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A linear ordering is called context-free if it is the lexicographic orderingof some context-free language and is called scattered if it has no densesubordering. Each scattered ordering has an associated ordinal, called itsrank. It is known that the isomorphism problem of scattered context-freeorderings is undecidable, if one of them has a rank at least two. In this paperwe show that it is decidable whether a context-free ordering has rank at mostone, and if so, its order type is effectively computable.

The order type of scattered context-free orderings of rank one is computable