barrenness vs inexistence

barrenness

noun
  • The property of being barren; the property of not supporting life. 

inexistence

noun
  • The state of not being, not existing, or not being perceptible. 

  • The state of existing in something 

  • That which exists within; a constituent. 

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