  We consider linear systems of recurrence equations whose coefficients are
given in terms of indefinite nested sums and products covering, e.g., the
harmonic numbers, hypergeometric products, $q$-hypergeometric products or their
mixed versions. These linear systems are formulated in the setting of
$\Pi\Sigma$-extensions and our goal is to find a denominator bound (also known
as universal denominator) for the solutions; i.e., a non-zero polynomial $d$
such that the denominator of every solution of the system divides $d$. This is
the first step in computing all rational solutions of such a rather general
recurrence system. Once the denominator bound is known, the problem of solving
for rational solutions is reduced to the problem of solving for polynomial
solutions.
