  We analyze the differential equations produced by the method of creative
telescoping applied to a hyperexponential term in two variables. We show that
equations of low order have high degree, and that higher order equations have
lower degree. More precisely, we derive degree bounding formulas which allow to
estimate the degree of the output equations from creative telescoping as a
function of the order. As an application, we show how the knowledge of these
formulas can be used to improve, at least in principle, the performance of
creative telescoping implementations, and we deduce bounds on the asymptotic
complexity of creative telescoping for hyperexponential terms.
