  We analyze the factorization process for lattice maps, searching for
integrable cases. The maps were assumed to be at most quadratic in the
dependent variables, and we required minimal factorization (one linear factor)
after 2 steps of iteration. The results were then classified using algebraic
entropy. Some new models with polynomial growth (strongly associated with
integrability) were found. One of them is a nonsymmetric generalization of the
homogeneous quadratic maps associated with KdV (modified and Schwarzian), for
this new model we have also verified the "consistency around a cube".
