  In this article, we consider the singular value asymptotics of compositions
of compact linear operators mapping in the real Hilbert space of quadratically
integrable functions over the unit interval. Specifically, the composition is
given by the compact simple integration operator followed by the non-compact
Ces`aro operator possessing a non-closed range. We show that the degree of
ill-posedness of that composition is two, which means that the Ces`aro operator
increases the degree of illposedness by the amount of one compared to the
simple integration operator.
