  All symmetric space $AdS_n$ solutions of type II supergravity have recently
been found for $n>2$. For the supersymmetric solutions (and their T-duals) it
is known that the Green-Schwarz string is classically integrable. We complete
the classification by ruling out integrability for the remaining
non-supersymmetric solutions. This is achieved by showing that tree-level
scattering on the worldsheet of a GKP or BMN string fails to factorize for
these cases.
