back down vs relent

back down

verb
  • To take a less aggressive position in a conflict than one previously has or has planned to. 

  • To withdraw from a commitment or position. 

relent

verb
  • To give in or be swayed; to become less hard, harsh, or cruel; to show clemency. 

  • To slacken; to abate. 

noun
  • Stay; stop; delay. 

How often have the words back down and relent occurred in a corpus of books? (source: Google Ngram Viewer )