  Recently Kazakov, Vieira and the author conjectured the Y-system set of
equations describing the planar spectrum of AdS/CFT. In this paper we solve the
Y-system equations in the strong coupling scaling limit. We show that the
quasi-classical spectrum of string moving inside AdS3 x S1 matches precisely
with the prediction of the Y-system. Thus the Y-system, unlike the asymptotic
Bethe ansatz, describes correctly the spectrum of one-loop string energies
including all exponential finite size corrections. This gives a very
non-trivial further support in favor of the conjecture.
