Sentence:  Since the <WSD>extreme points</WSD> are sorted in an ascending order, and it is known that there is no more event other than the event at the current leftmost <WSD>extreme point</WSD>, and therefore we traverse from the root of the tree to the bottom while we re-evaluating the new interval values of each node and testing the inclusion of the <WSD>extreme point</WSD> in the interval. 
Meaning of the word marked with <WSD> tags:  A leaf vertex of a tree data structure.