Systems of nonlinear difference equations over the field of complex numbers usually arise while constructing discrete-time models.
To the best of our knowledge, there is no algorithm that checks if a given system has a solution in the ring of sequences of complex numbers.
Being known, such an algorithm would provide a way of checking if a given model is feasible.

It can be proved that if a system of difference equations over complex numbers does not have a solution in the ring of sequences of complex numbers, then the equation $1 = 0$ is a consequence of the system.
One way of checking this is to use an upper bound on the number of shifts sufficient to derive this equation.
In this talk, we will provide such a bound for several classes of systems of difference equations.