  We generalize the initial steps of the Faddeev-Reshetikhin procedure to the
AdS_5 x S^5 superstring theory. Specifically, we propose a modification of the
Poisson bracket whose alleviated non-ultralocality enables to write down a
lattice algebra for the Lax matrix. We then show that the dynamics of the
Pohlmeyer reduction of the AdS_5 x S^5 superstring can be naturally reproduced
with respect to this modified Poisson bracket. This work generalizes the
alleviation procedure recently developed for symmetric space sigma-models. It
also shows that the lattice algebra recently obtained for the AdS_5 x S^5
semi-symmetric space sine-Gordon theory coincides with the one obtained by the
alleviation procedure.
