an accounting analysis of splaying when we perform splayingwe pay certain number of cyber-dollars (the exact value of the payment will be determined at the end of our analysiswe distinguish three casesif the payment is equal to the splaying workthen we use it all to pay for the splaying if the payment is greater than the splaying workwe deposit the excess in the accounts of several nodes if the payment is less than the splaying workwe make withdrawals from the accounts of several nodes to cover the deficiency we show below that payment of (log ncyber-dollars per operation is sufficient to keep the system workingthat isto ensure that each node keeps nonnegative account balance an accounting invariant for splaying we use scheme in which transfers are made between the accounts of the nodes to ensure that there will always be enough cyber-dollars to withdraw for paying for splaying work when needed in order to use the accounting method to perform our analysis of splayingwe maintain the following invariantbefore and after splayingeach node of has (wcyber-dollars in its account note that the invariant is "financially sound,since it does not require us to make preliminary deposit to endow tree with zero keys let ( be the sum of the ranks of all the nodes of to preserve the invariant after splayingwe must make payment equal to the splaying work plus the total change in ( we refer to single zigzig-zigor zig-zag operation in splaying as splaying substep alsowe denote the rank of node of before and after splaying substep with (wand ( )respectively the following proposition gives an upper bound on the change of ( caused by single splaying substep we will repeatedly use this lemma in our analysis of full splaying of node to the root