Gemara

Beraisa - R. Yehudah: If any of the following was lost and a replacement was separated, the extra animal must die:

The Par and Sa'ir of Yom Kipur or Se'irim to atone for Helam Davar of idolatry.

R. Eliezer and R. Shimon say, it is Ro'eh (it grazes until it gets a Mum, then it is redeemed) and the money goes to Nedavah, for a Chatas Tzibur need not die.

65b - Question: Why can't the Sa'ir be used next year?

Answer: This is a decree lest one offer a Chatas more than a year old.

Question: This is not a mere decree. The Sa'ir itself will be more than a year old next Yom Kipur!

Answer: This is like Rebbi. (It can still be within its year, e.g. if it was eight days old on Yom Kipur. If it is not a leap year it will be about 362 days old next Yom Kipur.)

Beraisa - Rebbi: (If one sells a house in a walled city, for one year he has the right to redeem it.) "Shanah Semimah" - we count 365 days, which is a solar year;

Chachamim say, we count 12 months. If it is a leap year, the year includes the extra month.

Erchin 31b - R. Aba bar Mamal: If lambs were born in the flocks of Reuven and Shimon on the 15th of Adar Rishon and Rosh Chodesh Adar Sheni, these lambs complete their years on the coming Adar 15 and Adar 1, respectively.

Question (Ravina): Reuven's lamb should finish its year earlier, for it was born first!

Answer: Since Shimon's was born during the added month, it does not receive an extra month.

R. Aba bar Mamal: If Reuven bought a Bayis Ir Chomah on the 15th of Adar Rishon, and Shimon bought on the first of Adar Sheni, Shimon's house is Chalut on the first of Adar, and Reuven's on Adar 15.

Question: Why must R. Aba teach both cases?

Answer: One might have thought that the extra month is included only regarding Bayis Ir Chomah, for there it says "Semimah";

R. Aba teaches that this also applies to a lamb. We learn from a Gezeirah Shavah "Shanah-Shanah."

Rishonim

Rambam (Hilchos Ma'aseh ha'Korbanos 1:11): Small animals (e.g. Kevasim Benei Shanah) are from eight days until a full year from day to day. If it was a leap year, the extra month is included in the year.

Rambam (Hilchos Bechoros 1:12): The year for a Bechor is a full lunar year of 12 months from day to day. If it was a leap year, it is 13 months. If one lamb was born on the 15th of Adar Rishon and another on the first of Adar Sheni, their years end on the 15th and first of the coming Adar, respectively.

Poskim

Shulchan Aruch (YD 306:10): The year of a Bechor (in which it must be eaten) is a full lunar year of 12 months. If it was a leap year, it is 13 months.

Shulchan Aruch (ibid. 11): If one lamb was born on the 15th of Adar Rishon and another on the first of Adar Sheni, their years end on the 15th and first of the coming Adar, respectively.

Question (Lechem Mishneh): The Tur cites this in the name of the Rambam. Why doesn't he cite an explicit Gemara (Erchin 31b) which says so?

Note: Surely, the Lechem Mishneh explains the Gemara like Rashi, that R. Aba discusses Bechoros, which must be offered or eaten in their first year. Presumably, the Tur holds that one could have explained like R. Gershom, who says that R. Aba discusses when they cease to be considered lambs, or he discusses the year for taking Ma'aser Behemah.

Shulchan Aruch (OC 55:10): If Reuven was born on Adar Rishon 29, and Shimon was born on Rosh Chodesh Adar Sheni, Shimon becomes Bar Mitzvah on Rosh Chodesh Adar of the 13th year if it is not a leap year, and Reuven is not Bar Mitzvah until the 29th.

Source (Beis Yosef DH Kasuv b'Sefer ha'Agur): We learn from R. Aba bar Mamal (Erchin 31b).

Question: Perhaps the extra month is included only regarding Bayis Ir Chomah (because it says "Semimah") and Bechor (which we learn from a Gezeirah Shavah from Bayis Ir Chomah)!

Answer (Chok Nosan Erchin 31b): We can learn about Bar Mitzvah through a Mah Matzinu. We need a Gezeirah Shavah to learn Bechor from Bayis Ir Chomah, for normally we do not learn Kodshim from Chulin to be lenient.

Mordechai (Yevamos 116, brought in Beis Yosef ibid): The extra month is included regarding years of Bar Mitzvah, Besulim, and all matters of Kedushah. When Beis Din declares an Ibur year, Simanim of adulthood delay to come in their proper time based on Chodesh ha'Ibur, and Hash-m causes the Besulim to grow back for girls (born in Adar) who returned to be less than three years old (Yerushalmi Kesuvos 1:2). We may also learn from rental that 'year' includes the Ibur month (Bava Metzi'a 102b).

Rema: If someone was born in Adar and his 13th year is a leap year, he is not Bar Mitzvah until (the day of the month on which he was born, in) Adar Sheni.

Magen Avraham (10): The Levush infers from the Mechaber that if the 13th year is not a leap year, the former is Bar Mitzvah in Adar Rishon. However, it seems that the Rema says that even someone born in Adar Rishon is not Bar Mitzvah until Adar Sheni. Erchin 31a requires a Shanah Temimah. In Adar Rishon a Shanah Temimah has not passed after he was 12 years old!

Mishnah Berurah (43): The consensus of Acharonim is like the Levush. Adar Rishon is not called Adar. We do not read the Megilah in it. Rather, it is called the Ibur Chodesh.

Magen Avraham (10): If one was born on Cheshvan 30 and in his 13th year Cheshvan has only 29 days, it is not clear whether or not he becomes Bar Mitzvah on Cheshvan 29. Nedarim 60b connotes that Rosh Chodesh (when it is one day) is really the 30th day of the previous month. (However, vows depend on the way people speak, and people consider it part of the new month.) It seems that he is not Bar Mitzvah until Rosh Chodesh Kislev.

R. Akiva Eiger (DH v'Ayen): The Bach says that if one was born on Rosh Chodesh Kislev in a year when Cheshvan was short, and in his 13th year Cheshvan is full, he becomes Bar Mitzvah on Cheshvan 30.