kind of constraints that we deduce from the
      request;</li>
</ul>
<ul>
<li>We remove from the state-space every packages and versions that
      are not needed: we are only considering (i) the installed root
      packages (with no specific version constraint); (ii) the new
      packages that the user might have asking to install or upgrade
      (with some eventual version constraints); and (iii) the
      transitive closure of (i) and (ii) (with the corresponding
      version constraints);</li>
</ul