NP-complete and polynomial time reduction A decision problem is NP-complete if it is in NP and all other problems in NP can be reduced to it by a reduction that runs in polynomial time. Why it is important to require that the reduction runs in polynomial time, as opposed to accepting any computable reduction.
If there is no resource bound for the reduction and you want to reduce problem A to problem B then there is a trivial "reduction" algorithm for any computable A - simply compute the answer for problem A.