(Lomdus alert: this question is not for beginners.)
In Maseches Demai (5:10-11) we learn that taking teruma from a vadai (=untithed produce) on demai (=possibly untithed produce) does not work, even on the vadai itself.
I totally don't understand why this should be. Either way: if the demai was not tithed, then they are both untithed, so the teruma should be good. And if the demai was tithed, then it turns out he just took extra-large teruma from the vadai. What's the problem, that the mishna requires him to take teruma again?