bow out vs give up

bow out

verb
  • To resign, or leave, with one's credibility still intact. 

give up

verb
  • To stop or quit (an activity, etc.) 

  • To admit defeat, capitulate 

  • Become fully taken over by a certain quality, activity, trait, &c. 

  • To abandon (someone or something) 

  • To relinquish (something) 

  • To execute a trade on behalf of another broker. 

  • To surrender (someone or something) 

  • To lose hope concerning (someone or something) 

How often have the words bow out and give up occurred in a corpus of books? (source: Google Ngram Viewer )