cut into
cut into {v.}
1. To make less; reduce.
The union made the company pay higher wages, which cut into the profits.
The other houses got old and shabby, and that cut into the value of his house.
At first Smith led in votes, but more votes came in and cut into his lead.
2. To get into by cutting in.
She heard the other women gossiping and cut into the talk.
While Bill was passing another car, a truck came around a curve heading for him, and Bill cut back into line quickly.
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Source: A Dictionary of American Idioms