From Longman Dictionary of Contemporary Englishbe over the limitbe over the limitDRUNKto have drunk more alcohol than is legal or safe for driving → limit
Examples from the Corpus
be over the limit• In a large proportion of fatal accidents it is found that one driver is over the limit.• Other estimates suggest that casualties in accidents where the driver is over the limit could be in excess of 35,000 annually.• He was caught driving over the limit and had to pay a large fine.• He was over the limit and will now lose his licence. 