Gemara

(R. Yanai): Produce need be tithed only once it sees (is brought in through) the opening of the house - "Bi'arti ha'Kodesh Min ha'Bayis."

(R. Yochanan): Even entering the Chatzer (yard) obligates tithing it - "they will eat in your gates and be satiated."

R. Yochanan learns from "Bi'arti ha'Kodesh Min ha'Bayis" that a Chatzer is Kove'a (obligates tithing before eating) only if it resembles a house, i.e. it is guarded.

R. Yanai learns from "vi'Sh'arecha" that a house is Kove'a Peros only if they entered (normally) through the gate, but not if they entered through the roof or Karfef (storage area).

Question (Mar Zutra brei d'Rav Nachman - Beraisa): One who eats Tevel (untithed Peros) that is finished (after final processing) is liable. The final processing is Hachnasah.

Suggestion: Hachnasah means gathering it, even in the field.

Answer #1: No, it is bringing it into the house.

Answer #2: R. Yanai said that entering the house is Kove'a only for grapes and olives, which have no Goren (threshing-floor to which they are gathered). For grain, the Torah explicitly says "ka'Dagan Min ha'Goren" (Bamidbar 18:27)!

Gitin 81a (R. Yochanan): Early generations brought their produce into the house through the Traksimon (gate), in order to obligate tithing it. Later generations bring their produce through the roof or yard in order to exempt it from tithes.

Rishonim

Rambam (Hilchos Ma'aser 3:3): Any one of the following six things are Kove'a for Ma'aser: the house, a sale... They are Kove'a only finished Peros.

Ra'avad: The exceptions are grain, wine and oil. The Torah says that final processing of these is in the Goren and winepress.

Rebuttal (Ri Korkus): What is the Ra'avad's source? R. Yanai's teaching is brought throughout Shas, without saying that it does not apply to grain, wine and oil! Bi'arti ha'Kodesh Min ha'Bayis refers to grain, wine and oil, and it is the source that the house is Kove'a! Mishnayos (Ma'aseros 1:5-6) discuss final processing of foods, including grain. This connotes they are equal! Perhaps the Ra'avad he learns from Bava Metzia. We said that R. Yanai said that entering the house is Kove'a only for grapes and olives, which have no Goren, but not for grain. The Ra'avad explains, like Rashi, that this discusses grapes and olives for eating, but if they will be squeezed, the winepress is their Goren. The Rambam could explain like this, but he did not rely on this answer, even though it is the latter answer, because the Gemara in Pesachim (9a) disagrees. (R. Oshaya exempts Peros in a Goren in the house. Rashi (Bava Metzia 88b DH Aval) says that he refers to any Peros, and he argues with Answer #2 in Bava Metzia.)

Kesef Mishneh: The Ra'avad learns from "...Trumaschem ka'Dagan Min ha'Goren vecha'Mle'ah Min ha'Yakev" that it is liable from the Goren, even if he plans to take it to the house. The Rambam holds that the verse discusses one who plans to sell it in the market, but not if he will take it to his house. The Ra'avad holds that mid'Oraisa, only grain, wine and oil are liable. If so, to what do we apply to the verse that obligates when it reaches the house?!

Note: The verse can apply to when he did not plan to squeeze grapes or olives (like Rashi said - see Ri Korkus above).

Rambam (4): If one plans to take Peros to the house, even if they were finished, he may eat Arai from them until bringing them into the house. After bringing them into the house they are Kove'a for Ma'aser, and he may not eat until tithing.

Kesef Mishneh: The Rambam rules like R. Yanai against R. Yochanan (who says that even the Chatzer is Kove'a), for R. Yanai was R. Yochanan's Rebbi. How can R. Yanai argue with Mishnayos that say that the Chatzer is Kove'a! Tosfos answers that he holds that it is Kove'a mid'Rabanan. The Rambam (4:1) obligates mid'Oraisa only when it enters the house.

Rebuttal (Gra YD 331:139): (The Kesef Mishneh holds that the Rambam omitted Chatzer here because it is not mid'Oraisa.) This is wrong. The Rambam lists all six things that are Kove'a, even though only the house is mid'Oraisa! Really, the Rambam rules like R. Yochanan, that the Chatzer is Kove'a mid'Oraisa (see 4:7, below). He did not list it here because it is Kove'a only if it is guarded.

Note: The Kesef Mishneh did not explicitly say why the Rambam omitted Chatzer here. Perhaps here he lists the six categories that are Kove'a. Below, he explains that a guarded Chatzer is (like, and is) included in 'house'.

Mishneh l'Melech: The Yerushalmi says that R. Yanai agrees that the Chatzer is Kove'a mid'Rabanan.

Rambam (4:7): Just like the house is Kove'a for Ma'aser, also the Chatzer. Once they enter the Chatzer through the gate they are Kavu'im, even though they did not enter the house.

Poskim

Shulchan Aruch (EH 331:83): Any one of the following six things is Kove'a for Ma'aser: the house...

Shulchan Aruch (ibid.): All of them are Kove'a only something that was finished. If one plans to take Peros to the house, even if finished, he may eat Arai from them until they enter his house.

Gra (140): The Yerushalmi says that his house is Kove'a.

Shulchan Aruch (ibid.): After they entered his house they are Kove'a for Ma'aser, and he may not eat until tithing. Just like the house is Kove'a for Ma'aser, also the Chatzer. If they entered the Chatzer through the gate, they are Kavu'im, even though they did not enter the house. If he brought Peros into the house before final processing, he may eat Arai. If he began final processing after they entered the house, he must tithe all of them.

Shach (112): Only the Chatzer and house are Kove'a mid'Oraisa. Since Bi'ur is from the house, we infer that they are Kavu'im only from when they enter the house. "They will eat in your gates and be satiated" shows that the Chatzer is Kove'a. The other four are Kove'a only mid'Rabanan. We could learn a Kal va'Chomer from the Chatzer to the house. The Torah mentions a house to teach that a Chatzer is Kove'a only if it is guarded, like a house.

Question (Nekudas ha'Kesef (the Shach's son)): The Levush and Shach rule that the Chatzer is Kove'a mid'Oraisa. What is their reason? We always follow R. Yanai against R. Yochanan, his Talmid! The Yerushalmi says that even R. Yochanan holds that the Chatzer is Kove'a only mid'Rabanan!

Tzlach (Berachos 35b DH Derech): Here, Rashi says that Traksimon is a Chatzer. The text here says that later generations entered Peros through the Chatzer to exempt them! R. Yochanan himself taught that a Chatzer is Kove'a! Rashi can say that they later generations entered through Chatzeros that are not guarded. However, Tosfos (Bava Metzia 88a DH Ad) says that R. Yochanan holds that such a Chatzer is Kove'a mid'Rabanan! Perhaps this is only for grain, wine and oil, for which Ma'aseros are mid'Oraisa.