eliminate vs rule out

eliminate

verb
  • To completely remove, get rid of, put an end to. 

  • To kill (a person or animal). 

  • To exclude (from investigation or from further competition). 

  • To record amounts in a consolidation statement to remove the effects of inter-company transactions. 

  • To excrete (waste products). 

rule out

verb
  • To disallow. 

  • To reject an option from a list of possibilities. 

  • To make something impossible. 

  • To cross an item out by drawing a straight line through it, as with a ruler. 

  • To make unavailable. 

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