  We previously designed Partial Order Conflict Driven Clause Learning
(PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a
partial order on decision levels, and showed that it can speed up the solving
on problems with a high independence between decision levels. In this paper, we
more thoroughly analyze the reasons of the efficiency of PO-CDCL. Of particular
importance is that the partial order introduces several candidates for the
assertion level. By evaluating different heuristics for this choice, we show
that the assertion level selection has an important impact on solving and that
a carefully designed heuristic can significantly improve performances on
relevant benchmarks.
