Using Marc'Antonio Alessi's suggestion is problematic if the original regions have 'islands'.
have you an example?
If you subtract a region from another region, the result can be a new region with an island or hole at its center. Inside that hole a different region may be located that does not at any point overlap the region containing the hole.
Ok, I meant to ask a graphic example... in the case of islands perhaps the subtract method is better.
I do not know if this can be faster: use (vlax-invoke Obj "Explode") and then go through all the segments obtained with ssget "_f" and see if r1 intersect... or... decode Acis info?...!