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Interval INT should backup only if the oldest snapshot in INT-1 is older than INT's period #4
When deciding to do a backup for interval INT, there should be a check that the oldest snapshot in INT-1 interval is older than the threshold for the INT interval. Otherwise the INT interval will be populated with backups more frequent than desired and it is possible older backups in INT interval to completely lost.
The condition should be:
This extra check should probably added in