Cost of Splay Steps Lemma => Investment Lemma
Let r(i)(P) denote the rank of P after i steps of the splay operation have been carried out.
By CSSL, the total investment of new money needed to carry out splay is <=
3(r’(P) - r(P))
+ 3(r(2)(P) - r’(P))
+ ...
+ 3( r(k)(P) - r(k-1)(P)) + 1
where k is the number of steps needed to bring P to root.
But r(k)(P) is the rank of the original root <= floor (log n)
Total <= 3( r(k)(P) - r(P)) + 1 <= 3 floor (log n) + 1