cave in vs go to the bottom

cave in

noun
  • The act of relenting. 

  • The location where something has caved in. 

  • The act of something collapsing or caving in. 

verb
  • To collapse inward or downward. 

  • To relent; to grant approval against one's initial will. 

go to the bottom

How often have the words cave in and go to the bottom occurred in a corpus of books? (source: Google Ngram Viewer )