back down vs cop out

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. 

cop out

verb
  • To avoid or shirk, either by failing to perform, or by performing in a grossly insufficient, negligent, or superficial manner. 

  • To plead guilty and ask for mercy. 

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