Decidability of whether a context-free ordering has rank at most one and effective computability of its order type when the answer is yes.
RAIRO - Theoretical Informatics an d Appli- cations - Informatique Théorique et Applications 14(2), 131–141 (1980), http://www.numdam.org/item/ITA_1980__14_2_131_0
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The order type of scattered context-free orderings of rank one is computable
Decidability of whether a context-free ordering has rank at most one and effective computability of its order type when the answer is yes.