Etymology
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Words related to rival

*rei- 
Proto-Indo-European root meaning "to flow, run."

It forms all or part of: derive; ember-days; rennet (n.1); Rhine; rialto; rill; rio; rival; rivulet; run; runnel.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rinati "causes to flow," ritih "stream, course;" Latin rivus "stream;" Old Church Slavonic reka "river;" Middle Irish rian "river, way;" Gothic rinnan "run, flow," rinno "brook;" Middle Low German ride "brook;" Old English riþ "stream;" Old English rinnan, Old Norse rinna "to run," Dutch ril "running stream."
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arch-rival (n.)
also archrival, by 1805, from arch- + rival (n.).
rivalry (n.)

"act of rivaling, competition, strife or effort to attain an object another is pursuing," 1590s; from rival (n.) + -ry. Shakespeare has rivality ("Antony and Cleopatra"), but meaning "association, partnership, equality in rank," from the secondary sense of the Latin adjective. Jonson has rivalship (1630s); rivaltry (1640s) also was used.

unrivalled (adj.)
also unrivaled, 1590s, from un- (1) "not" + past participle of rival (v.).