bicker vs fight like cat and dog

bicker

verb
  • To skirmish; to exchange blows; to fight. 

  • To quarrel in a tiresome, insulting manner. 

  • To brawl or move tremulously, quiver, shimmer (of a water stream, light, flame, etc.) 

  • To patter. 

noun
  • A skirmish; an encounter. 

  • The process by which selective eating clubs at Princeton University choose new members. 

  • A wrangle; also, a noise, as in angry contention. 

  • A wooden drinking-cup or other dish. 

fight like cat and dog

verb
  • To fight frequently or irreconcilably. 

How often have the words bicker and fight like cat and dog occurred in a corpus of books? (source: Google Ngram Viewer )