cut in vs put one's oar in

cut in

verb
  • To pull in front of another vehicle in traffic, especially to do so dangerously or unfairly. 

  • To begin riding a wave in front of someone else whose legitimate turn it is. 

  • To join a queue in the middle, as opposed to at the back. 

  • When painting, to paint edges, corners, or trim in preparation for rolling larger areas. 

put one's oar in

verb
  • Synonym of stick one's oar in (“to interfere”) 

How often have the words cut in and put one's oar in occurred in a corpus of books? (source: Google Ngram Viewer )