  Qualitative formal verification, that seeks boolean answers about the
behavior of a system, is often insufficient for practical purposes. Observing
quantitative information is of interest, e.g. for the proper calibration of a
battery or a real-time scheduler. Historically, the focus has been on
quantities in a continuous domain, but recent years showed a renewed interest
for discrete quantitative domains.
  Cost Linear Temporal Logic (CLTL) is a quantitative extension of classical
LTL. It integrates into a nice theory developed in the past few years that
extends the qualitative setting, with counterparts in terms of logics, automata
and algebraic structure. We propose a practical usage of this logics for
model-checking purposes. A CLTL formula defines a function from infinite words
to integers. Finding the bounds of such a function over a given set of words
can be seen as an extension of LTL universal and existential model-checking. We
propose a CEGAR-like algorithm to find these bounds by relying on classical LTL
model-checking, and use B\"{u}chi automata with counters to implement it. This
method constitutes a first step towards the practical use of such a discrete
quantitative logic.
