Related for Rosh Hashanah 14:7
באחד באלול ר"ה למעשר בהמה: מני רבי מאיר היא (דתניא) ר"מ אומר באחד באלול ראש השנה למעשר בהמה
ON THE FIRST OF ELUL IS NEW YEAR FOR THE TITHE OF CATTLE. Who is the authority for this? - It is R'Meir, as it has been taught: R'Meir says, On the first of Elul is New Year for the tithe of cattle'.
Tosefta Rosh Hashanah (Lieberman)
How [one should understand]: "for house rent"? [Answer:] If he rents a house to another for a year, he counts twelve months from the day he started renting it to him. But if he says: For this year, even if he rented it from him only on the first of Adar, he owns it only up to the first of Nisan.
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