Just to show that it's not too complicated with a regex:

do
{   
    # your stuff here
    print "\t\t$path\n";
} while $path =~ s#(?:(^/)|/)[^/]+$#$1?$1:''#e;
[download]

You can use a subroutine as well, then the regex is pretty simple if you handle the special case beforehand:

sub pathtrim {
    my ($path) = @_;
    return '/' if ($path =~ m#^/[^/]+$/);
    $path =~ s#/[^/]+$##;
    return $path;
}
[download]

Update: Fixed small bug in the subroutine.

-- Hofmator