This is for computer science? So I'm not all that familiar with arrays, but what I'm getting from A[i]=b and A[i+1]>=b-1, is that each successive number that the array represents is greater than or equal to the number before. So the array is increasing? Also by length of interval, do you mean the distance between k and l or the distance between A[K] and A[l]?
So we need to start by assuming the right part x<=j and i+A[i]=j holds. x<=j implies A[x]<=A[j]. If you can show |A[k..l]|<=A[i] you will be done. It probably uses the fact that i+A[i]=j holds as well as the array is increasing. I'm confused as the meaning of length thought. This is an interesting problem.