  We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model
on AdS_5 x S^5. We find the canonical su(2|2)^2 invariant S-matrix satisfying
the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave
expansion matches exactly the leading order term recently obtained by the
direct perturbative computation. We also show that the S-matrix obtained by
Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter
equation, and, as a consequence, the corresponding ZF algebra is twisted. The
S-matrices in gauge and string theories however are physically equivalent and
related by a non-local transformation of the basis states which is explicitly
constructed.
