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I want to create a splay tree with these two additional rules:

enter image description here

does these two rules change the access time of splay tree(access lemma) ?

if no , how can I prove it?

abdolahS
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    If no, then you should be able to mimic the proof given in the document that you linked to, which uses as a potential function the sums of the logs of the ranks of the nodes and bounds the sum of potential changes for a splay. The customary splay operations are carefully chosen so that this sum telescopes. – David Eisenstat May 02 '14 at 13:18
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    If yes, then it may be instructive to understand why rotate-to-root, the scheme that inspired splay trees, didn't work. – David Eisenstat May 02 '14 at 13:25

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