  It was recently conjectured that every component of a discrete-time rational
dynamical system is a solution to an algebraic difference equation that is
linear in its highest-shift term (a quasi-linear equation). We prove that the
conjecture holds in the special case of holonomic sequences, which can
straightforwardly be represented by rational dynamical systems. We propose two
algorithms for converting holonomic recurrence equations into such quasi-linear
equations. The two algorithms differ in their efficiency and the minimality of
orders in their outputs.
