by double rotation in both cases the effect is the same as rotating between ' child and grandchildand then between and its new child we will continue our previous example by inserting through in reverse orderfollowed by and then inserting is easysince it does not destroy the balance propertybut inserting causes height imbalance at node this is case which is solved by right-left double rotation in our examplethe right-left double rotation will involve and in this casek is the node with item is the node with item and is the node with item subtrees abcand are empty before after next we insert which also requires double rotation here the double rotation that will restore the tree is again right-left double rotation that will involve and in this casek is the node with item is the node with item and is the node with item subtree is the tree rooted at the node with item subtree is the empty subtree that was originally the left child of the node with item subtree is the tree rooted at the node with item and finallysubtree is the tree rooted at the node with item before after if is now insertedthere is an imbalance at the root since is not between and we know that the single rotation will work