Let describe this automatic tool by its author, Manuel Iglesias:
(extracted from email exchanges):
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 To make it easier to use I have written a shell script with the following
features:
    -It assumes all backup files are in an accessible directory. From there
     the user can copy them to removable media.
    -Easy to configure different backups: Make a copy of the script and edit
     'BACKUP SETUP.' in the new file. Configuration file 'darrc' is not
     necessary.
    -Mounts, makes a backup and then un-mounts filesystems: A mounted file
     system could be an external H.D. where the backup files could be written.
    -Decides/recommends which backup mode is the most suitable: Create
     FullBackup, Rewrite FullBacup, Create DiffNN, Rewrite DiffNN, .......
    -Fully automatic: Use '-auto' option to use with cron. I have studied my
     system (I am new to Linux :-(.) and cron only sends mail if files in
     /etc/cron.{hourly,daily,weekly,monthly} exit with code != 0. I have
     written some shell scripts to handle cron jobs.
    -Different backups can use the same 'Destination' directory: Backups are
     created with base names made up of the shell script name: Shell script
     'LoveLettersBackup' creates:
      -LoveLettersBackupFull.1.dar
      -.......
      -LoveLettersBackupFull.N.dar
      -LoveLettersBackupDiff01.1.dar
      -.......
      -LoveLettersBackupDiff01.N.dar
      -.......
      -LoveLettersBackupDiffNN.N.dar
      -LoveLettersBackupDataBase
    -Creates and keeps updated a Data Base file for later use by dar_manager.

  The backup mode algorithm is the following:
    -If there are not FullBackup files then create FullBackup.
    -If there are not DiffBackup01 files then create DiffBackup01.
    -If the sum of all DiffBackup files is less than %OfFullBackup
     (% set in 'BACKUP SETUP.') then rewrite DiffBackup01.
    -If the sum of all DiffBackup files is greater than %OfFullBackup
     (% set in 'BACKUP SETUP.') then rewrite FullBackup.
    -If DiffBackupXX is less than sum(DiffBackup(XX+1)..DiffBackupNN) then
     rewrite DiffBackupXX.

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 In my last E-mail I forgot to mention another condition which the backup
mode algorithm takes in account: NrOfDiffBackups.
  In the copies of the script I sent you: -If NrOfDiffBackups is greater than
MaxNrOfDiffBackups (set in 'BACKUP SETUP.') then rewrite FullBackup.

  In the meanwhile I have decided it is better to rewrite DiffBackup01 in that
situation and I have modified the script accordingly. The backup mode
algorithm is now the following:
    -If there are not FullBackup files then create FullBackup.
    -If there are not DiffBackup01 files then create DiffBackup01.
    -If the sum of all DiffBackup files is less than %OfFullBackup
     (% set in 'BACKUP SETUP.') then rewrite DiffBackup01.
    -If NrOfDiffBackups is greater than MaxNrOfDiffBackups (set in
     'BACKUP SETUP.') then rewrite DiffBackup01.
    -If the sum of all DiffBackup files is greater than %OfFullBackup
     (% set in 'BACKUP SETUP.') then rewrite FullBackup.
    -If DiffBackupXX is less than sum(DiffBackup(XX+1)..DiffBackupNN)
     then rewrite DiffBackupXX.

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