challenge vs withdraw

challenge

verb
  • To dispute (something). 

  • To question or demand the countersign from (one who attempts to pass the lines). 

  • To dare (someone). 

  • To invite (someone) to take part in a competition. 

  • To be difficult or challenging for. 

  • To call something into question or dispute. 

  • To object to the reception of the vote of, e.g. on the ground that the person is not qualified as a voter. 

  • To take (a final exam) in order to get credit for a course without taking it. 

  • To make a formal objection to a juror. 

noun
  • The act of appealing a ruling or decision of a court of administrative agency. 

  • An antagonization or instigation intended to convince a person to perform an action they otherwise would not. 

  • A bid to overcome something. 

  • The act of seeking to remove a judge, arbitrator, or other judicial or semi-judicial figure for reasons of alleged bias or incapacity. 

  • An act of seeking to have a certain person be declared not legally qualified to vote, made when the person offers their ballot. 

  • The act of a sentry in halting a person and demanding the countersign, or (by extension) the action of a computer system demanding a password, etc. 

  • A summons to fight a duel; also, the letter or message conveying the summons. 

  • A difficult task, especially one that the person making the attempt finds more enjoyable because of that difficulty. 

  • An attempt to take possession; a tackle. 

  • An attempt to have a work of literature restricted or removed from a public library or school curriculum. 

  • The opening and crying of hounds upon first finding the scent of their game. 

  • A judge's interest in the result of a case, constituting grounds for them to not be allowed to sit the case (e.g., a conflict of interest). 

withdraw

verb
  • To disregard (something) as belonging to a certain group. 

  • To take away or take back (something previously given or permitted); to remove, to retract. 

  • To take back (a comment, something written, etc.); to recant, to retract. 

  • To remove (someone or (reflexive, archaic) oneself) from a position or situation; specifically (military), to remove (soldiers) from a battle or position where they are stationed. 

  • To distract or divert (someone) from a course of action, a goal, etc. 

  • To cause or help (someone) to stop taking an addictive drug or substance; to dry out. 

  • To take (one's eyes) off something; to look away. 

  • To draw or pull (something) away or back from its original position or situation. 

  • To stop talking to or interacting with other people and start thinking thoughts not related to what is happening. 

  • To remove (a topic) from discussion or inquiry. 

  • Of soldiers: to leave a battle or position where they are stationed; to retreat. 

  • To extract (money) from a bank account or other financial deposit. 

  • Of a man: to remove the penis from a partner's body orifice before ejaculation; to engage in coitus interruptus. 

  • To stop taking an addictive drug or substance; to undergo withdrawal. 

  • To stop (a course of action, proceedings, etc.) 

  • Chiefly followed by from: to leave a place, someone's presence, etc., to go to another room or place. 

  • Chiefly followed by from: to stop taking part in some activity; also, to remove oneself from the company of others, from publicity, etc. 

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