Mathematics for Commuting - on temporal data algorithms

Basically, I would like to extend the algorithm explained and implemented to the case of the full DatalogMTL language (without _nr) on a research paper I came along.
Would also require some theoretical analysis first, because Theorem 9 says the language is P-hard and the P upper bound (so, polynomial time algorithm) is not known.
Will provide the journal article to be read in order to understand the task.