Thanks to all who pointed out:
xmin1 <= xmax2 && xmax1 >= xmin2 && ymin1 >= ymax2 && ymax1 >0 ymin2
I should have realised how trivial the solution is!
The subject says it all. All help appreciated.
Stephen Crane, Dept of Computing, Imperial College of Science, Technology and
ObFortune: "Kirk to Enterprise -- beam down yeoman Rand and a six-pack."