Original sentence: It is assured that all the basis vectors are of length at least 1, and that  and that  where  is the dimension
Edited sentence: For large  (), the problem is equivalent to  because a preprocessing done using the LLL algorithm makes the second condition (and hence, ) redundant.It is assured that all the vectors in the Gram-Schmidt orthogonalization are of length at least 1, and that  and that  where  is the dimension