  Open Answer Set Programming (OASP) is an attractive framework for integrating
ontologies and rules. In general OASP is undecidable. In previous work we
provided a tableau-based algorithm for satisfiability checking w.r.t. forest
logic programs, a decidable fragment of OASP, which has the forest model
property. In this paper we introduce an optimized version of that algorithm
achieved by means of a knowledge compilation technique. So-called unit
completion structures, which are possible building blocks of a forest model, in
the form of trees of depth 1, are computed in an initial step of the algorithm.
Repeated computations are avoided by using these structures in a
pattern-matching style when constructing a model. Furthermore we identify and
discard redundant unit completion structures: a structure is redundant if there
is another structure which can always replace the original structure in a
forest model.
