Extending CSR decomposition to tropical inhomogenous matrix products

This article presents an attempt to extend the CSR decomposition, previously introduced for tropical matrix powers, to tropical inhomogeneous matrix products. The CSR terms for inhomogeneous matrix products are introduced, and then, a case is described where an inhomogeneous product admits such CSR decomposition after some length and a bound on this length is given. In the last part of the paper, a number of counterexamples are presented to show that inhomogeneous products do not admit CSR decomposition under more general conditions.