Conjunctive query entailment over S description logic knowledge bases is 2ExpTime-complete even with two transitive roles and Boolean queries, but drops to coNExpTime for rooted queries or single transitive role.
The reader might have noticed that Definition 18 does not mention any tree structure, unlike the intuition given in the beginning of the proof
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Revisiting Conjunctive Query Entailment for $\mathcal S$
Conjunctive query entailment over S description logic knowledge bases is 2ExpTime-complete even with two transitive roles and Boolean queries, but drops to coNExpTime for rooted queries or single transitive role.