Proof of Cost of Splay Steps Lemma, cont.
Case 2: zig zig
to maintain money invariant need to add
r’(p) + r’(q) + r’(r) - r(p) - r(q) - r(r)
= r’(p) + r’(r) - r(p) - r(q)
<= 2(r’(p) - r(p))
Case (a): r’(p) > r(p). Then there are $ left over to pay for rotations
Case (b): r’(p) = r(p)