Deciding Boundedness of Monadic Sirups

We show that deciding boundedness (aka FO-rewritability) of monadic single rule datalog programs (sirups) is 2\Exp-hard, which matches the upper bound known since 1988 and finally settles a long-standing open problem. We obtain this result as a byproduct of an attempt to classify monadic 'disjunctive sirups'---Boolean conjunctive queries $\q$ with unary and binary predicates mediated by a disjunctive rule $T(x) łor F(x) łeftarrow A(x)$---according to the data complexity of their evaluation. Apart from establishing that deciding FO-rewritability of disjunctive sirups with a dag-shaped $\q$ is also 2\Exp-hard, we make substantial progress towards obtaining a complete FO/Ł-hardness dichotomy of disjunctive sirups with ditree-shaped $\q$.