. For if he (i.e., the priest) had made two burnt offerings, perhaps he would do them from one nest, and every couple of birds concerning which it has not yet been decided which is to be the burnt offering, and which is to be the sin-offering.

המועט כשר – if one couple of birds concerning which it has not yet been decided which is to be the burnt offering, and which is to be the sin-offering that was mixed up with two or three other couples of birds, he (i.e., the priest) is not able to offer up other than one set of birds, a single pigeon for a sin-offering and a single pigeon for a burnt-offering. But he (i.e., the priest) cannot make two burnt-offerings, lest he take the couple of birds that has been first selected for a woman who gave birth, who cannot make from it other than one for a sin-offering and one for a burnt-offering. And similarly, if ten couples of birds were mixed with one-hundred, he (i.e., the priest) does not offer up from all of them other than ten sets of birds, some of them for sin-offerings and some of them for burnt-offerings and he rest of them are invalid, and that which is the smaller thing is kosher/fit.

בין משם אחד – one birth and another birth, a woman who experiences a flow of menstrual-type on three consecutive days during a time of the month in which she is not due to experience menstrual bleeding with another woman who experiences a flow of menstrual-type on three consecutive days during a time of the month in which she is not due to experience menstrual bleeding.

בין משני שמות – a woman who has given birth with a woman who experiences a flow of menstrual-type on three consecutive days during a time of the month in which she is not due to experience menstrual bleeding, whether from two women whether from one woman, as will be explained further on.

רבי יוסי אומר כו' – not because Rabbi Yossi holds that there is a retroactive designation, and we should say that when the Kohen offered up one set of birds for one single denomination/class of them, the matter became clarified retroactively that from the beginning at the time of the taking of the set of birds, this set of birds was hers, but rather, the Gemara (Tractate Eruvin 37a) in the chapter: “With any [food] do they prepare an Eruv” that Rabbi Yossi is speaking that they made a condition at the time of purchase that the Kohen is able to make a set of birds that he desires for the sake of whichever woman that he wants. And the Halakha is according to Rabbi Yossi.