In any case the name RSI has stuck - the idea doesn't change or make any more sense by giving it a different name.
You can search twice without waiting for the results of your first search: iteration.
You can't if the thing you need to search for is the results of your first search: recursion.
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Version 1 -> Version 2 -> Version 3 -> ...
You can call it krispy kreme donuts if you want to.
In any case the name RSI has stuck - the idea doesn't change or make any more sense by giving it a different name.