There exist two approaches for exact probabilistic inference of UCQs on tuple-independent databases. In the extensional approach, query evaluation is performed within a DBMS by exploiting the structure of the query. In the intensional approach, one first builds a representation of the lineage of the query on the database, then computes the probability of the lineage. In this paper we propose a new technique to construct lineage representations as deterministic decomposable circuits in PTIME. The technique can apply to a class of UCQs that has been conjectured to separate the complexity of the two approaches. We test our technique experimentally, and show that it succeeds on all the queries of this class up to a certain size parameter, i.e., over $20$ million queries.