By verification I do not mean the puzzle solving/hash calculating part but the part involving searching all of the blocks to check if the transaction is valid or not?
For example if A transferred some coins to B ten years ago and after that A didn't make any transaction. Now A wants to make some transaction. To verify this transaction, the miners need to know A's balance which was last updated ten years ago. To do this the miners have to traverse through huge number of blocks to the block of then, won't it take much time?