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We show that graphs generated by collapsible pushdown systems of level 2 aretree-automatic. Even when we allow $\epsilon$-contractions and add areachability predicate (with regular constraints) for pairs of configurations,the structures remain tree-automatic. Hence, their FO theories are decidable,even when expanded by a reachability predicate. As a corollary, we obtain thetree-automaticity of the second level of the Caucal-hierarchy.

Collapsible Pushdown Graphs of Level 2 are Tree-Automatic