Etymology
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rout (n.)

1590s, "a defeat (of an army, etc.) followed by disorderly retreat," from French route "disorderly flight of troops," literally "a breaking off, rupture," from Vulgar Latin *rupta "a dispersed group," literally "a broken group," from noun use of Latin rupta, fem. past participle of rumpere "to break" (see rupture (n.)).

The archaic English noun rout "group of persons, assemblage," is the same word, from Anglo-French rute, Old French route "host, troop, crowd," from Vulgar Latin rupta "a dispersed group," here with sense of "a division, a detachment." It came to English meaning "group of soldiers" (early 13c.), also "gang of outlaws or rioters, mob" (c. 1300) before the more general sense developed 14c.: "large social assemblage, a general gathering of guests for entertainment." But it also kept its sense of "disorderly or confused mass of persons, the rabble," and was a legal term in this meaning. A rout-cake (1807) was one baked for use at a reception.

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rout (v.)

"drive (a body of troops) into disordered flight by defeat," c. 1600, from rout (n.). Hence "defeat or repulse thoroughly." Related: Routed; routing.

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router (n.)
"cutter that removes wood from a groove," 1818, from rout "poke about, rummage" (1540s), originally of swine digging with the snout; a variant of root (v.1).
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discomfiture (n.)

mid-14c., "defeat in battle, overthrow," from Old French desconfiture "rout, defeat" (12c.; Modern French déconfiture), from desconfire (see discomfit). Sense of "frustration, disappointment" is from late 14c. Confused since 15c. with discomforture "discouragement, distress."

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febrifuge (n.)
"medicine that reduces fever," 1680s, from French fébrifuge, literally "driving fever away," from Latin febris (see fever) + fugare "cause to flee, put to flight, drive off, chase away, rout," also used in reference to banishment and exile, derived verb from fuga "flight," from PIE *bhug-a-, suffixed form of root *bheug- (1) "to flee" (see fugitive (adj.)).
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revel (n.)

late 14c. (c. 1200 as a surname), "riotous merry-making," also an occasion of this, from Old French revel, resvel "entertainment, revelry," verbal noun from reveler, also rebeller (14c.) "be disorderly, make merry" (see rebel (adj.)). "The development of sense in OF. is 'rebellion, tumult, disturbance, noisy mirth'" [OED].

Formerly especially a kind of dance or performance given in connection with masks or pageants, a dancing procession (usually revels). Related: revel-rout "riotous throng."

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Pyrrhic (adj.)

"of or pertaining to King Pyrrhus of Epirus," 1885, usually in the phrase Pyrrhic victory "success obtained at too great a cost," in reference to Pyrrhus's rout of Roman armies at Asculum, in Apulia, 279 B.C.E., which came at such cost to his own troops that he was unable to follow up and attack Rome itself, and is said to have remarked, "one more such victory and we are lost." The name is Greek and means "reddish" or "red-haired," from pyrrhos "flame-colored," from pyr "fire" (from PIE root *paewr- "fire").  

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flight (n.2)
"act of fleeing," c. 1200, flihht, not found in Old English, but presumed to have existed and cognate with Old Saxon fluht, Old Frisian flecht "act of fleeing," Dutch vlucht, Old High German fluht, German Flucht, Old Norse flotti, Gothic þlauhs, from Proto-Germanic *flugti-, suffixed form of PIE root *pleu- "to flow." To put (someone or something) to flight "rout, defeat" is from late 14c., the earlier verb form do o' flight (early 13c.).
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trophy (n.)

early 15c., trophe, "an overwhelming victory;" 1510s, "a spoil or prize of war," from Old French trophée (15c.) from Latin trophaeum "a sign of victory, monument," originally tropaeum, from Greek tropaion "monument of an enemy's defeat," noun use of neuter of adjective tropaios "of defeat, causing a rout," from trope "a rout," originally "a turning" (of the enemy); from PIE root *trep- "to turn."

In ancient Greece, spoils or arms taken in battle and set up on the field and dedicated to a god. Figurative extension to any token or memorial of victory is first recorded 1560s. As "a symbolic representation of a classical trophy" from 1630s.

Trophy wife "a second, attractive and generally younger, wife of a successful man who acquires her as a status symbol" was a trending phrase in media from 1988 ("Fortune" magazine did a cover story on it in 1989), but is older in isolated instances.

Variations on this theme ['convenience-wife'] include the HOSTESS-WIFE of a businessman who entertains extensively and seeks  a higher-level, home-branch version of his secretary; the TROPHY-WIFE — the woman who was hard to get because of birth or wealth or beauty — to be kept on exhibition like a mammoth tusk or prime Picasso ... [Phyllis I. Rosenteur, excerpt from "The Single Women," published in Philadelphia Daily News, Dec. 12, 1961]

The excerpt distinguishes the trophy wife from the "showcase wife," "chosen for her pulchritude and constantly displayed in public places, dripping mink and dangling diamonds," which seems more to suit the later use of trophy wife.

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demolition (n.)

1540s, figurative, "destruction, overthrow;" 1610s, literal, "action of pulling down or destroying (a structure); fact of being demolished," from French demolition "demolition; defeat, rout" (14c.), from Latin demolitionem (nominative demolitio), noun of action from past-participle stem of demoliri "to tear down," from de "down" (see de-) + moliri "build, construct," from moles (genitive molis) "massive structure" (see mole (n.3)).

Mencken noted demolition engineer for "house-wrecker" by 1936. Demolition derby is recorded from 1956, American English, defined by OED as "a contest in which old cars are battered into one another, the last one running being declared the winner."

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