Single$-$Piece King Moves

Create a PDDL domain definition, king in file single$-$king$-$domain.pddl$,$ for a single king chess piece moving on an arbitrary sized board. You must use the following predicates, and no others:

$($at $?$p $?$x $?$y$)-$ Indicates that piece $?$p is at the square $?$x$,?$y

$($adjacent $?$y$1?$y$2)-$ Indicates that the x$-$ or y$-$ coordinates $?$y$1,?$y$2$ are adjacent

$($occupied $?$x $?$y$)-$ Indicates that the square $?$x$,?$y is occupied by another $($untitled$)$ piece The domain definition must define a move action with the following signature:

$($:action move

:parameters $(?$p $?$x$1?$y$1?$x$2?$y$2)$

Create a compatible PDDL problem definition, single$-$king$-$problem in file single$-$king$-$problem.pddl$,$ for an $8$x$7(8$ squares along y direction, and $7$ along x direction$)$ board, with the following initial state:

The king starts out from the lower left corner of the board $(1,1).$

Mark the coordinates $(7,7)$ and $(6,7)$ as occupied.

The final condition should be for the king to reach $(7,8)$ Your objects section must contain only the following:

$($:objects

king

x$1$ x$2$ x$3$ x$4$ x$5$ x$6$ x$7$

y$1$ y$2$ y$3$ y$4$ y$5$ y$6$ y$7$ y$8$

$)$

The domain definition must be precise enough to ensure that all valid moves are permissible and that all invalid moves are disallowed $-$ we will test your domain definition for correctness.

What to turn in: The file single$-$king$-$domain.pddl $,$ which defines the king's move, and the file single$-$king$-$problem.pddl that defines the above problem.