Using your Head is Permitted

Answer either or both parts. Separate solvers' lists will be kept for each part.

Part 1:

For reasons that will remain between Larry and his employer, Larry's objective is to perform this task so that it will take the greatest amount of time.

The strategy he has opted for is as follows: in the beginning of each day, he looks through the volumes until he finds one that is too far to the right. A volume that is too far to the right is simply a volume whose number is x and which is currently in the y'th position from the left on the shelf, with x<y. Notably, Larry does not have to pick the volume by lowest x or lowest y or any other criterion. Any volume that is too far to the right will do.

Once Larry has chosen a volume, he picks it up from its current position on the shelf and brings it to its correct position (the x'th position from the left), pushing the rest of the volumes to the side in order to make space for it.

Larry repeats this procedure once a day, until the encyclopedia volumes are all sorted.

The question: prove that this strategy does, indeed, eventually result in all volumes of the encyclopedia reaching their sorted order. Find the maximal number of days that Larry may need in order to complete the sort (from the unsorted arrangement that maximizes this number).

Part 2:

The question: does Laura's strategy still guarantee that the volumes will, eventually, be sorted?

All answers should be accompanied by proofs.

List of solvers:

Part 1:

Part 2: