Nazir chapter 6, mishnah 10. The mishnah deals with a nazir who shaved his head at the conclusion of his nezirus on the strength of a sacrifice that turned out to be invalid, and with the status of the other sacrifices he brought.
"Gilach al hazevach venimtza pasul":
A person brought a sacrifice for nezirus of purity, completed his nezirus and shaved his head assuming the sacrifice was valid, and in the end it turned out that the sacrifice was invalid - for example, the blood spilled and it was impossible to sprinkle it on the altar, or it became tamei. It turns out that the sacrifice he relied upon has no validity, and from this two rulings follow:
"Tigalachto pesulah" - the shaving he performed is invalid, and this is like someone who shaved his head in the middle of his nezirus. Therefore he loses thirty days, and he must count thirty days of nezirus anew.
"Uzevachav lo alu lo" - the other sacrifices he brought in connection with that shaving do not count for him, since as he must go back and count thirty days, they are like sacrifices brought in the middle of the nezirus and not at its conclusion.
"Gilach al chatas shelo lishmah":
A person shaved his head on the strength of a chatas offering, but he brought the chatas not for its own sake - for instance, he intended it as an olah, when in truth it was a chatas. A chatas brought not for its own sake is invalid, and therefore this is the very same scenario. And even if afterwards "heivi korbanos lishman" - he brought the sacrifices for their own sake - "tigalachto pesulah uzevachav lo alu lo": the shaving is invalid, and the other sacrifices are not valid for him, for he will have to be a nazir for another thirty days, and the sacrifices are as though they were brought in the middle of the nezirus and not at its conclusion.
"Gilach al ha'olah o al hashelamim shelo lishman":
Here he shaved on the strength of the olah of the nezirus or the shelamim of the nezirus, but he performed them not for their own sake, while the other sacrifices he brought for their own sake - for example, he performed the olah not for its own sake and brought the shelamim and the chatas for their own sake, or he performed the shelamim not for its own sake and brought the chatas and the olah for their own sake.
The halachah is that an olah and shelamim brought not for their own sake are valid, except that they do not count toward the purpose for which they were brought - in our case, for the sake of nezirus. The question, then, is this: someone who shaves on the strength of a voluntary olah or voluntary shelamim - sacrifices that were not brought for the sake of nezirus - is his shaving considered a valid shaving or not? On this the Tannaim disagree:
The first Tanna: "Tigalachto pesulah uzevachav lo alu lo" - as in the previous cases: the shaving is invalid, and the other sacrifices he brought are considered as though they were brought in the middle of the nezirus, and therefore they do not count for him.
Rabbi Shimon: "Af hazevach lo alah lo" - that sacrifice which was brought not for its own sake does not count toward the nezirus, since he is not bringing it as a nezirus sacrifice but as a voluntary offering - a voluntary olah or voluntary shelamim. However, "she'ar zevachim alu lo" - the other sacrifices that he brought for their own sake do count for him, and we do not view them as though they were brought in the middle of the nezirus, because in Rabbi Shimon's view, one who shaves on the strength of a voluntary olah or shelamim - even that shaving is a valid shaving of nezirus. All he must do is bring a sacrifice in place of the one he performed not for its own sake.
"Gilach al sheloshtan venimtza echad meihen kasher":
In a further scenario he shaved after bringing all three sacrifices, and it turned out that they were all invalid except for one of them, which was found to be valid. "Tigalachto kesheirah" - the shaving is valid, since he performed it on the strength of a sacrifice that was effective. However, "yavi she'ar hazevachim" - he must bring the remaining sacrifices in place of those that were invalidated, and in this way he will properly complete his nezirus.
In summary: in this mishnah we learned that one who shaves on the strength of a sacrifice that was found to be invalid, or on the strength of a chatas brought not for its own sake - his shaving is invalid, he loses thirty days, and his other sacrifices likewise do not count for him, since they are like sacrifices brought in the middle of the nezirus. Where he shaved on the strength of an olah or shelamim brought not for their own sake there is a dispute: according to the first Tanna his shaving is invalid and his sacrifices do not count for him, while according to Rabbi Shimon his shaving is a valid shaving, and only that particular sacrifice does not count for him while the other sacrifices do count. And where he shaved on the strength of all three and one of them was found to be valid - his shaving is valid, and it is enough for him to bring the remaining sacrifices.