Help wanted with phrasing of rules (and their German translation.)

[euklid]

My suggestion:

If two (diagonally or orthogonally) neighboring cells within the same box contain consecutive numbers the cell with the higher number is shaded. All possible shaded cells are given.

I am not completely sure about my proposal but I post it for discussion purposes. I think that Dandelo's suggestion misses the "in the same box" constraint.