Clear Copy Cloner will back up everything including making a clone of your recovery partition. A good thing to have moving forward, in my opinion.
I think you mean Carbon Copy Cloner.
And restoring the recovery partition can be done fairly easily.
----------
I'm not familiar with the recovery partition. So I'm in the process of downloading Mavericks and will do a clean install.
I was wondering if I should have used Time Machine to do back ups and not the SuperDuper app. I suppose in the case of going back to Mavericks, I should have used Time Machine. Am I correct?
No, SuperDuper! works very well.
the way to restore is very simple.
Plug in your backup and start the Mac whilst holding down the option key.
Select your backup disk and your Mac will boot into Mavericks (exactly as it was when you made the backup).
Re-partition the internal disk. using disk utility from your backup.
Run SuperDuper and clone from backup drive to internal.
BTW the restore partition wouldn't be saved in Time Machine either. SuperDuper! is quicker and will achieve exactly the same result.
Carbon Copy Cloner has one advantage over SuperDuper! and that is that it can recreate the recovery partition.
BTW if your Mac originally came with Mavericks, you don't need the recovery partition, because using Cmd+R for internet recovery will always clean install Mavericks!