A paper review I've undertaken turning out to be harder than expected I recently agreed to review a journal paper (in theoretical computer science). After I started to read it in depth, I found out it is much harder than I expected - over 60 pages with over 20 theorems with detailed proofs. Also, the topic is not exactly my expertise - I do not know a lot of the related works that the authors base their results on. 
So far, I managed to verify about 10 of the shorter theorems. They seem correct, though I have some minor comments. The other theorems seem so long and complex that it will take me weeks to review, especially if I would need to read and understand the theorems in the cited papers that these theorems are based on. What should I do?

I thought of writing to the editor and explaining the situation in detail. Maybe the editor will be able to find another reviewer that will verify the other theorems. But I do not know how such letter will be perceived. In particular:


Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?
On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?
Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?


I have done that on at least two occasions. Sometimes it is the only honest option.


  On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?


Not really. It is commonly considered a duty of a career mathematician to contribute to peer review of mathematical works (at least) proportionally to their own publishing. Whether you achieve this by refereeing some really tough papers or a lot of simple ones is up to you.