back down vs renounce

back down

verb
  • To withdraw from a commitment or position. 

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

renounce

verb
  • To abandon, forsake, discontinue (an action, habit, intention, etc), sometimes by open declaration. 

  • To cast off, repudiate. 

  • To fail to follow suit; playing a card of a different suit when having no card of the suit led. 

  • To make a renunciation of something. 

  • To give up, resign, surrender. 

  • To surrender formally some right or trust. 

  • To decline further association with someone or something, disown. 

noun
  • An act of renouncing. 

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