$(19$ points$)$ A robot moves around in a grid$-$like environment on a factory floor as shown below, subject to the following constraints:

$-$ In each move, it can only move one step to the right, OR one step up$,$ from one grid point to another.

$-$ It has to remain within the $\backslash (\backslash$mathbf$\{8$ x $8\}\backslash )$ grid. That is$,$ it cannot move off the grid.

$-$ Assume that the location of the robot at any moment is represented by a tuple of the form $\backslash ([\backslash$mathbf$\{$X$\},\backslash$mathbf$\{$Y$\}]\backslash )$

$($a$)(6$ points$)$ Recall that the robot can only move one step to the right, or one step up from any location, and it has to remain on the grid. Write two move predicates $($in Prolog$)$ that describe the two possible moves the robot can make at any time. Your move predicates will look like move$($current location, "type of move", new location$)$ :$-$ right hand side. Hint: Recall that the Prolog predicate $\backslash (\backslash$boldsymbol$\{$A$\}\backslash )$ is $\backslash (\backslash$boldsymbol$\{$B$\}+\backslash$boldsymbol$\{1\}\backslash )$ is true only if A has the value $\backslash (\backslash$mathrm$\{$B$\}+1\backslash ).$