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By adapting the iterative yardstick construction of Stockmeyer, we show thatthe reachability problem for vector addition systems with a stack does not haveelementary complexity. As a corollary, the same lower bound holds for thesatisfiability problem for a two-variable first-order logic on trees in whichunbounded data may label only leaf nodes. Whether the two problems aredecidable remains an open question.

The reachability problem for vector addition systems with a stack is not elementary