This paper extends our seminal paper on KnoBAB for efficient Conformance Checking
computations performed on top of a customised relational model. After defining our proposed
temporal algebra for temporal queries (xtLTLf ), we show that this can express existing temporal
languages over finite and non-empty traces such as LTLf . This paper also proposes a parallelisation
strategy for such queries thus reducing conformance checking into an embarrassingly parallel
problem leading to super-linear speed up. This paper also presents how a single xtLTLf operator (or
even entire sub-expressions) might be efficiently implemented via different algorithms thus paving
the way to future algorithmic improvements. Finally, our benchmarks remark that our proposed
implementation of xtLTLf (KnoBAB) outperforms state-of-the-art conformance checking software
running on LTLf logic, be it data or dateless.