  We prove that the normalized edit distance proposed in [Marzal and Vidal
1993] is a metric when the cost of all the edit operations are the same. This
closes a long standing gap in the literature where several authors noted that
this distance does not satisfy the triangle inequality in the general case, and
that it was not known whether it is satisfied in the uniform case where all the
edit costs are equal. We compare this metric to two normalized metrics proposed
as alternatives in the literature, when people thought that Marzal's and
Vidal's distance is not a metric, and identify key properties that explain why
the original distance, now known to also be a metric, is better for some
applications. Our examination is from a point of view of formal verification,
but the properties and their significance are stated in an application agnostic
way.
