loosen vs tie up

loosen

verb
  • To become unfastened or undone. 

  • To make loose. 

  • To free from restraint; to set at liberty. 

  • To relieve (the bowels) from constipation; to promote defecation. 

  • To become loose. 

  • To disengage (a device that restrains). 

tie up

verb
  • To occupy, detain, keep busy, or delay. 

  • To immobilize a capital: make a capital investment that makes that capital unavailable. 

  • To complete, finish, or resolve. 

  • Don't forget to tie up your hair before you bake. 

  • To secure with rope, string, etc. 

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