chew the/(one's) cud
To contemplate something. ("Cud" is partially digested food that is regurgitated to be chewed again, a common behavior of cows.) I've been chewing my cud for days, but I still haven't decided whether I'm taking the job or not. Sometimes you just need to stop chewing the cud and make a decision.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
chew one's cud
Fig. to think deeply; to be deeply involved in private thought. (Alludes to the cow's habit of bringing food back from the first stomach into the mouth to chew it, called chewing the cud.) He's chewing his cud about what to do next.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.