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Ever since [1] we allow a second representation for the month (namely,
the numerical one). Since we lose this information during parsing,
pretty printing is now not a proper postinverse of parsing (it still is
a proper preinverse, however).
Thus, we can't simply check for an inverse anymore. However, the
operations still form an inverse semigroup [2], which is something
that's easily checkable. For simplicity, do this in both directions and
completely forget about linearity for now.
[1]: 91f1a0de1e
(Fix date parsing issue
for org mode plugin)
[2]: https://en.wikipedia.org/wiki/Inverse_semigroup