Joshua 18:13

And the border went over from thence towards Luz
From Bethaven, where the northern border ended, the western began, and went on to Luz:

to the side of Luz, which is Bethel, southward;
that is, passed along, leaving that city to the south, which formerly was called Luz, but now Bethel, which though distinct places formerly, yet being very near, might in process of time be joined; (See Gill on Joshua 16:2);

and the border descended to Atarothadar,
the same with Archiataroth, (See Gill on Joshua 16:2), and (See Gill on Joshua 16:5):

near the hill that [lieth] on the south side of the nether Bethhoron;
so called to distinguish it from Bethhoron the upper, situated on an hill or mountain, ( Joshua 16:5 ) ; this was rebuilt by Solomon, ( 1 Kings 9:17 ) .