When looking into this we realized that the progression implementation currently does not match the definition in the paper. Specifically when progressing greedy necessary and reasonable orderings of the transition s -> s', we use the past information of s' instead of s, and for greedy necessary orderings we don't test if B is true in s'. 

As long as we 
1) ensure that the landmark progression (which is the only one changing past information) is done before the orderings progression, and
2) don't test for ordering violations
the result is correct. 

We tested changing the progression to match the paper, but this resulted in a roughly 10% search time increase for lama-first since we need to do more checks. We thus do not want to change for the moment, but once we test for ordering violations we need to reconsider this. The change might also be cheaper at that point, since the proper checks somewhat overlap with checks for orderings violations.

In the paper about the new landmark progression we defined so-called "dead-end aware" progression, that will return a dead-end if an order is violated. We did however not implement this dead-end detection in issue1036, most likely because current landmark generation methods cannot generate orders that can be violated. We would nevertheless like to implement it now for two reasons:
1) Future generation methods might be able to generate such orders.
2) Bugs can introduce "wrong" orders and the dead-end detection can be useful in finding such wrong orders (like issue247 and issue442).

Of course, adding additional checks can decrease performance, so part of the issue is finding out how badly it affects performance.