'rm -fr' mishandles unreadable empty directories

[Paul Eggert]

(I found this while testing a new version of 'install-sh'.)

Here's a scenario illustrating the problem.

   $ mkdir -m a-r -p a/b
   $ rm -fr a
   rm: cannot open directory `a/b': Permission denied
   rm: cannot remove directory `a': Directory not empty
   $ ls -ld a a/b
   drwxr-xr-x 3 eggert eggert 4096 Jun 26 00:51 a
   d-wx-wx-wx 2 eggert eggert 4096 Jun 26 00:51 a/b

My reading of POSIX is that, though a diagnostic is allowed here and
rm can exit with nonzero status because a/b is unreadable, "rm" is
still required to rmdir both a/b and a here, so this is a
POSIX-conformance issue.

Solaris 10 'rm' gets it right: when it discovers that "a/b" is
unreadable (openat fails) it tries rmdir("a/b"), and this works.  No
diagnostics are issued.

This problem is in both coreutils 5.97 and CVS trunk.

One other test case:

   $ mkdir -m 0 -p a/b
   $ rm -fr a
   rm: cannot chdir from `a' to `b': Permission denied
   $ ls -ld a a/b
   drwxr-xr-x 3 eggert eggert 4096 Jun 26 01:00 a
   d--------- 2 eggert eggert 4096 Jun 26 01:00 a/b

This omits the "Directory not entry" diagnostic.  It's a bit odd that
the diagnostic is omitted here but not for the first test case -- is
that intended?