  For static lifted inference algorithms, completeness, i.e., domain
liftability, is extensively studied. However, so far no domain liftability
results for temporal lifted inference algorithms exist. In this paper, we close
this gap. More precisely, we contribute the first completeness and complexity
analysis for a temporal lifted algorithm, the socalled lifted dynamic junction
tree algorithm (LDJT), which is the only exact lifted temporal inference
algorithm out there. To handle temporal aspects efficiently, LDJT uses
conditional independences to proceed in time, leading to restrictions w.r.t.
elimination orders. We show that these restrictions influence the domain
liftability results and show that one particular case while proceeding in time,
has to be excluded from FO12 . Additionally, for the complexity of LDJT, we
prove that the lifted width is in even more cases smaller than the
corresponding treewidth in comparison to static inference.
