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DEMONSTRATION VIII: (Mate in Four) Black has just played R j5-j4 Check.
Black's only other piece is Rook at b8. White has full complement of ten
8  __R__ __ __ __ __ __ __ __      pieces/ten pawns. The Two Rooks Alone 
7  __ __ __ __ __K__ __ __ __      checkmate in at most four moves by 
6  __ __ __p__ __p__ __b__ __      Rook at j4 in turn capturing any
5 p__ __p__ __p__ __p__p__p__      interposer across the entire rank 4 
4 k__ __ __ __ __ __ __ __ __R     to White King.  At most, in turn,
3 r__ __q__ __ __ __ __ __ __      White Champion(BN), Marshall(RN), 
2 p__ __p__ __ __m__ __ __ __c     Queen and Pawn-c2 interpose only to
1  __b__ __n__ __ __ __n__ __r     be captured. So what?  Well, it is a
  a  b  c  d  e  f  g  h  i  j     rather straightforward unpeculiar
position(only omitting any other logical Black pieces as irrelevant).  Get a feel for how there is simply no subtle move-order for White to consider: Queen first only makes it mate in one or two instead. Whether Marshall goes -e4, -e5, or -e6 same outcome; ponderous, is that not so?  Just play abstractly the doomed line of bowling pins across Rank 4 for the awkward constraint RN/BN pair tend to impose. As infinite in variety as tired 8x8 itself they may be, yet Cardinal/Marshall 8x10 positions typically present such rather uninteresting interactions.  Cannot future composers find more promising piece material for their skills to work? Are there not some other optimizations than top-heavy ancient Carrera-Centaur and Carrera-Champion?