Gemara

(Rava): "Bakar va'Tzon" were written to teach (by inference) that only they may not be tithed together, but all Tzon may be tithed together.

However, we cannot say that 'Dagan' was written to teach that grain may not be tithed with grapes or oil, but all grains may be tithed together. It is needed to exclude other species from Ma'aser!

Bava Metzi'a 89a (Beraisa): "B'Disho (threshing)" is before final processing that is Kove'a (fixed) for Ma'aser, and a worker may eat.

One who separates dates and figs that stuck together may not eat, for they are Kevu'im for Ma'aser.

Rosh Hashanah 12a (Beraisa): (Tishrei 1 is Rosh Hashanah) for Yerek (vegetables in which one eats the plant itself) and Ma'aser.

Question: Yerek refers to Ma'aser of Yerek. Why does the Beraisa again teach Ma'aser?

Answer: It teaches (Ma'aser of Yerek, which is) mid'Rabanan and (others Ma'aser that is) mid'Oraisa.

Berachos 36a: Ma'aser of trees is mid'Rabanan even in Eretz Yisrael.

Chulin 120b (Mishnah - R. Yehoshua): If a Zar drank b'Shogeg honey of Terumah dates, he is exempt from an added fifth.

He holds Dun Minah (we learn from Bikurim that liquids are like the solid they came from) v'Uki b'Asrah (but apply this to the laws of Terumah, which is mid'Oraisa only for grain, wine and oil).

(Mishnah): The only liquids we may bring for Bikurim are wine and olive oil.

This is like R. Yehoshua, who holds Dun Minah v'Uki b'Asrah. He learns Bikurim from Terumah.

Beitzah 3b: The following Tana holds that anything normally counted is never Batel, even regarding (an Isur) mid'Rabanan, and all the more so regarding mid'Oraisa. (It is a Tosefta in Terumos. Clearly it discusses Terumah figs.)

(Beraisa - R. Yehudah): If a Litra of figs was pressed onto the top of a barrel, and we are unsure which barrel, R. Yehoshua says that even if there are 300 tops of barrels, it is not Batel.

Eruvin 32a (Rav Sheshes): There is a Chazakah that a Shali'ach fulfills his mission:

(Beraisa - Rebbi): If Reuven (a Chaver, i.e. he is trustworthy about Ma'aser) told Shimon 'go fill this basket with dates from my tree', Shimon may eat without tithing. (Surely, Reuven tithed it.)

Rejection (Rav Nachman): That is an exception, for there is a Chazakah that a Chaver does not allow Tevel to leave his Reshus.

Makos 19b (Beraisa - R. Yosi): If one had a Tevel fig, and he said 'the Terumah is at the stem. Ma'aser Rishon is in the north. Ma'aser Sheni is in the south', and he ate it:

If he is a Kohen, he is lashed once (the Ma'aser Rishon is Tevel, for Terumas Ma'aser was not separated from it). If he is a Zar, he is lashed twice (also for Terumah).

Yevamos 81a (Reish Lakish): A Beraisa teaches that Terumah is mid'Rabanan nowadays;

(Beraisa): A ring (of figs of Terumah that was mixed with rings of Chulin) becomes Batel. (If Terumah were mid'Oraisa, we would be stringent to say that something sold by number is not Batel!)

Parah 11:3 (Mishnah): If a Terumah date-cake fell into Mei Chatas, and one took it and ate it, if it is a k'Beitzah, whether it was Tamei or Tamei, one who eats it is Chayav Misah

Rishonim

Rambam (Hilchos Ma'aser 1:9): Ma'aser of carobs is only mid'Rabanan, since most people do not eat them.

Rebuttal (Ra'avad): Also Ma'aser of other trees is only mid'Rabanan, except for grapes and olives.

Radvaz: Why didn't the Ra'avad comment in Hilchos Terumos, where the Rambam explicitly says that the Torah obligates tithing all fruits? The Yerushalmi says so. Also the Bavli (Rosh Hashanah 15b) holds like this. It says 'Ma'aser of carobs is mid'Rabanan. Shevi'is is mid'Oraisa.'

Kesef Mishneh: There is no proof from Rosh Hashanah. We can say that all trees (except for grapes and olives) are exempt.

Rambam (Hilchos Terumos 2:1): One must take Terumah from any food for people that is guarded and grows from the ground. It says "Reishis Degancha Tiroshcha v'Yitzharecha". Just like grain, wine and oil are foods for people that grow from the ground and they have owners, one must take Terumah and Ma'aser from everything similar.

Kesef Mishneh: Even though the verse says grain, wine and oil, the Rambam holds that the Torah obligates also everything that resembles them. The Yerushalmi and Sifri support him. Bava Metzi'a 89a proves that the Torah obligates figs. Also Rosh Hashanah 12a is a proof for the Rambam.

Mishneh l'Melech: See Parah 11:3 (which connotes that Terumah of dates is mid'Oraisa). Bechoros 54b proves that what is not written in the Torah is mid'Rabanan. This requires investigation.

Chazon Ish (Shevi'is 7:23 DH v'Harbeh): The Rambam must say that "Tirosh v'Yitzhar" includes all fruits, and 'other produce' refers to vegetables. This is difficult.

Or Some'ach: Tosfos brought many proofs that only grain, wine and oil are mid'Oraisa. However, several Mishnayos and Sugyos are like the Rambam, e.g. Parah 11:3, Makos 19b, Vayikra Rabah 33:1. Tosfos in Bechoros says that he is lashed only mid'Rabanan.

Tosfos (Rosh Hashanah 12a DH Tana): It says that Ma'aser of Yerek is mid'Rabanan. This connotes that Ma'aser of other Peros is mid'Oraisa. Also the Yerushalmi (Reish Ma'aseros) expounds Ma'aser of everything except for Yerek, and says that Yerek is mid'Rabanan. The Yerushalmi at the end of Chalah connotes similarly. However, this cannot be. The Gemara says that Ma'aser of carobs (15b), of Tzlaf (Berachos 36a) and of spices (Pesachim 44a) is mid'Rabanan. Even Ma'aser of figs, dates and pomegranates, which are among the seven species, is only mid'Rabanan. The Torah obligates only grain, wine and oil, like it says in Bechoros. In Chulin we equate Kodshim (Bikurim) to Terumah, i.e. only for grain, wine and oil. In Yevamos we say that Terumah figs are Batel if Terumah is mid'Rabanan nowadays. Even though Terumah figs are always mid'Rabanan, Chachamim enacted like Torah law. In Makos, we say that one is lashed for a Terumah fig, and in Parah we say that one is Chayav Misah for Terumah dates. These are mere Simanim, to teach that one is Chayav lashes or Misah for species for which Terumah is mid'Oraisa. Alternatively, one is lashed mid'Rabanan, and Misah refers to burying him among utter Resha'im. In Nedarim (55a) we say that anything that is piled up is called "Degen", even legumes. That refers to (Nedarim, which are based on) the way people speak. The Yerushalmi calls Ma'aser of Yerek mid'Rabanan because there is no Asmachta for it. Even though the Sifri and Sifra expound Yerek from "v'Chol Ma'aser", this is not a proper Asmachta, for the verse does not connote Yerek. Alternatively, this is unlike the Tana who calls Ma'aser of Yerek mid'Rabanan.

Aruch l'Ner (Makos 19b DH bi'Gmara): One is lashed mid'Oraisa only for a k'Zayis. To be lashed for Ma'aser Rishon, the fig would have to be 10 k'Zeisim. This is difficult, for a dried fig is less than k'Beitzah! Also, one is lashed only for figs of Eretz Yisrael, which are smaller than those of Chutz la'Aretz (Kelim 17:7). We must say that it is a mere Siman, that one would be lashed if the fig was so big. In any case Tosfos says that it is merely a Siman, since Terumah of figs is only mid'Rabanan! Tosfos also answered that one is lashed mid'Rabanan.

Or Some'ach: Tosfos in Zevachim (54a DH u'Shnei) says that it discusses Bikurim, which are called Terumah. This is very difficult. The Torah calls Bikurim Terumah, but we do not find that Chachamim called them Terumah! The Yerushalmi (Terumos 6:3) says that if a Zar ate dates of Terumah, he may pay figs (and they become Terumah). If he ate grapes, he may pay wine. However, if he ate grapes he may not pay figs, for the former is mid'Oraisa and the latter is mid'Rabanan. (Note: Our Yerushalmi does not say so. Either the Or Some'ach had a different text, or this is his inference.) Therefore, we cannot say that Parah discusses dates paid for Terumah mid'Oraisa. Rather, it is a proof for the Rambam. Beitzah 3b connotes like Tosfos. Do not say that it discusses Terumah nowadays, which is only mid'Rabanan, for it is like R. Yochanan, who holds that even nowadays Terumah is mid'Oraisa (Yevamos 82a). R. Chananel says that Beitzah discusses when there is a majority if Chulin in each barrel, so mid'Oraisa the Terumah is Batel and it is only an Isur mid'Rabanan.

Tosfos (Yevamos 81a DH Mai): If Reish Lakish holds that nowadays Terumah is mid'Rabanan because Eretz Yisrael lost its Kedushah, if so also Kil'ayim is mid'Rabanan. If so, why is Kil'ayim (of things that are counted) not Batel? We can say that figs are more lenient, for even when the Mikdash stands, Terumah of figs is only mid'Rabanan.

Tosfos (Eruvin 32a DH Te'enim): Even though Ma'aser of Peros is mid'Rabanan, and Rav Nachman agrees that for mid'Rabanan laws, we rely on the Chazakah that a Shali'ach fulfills his mission, since the source of Ma'aser is mid'Oraisa, he considers this like mid'Oraisa.

Poskim

Shulchan Aruch (YD 331:13): One must take Terumah from any food for people that is guarded and grows from the ground.

Taz (5): Berachos 36a says that Ma'aser of trees is only mid'Rabanan even in Eretz Yisrael.

Shulchan Aruch (14): We do not separate Terumah and Ma'aser from Yerek in Chutz la'Aretz, even in places that Chachamim obligated. Yerek that comes to Eretz Yisrael from Chutz la'Aretz is exempt, even if there is earth on its roots.

Shach (24): This is because Ma'aser Yerek is mid'Rabanan even in Eretz Yisrael, for it says "Tevu'as Zarecha", and Yerek is not Tevu'ah. Similarly it is exempt from Terumah, for it is not like grain, wine and oil.