trees figure single rotation fails to fix case figure left-right double rotation to fix case tree may be viewed as four subtrees connected by three nodes as the diagram suggestsexactly one of tree or is two levels deeper than (unless all are empty)but we cannot be sure which one it turns out not to matterin figure both and are drawn at levels below to rebalancewe see that we cannot leave as the rootand rotation between and was shown in figure to not workso the only alternative is to place as the new root this forces to be ' left child and to be its right childand it also completely determines the resulting locations of the four subtrees it is easy to see that the resulting tree satisfies the avl tree propertyand as was the case with the single rotationit restores the height to what it was before the insertionthus guaranteeing that all rebalancing and height updating is complete figure shows that the symmetric case can also be fixed figure right-left double rotation to fix case