Etymology
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overrun (v.)

also over-run, Middle English overrennen, from Old English oferyrnan "to run across, pass over;" see over- + run (v.). Meaning "continue beyond a specified time" is from early 14c. Meaning "to ravage (a land), maraud, plunder" is by mid-14c. Of weeds, etc., "to grow over, cover all over," by 1660s. The noun meaning "excess expenditure over budget" is from 1956. Related: Overran; overrunning.

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Definitions of overrun
1
overrun (v.)
invade in great numbers;
Synonyms: infest
overrun (v.)
occupy in large numbers or live on a host;
Synonyms: invade / infest
overrun (v.)
flow or run over (a limit or brim);
Synonyms: overflow / well over / run over / brim over
overrun (v.)
seize the position of and defeat;
the Crusaders overran much of the Holy Land
overrun (v.)
run beyond or past;
The plane overran the runway
2
overrun (n.)
too much production or more than expected;
Synonyms: overproduction
From wordnet.princeton.edu