They gave up the search.
1 to stop using etc -- ngừng làm
2 to hand over (eg oneself or something that one has) to someone else -- trao; nộp
He was eventually persuaded to give up the stolen jewels.
3 to devote (time etc) to doing something -- đam mê
4 (often with asor for) to consider (a person, thing etc) to be -- coi như