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From non- + rivalry.
nonrivalry (uncountable)
- A lack of rivalry.
2015 July 5, David Waldstein, “A $530 Motivational Tool That Helped Turn CoCo Vandeweghe Around”, in New York Times[1]:Theirs is a nonrivalry of sorts, considering the many lopsided outcomes of past encounters between them, but it always proves to be intriguing.