Solve for x
x=c
z\leq 6-d-c\text{ and }z\leq d-c+10\text{ and }z\geq c-d-8\text{ and }z\geq 0\text{ and }b=d\text{ and }y=d\text{ and }a=c
Solve for z
\left\{\begin{matrix}z\in \begin{bmatrix}c-d-8,6-d-c\end{bmatrix}\text{, }&c\geq d+8\text{ and }c\leq 7\text{ and }d>-2\text{ and }a=c\text{ and }x=c\text{ and }b=d\text{ and }y=d\\z\in \begin{bmatrix}0,10+d-c\end{bmatrix}\text{, }&c<d+8\text{ and }d\leq -2\text{ and }a=c\text{ and }x=c\text{ and }b=d\text{ and }y=d\\z\in \begin{bmatrix}c-d-8,10+d-c\end{bmatrix}\text{, }&c\geq d+8\text{ and }c\leq d+9\text{ and }d\leq -2\text{ and }a=c\text{ and }x=c\text{ and }b=d\text{ and }y=d\\z=6-d-c\text{, }&c=6-d\text{ and }d\geq -1\text{ and }a=6-d\text{ and }x=6-d\text{ and }b=d\text{ and }y=d\\z\in \begin{bmatrix}0,6-d-c\end{bmatrix}\text{, }&c<6-d\text{ and }c<d+8\text{ and }d>-2\text{ and }a=c\text{ and }x=c\text{ and }b=d\text{ and }y=d\end{matrix}\right.
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