Oooo. I like that. I didn't realize it before.
Binary search has worst-case O(logn).
Finding split point is O(n), so finding the point of rotation is several times more expensive than search itself.
Since array is sorted, recursive split can be used to determine which half is out of order. Predicates for binary search are: left < mid < right (equalities optional)
And in my crusade against spambots, I accidentally downvoted this post. And apparently I cannot undo it. So someone upvote it.