The defining feature of a climbing rope (arguably) is its dynamic properties, i.e. it stops your fall gradually to decrease the peak force. Not exceeding a fixed peak force is a/the integral criterion in the norming procedure of climbing ropes. It is clear, that hard falls deteriorate the rope long-term, i.e. it loses some of this ability to break gradually and thus needs eventually needs to be retired.
However I am not interested in this long-term effect, but the immediate effects after a fall. Even if the rope behaved like a perfect elastic and linear string, there would be a characteristic time after elongation until it is back in its "initial" state. However a climbing rope is not perfectly elastic (and definitely not linear), e.g. in this fall experiment during the "second bounce" the breaking phase starts lower than on the first (rope still elongated).
How long does it take until a climbing rope is (approximately) in its initial state after a fall?
By initial state I mean same length and same breaking characteristics. And by same I mean equal except for the long-term effects the fall has on the ropes characteristics.
I am aware that there is most likely no single answer, i.e. it depends on factors like rope, fall factor, climber weight, ... — but I am interested in any (hard) information on the magnitude for any scenario that could happen when climbing.
There is this phrase among friends that "whatever doesn't hold you at least brakes" (loosely translated, sounds better in its original variant :P ). That's obviously mostly fun, but I'd still be interested whether it has some truth or is totally counter productive, i.e. the elongation on the failing protection causes less dynamic breaking on the second pro, thus net higher forces than if the failing pro wasn't used in the first place..