(Chevraya citing R. Yochanan): (According to R. Yochanan's earlier reason that one shouldn't cause extra effort to be done by the Kohanim) even if the owner actually crushed the olives before he gave them to the Kohen, it is still invalid Terumah.

(R. Chananya/ R. Imi citing R. Yochanan): (Disagreeing with the Chevraya) Beis Shammai hold that when he makes his olives Terumah, it's as if he said that it should be Terumah for it (the olives in the press) and for that which is under it (i.e. the oil that drained out of it when it was crushed).

R. Chananya suggested that this applies only to its own species.

(R. Zeira to R. Chananya): Don't accept that view (of R. Yochanan that 'it's as if he said') - (it in fact applies even to other species) - once he said, "This is...'', it exempts that which is in his hand and the rest is Chulin, and how can Chulin exempt Tevel?!

(R. Chananya son of R. Hillel): He exempts at the same time both that which is in his hand and the rest of it.

(R. Chanina): This appears correct for Terumah Gedolah, for which he must separate from that which is in close proximity, but Terumas Maaser must be separated according to measure, weight or number.

(Mishnah in 2nd Perek): One may not separate from Tamei for Tahor.

(Baraisa citing R. Yosi): If one separated from Tamei for Tahor, whether inadvertently or intentionally, it is valid Terumah.

What does R. Yosi reason? If over there, when he separated Tamei Terumah, it is completely prohibited to the Kohen, and nevertheless what he did was valid; here, when he intentionally separated from the olives for the oil, where it is not completely lost to the Kohen (and it merely involves extra effort by the Kohen), certainly it should be valid!

A later Mishnah (Terumos 1:4) in the name of R. Yosi was found - One may not separate Terumah from olives for oil or from grapes for wine, but if he did, Beis Shammai say that it's valid Terumah only for them (i.e. the olives or grapes) themselves. Beis Hillel say that it is not Terumah at all.

Question: The opinion of R. Yosi seems to have switched - There he said that if he did it, it is valid Terumah; here he said that it is not Terumah...?

Answer: There, it is uncommon that (a person would separate Terumah from Tamei for Tahor) and people don't mistakenly think that one may tithe from one for the other; but separating from olives for oil and grapes for wine is common and if we say that the separation was valid, one might come to think that it is permitted to separate olives for oil and grapes for wine.