counter- vs non-

counter-

prefix
  • In opposition to. 

non-

prefix
  • Used in the sense of no or none, to show lack of or failure to perform; or in the sense of not, to negate the meaning of the word to which it is prefixed. 

  • prevocalic form of nona- 

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