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Let $W$ be a finite set which simultaneously serves as the universe of anyposet $(W,\preceq)$ and as the vertex set of any graph $G$. Our algorithm,abbreviated A-I-I, enumerates (in a compressed format using don't-care symbols)all $G$-independent order ideals of $(W,\preceq)$. For certain instances thehigh-end Mathematica implementation of A-I-I compares favorably to thehardwired Mathematica commands {\tt BooleanConvert} and {\ttSatisfiabilityCount}. The A-I-I can be parallelized and adapts to a polynomialtotal time algorithm that enumerates the modelset of any Boolean 2-CNF.

Compression with wildcards: All models of a Boolean 2-CNF