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