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The regeneration cycle was the time during which the process of regeneration occurred. Every time a Time Lord regenerated into a new incarnation, it would take fifteen hours for the process to be finished. During this time there were moments of disorientation as the Time Lord healed.
Time Lords had a regeneration cycle consisting of thirteen lives. Engin observed during the Master's attempt to use the assassination of the Lord President after his ally Goth had died, that after the twelfth regeneration "there was no plan that could postpone death", when his own attempt to restore his ability to regenerate. (TV: The Deadly Assassin)
The newly regenerated Tenth Doctor credited the manifestation of a new hand to replace the one severed by Fadros Pallujikaa to having still been within the first fifteen hours of his regeneration cycle, which provided him with "just enough" residual cellular energy to regrow his severed limb. (TV: The Christmas Invasion)
As they saw what appeared to be the Eleventh Doctor shot down whilst in the process of regenerating by an astronaut, River Song claimed to Amy that the Doctor had been killed in the middle of his regeneration cycle: "His body was already dead. He didn't make it to the next one." (TV: The Impossible Astronaut)
"Regeneration cycle" was also used by the Eleventh Doctor to refer to the new life cycle that the Time Lords had granted him. (TV: The Time of the Doctor) Spandrell used the same term when he noted that the Master had come to the end of his regeneration cycle. (TV: The Deadly Assassin) Mantus used the term when he offered a new regeneration cycle to Narvin during the Last Great Time War. (AUDIO: Assassins)
The Doctor was revealed to be the progenitor of the Time Lords, being the Timeless Child, they had unlimited regenerations. After the Time Lords redacted their memory, (TV: The Timeless Child) the Doctor appeared to be limited to twelve regenerations, until they were seemingly given a new regeneration cycle by the Time Lords. (TV: The Time of the Doctor)