Zevachim Chapter 8, Mishnah 4. In this Mishnah we are dealing with limbs of a chatas that became mixed with limbs of an olah. We are not talking about random pieces of meat, but rather whole limbs, since there is a specific way in which the olah is cut and brought to the fire in specific limbs. For example: we have before us two legs, one being the leg of the olah and the other the leg of the chatas, and it is unknown which is which.
Seemingly, a dead end is created here: the olah is not eaten at all, while the chatas is not meant to be burned but rather eaten. How, then, should we proceed? Rabbi Eliezer and the Sages disagree on this question.
The view of Rabbi Eliezer:
Rabbi Eliezer deduces from the verses that even though it is forbidden to burn the meat of the chatas - which is meant to be eaten - in principle it can be brought up to the altar, provided there is no intention for it to be a pleasing aroma, meaning it is not burned for the sake of offering. Therefore, the kohen may say: the limb of the chatas is placed here not as a sacrifice, not for a pleasing aroma, and not for offering, but merely as fuel for the fire, like a piece of wood.
This is certainly not the ideal way, since it would have been better to eat the meat of the chatas, but in this way at least one of the two is fulfilled. For if we say that the olah cannot be eaten and the chatas cannot be burned, neither of the laws will be fulfilled; whereas when the leg of the chatas is treated as a fuel source, like a piece of wood, it indeed will not be eaten, but the leg of the olah will be burned according to its law. It is better this way, says Rabbi Eliezer.
The view of the Sages:
The Sages reject his derivation and hold that limbs of a chatas may not be offered on the altar, even if there is no intention for a pleasing aroma. In their opinion, a dead end is indeed created here.
The text of the Mishnah:
"Eivrei chatas shenisarvu b'eivrei olah" - the two limbs that became mixed together. "Rabbi Eliezer omer: yiten lemaalah" - he should bring them both up above, onto the burning arrangement of wood on top of the altar. "Vero'eh ani es besar hachatas lemaalah ke'ilu hu etzim" - the limb from the chatas, whichever it may be, is considered as a source of fuel, like the wood burning there for the burning of the olah, and this is permitted as long as it is explicit in his mind that it will not be for a pleasing aroma.
However, for the olah, one must specifically intend that it be for a pleasing aroma. Therefore, the kohen brings up the two limbs and makes an explicit condition: whichever of the limbs is the olah - it shall specifically be for a pleasing aroma, and the one that is a chatas, whichever it may be - it shall not be for a pleasing aroma. In this way the matter is effective, according to Rabbi Eliezer.
"Vachachamim omrim: te'ubar tzuratan" - in their opinion, one may not initially bring a limb of a chatas up to the altar for burning, and therefore one must wait until its form is altered. This is the literal translation of the words, and the idea is that when the meat is left past its time, it is no longer permitted to be eaten, and this apparently refers to it becoming spoiled meat. The halachic point is that they wait until the time passes, and for both the chatas and the olah, this would be the next morning. They do not burn the meat today, since it is impossible to burn it while it is still valid chatas meat; but the next day, once it becomes invalid, there is an obligation to burn it.
"Veyisaref bebeis hasereifah" - the burning is not done on the altar, since it is no longer a valid sacrifice; even the limb of the olah has become invalid. Therefore, the limbs are taken to the place of burning, the place where all invalid sacrifices are burned.
It is worth noting: generally, once a korban becomes invalid, it must be burned immediately rather than waiting until the next day. Here, there is no option to burn it immediately, since doing so would destroy the limbs of the valid, legitimate korban, and this is forbidden. Therefore, they wait until its time passes - which is 'te'ubar tzurasan' in the language of the Mishnah and halachah - and at that point, once it is completely disqualified, both legs are burned together.
In summary: In this Mishnah we learned the law regarding the limbs of a chatas that became mixed with the limbs of an olah. According to Rabbi Eliezer, one should bring both of them up to the pyre, and explicitly stipulate that the chatas limb is not being offered for a pleasing aroma, but rather as wood to fuel the fire, and in this way the requirement to burn the olah is at least fulfilled. The Sages reject this derivation, holding that a chatas limb may not be burned on the altar at all. Therefore, they wait until their form decays the next morning, and then both limbs are burned together in the place of burning.