,

กฏข้อแรกคำนวณได้ง่ายที่สุด ทดลองคำนวณค่าดู

\begin{eqnarray*}
G\left(1,0\right) & = & 3\\
G\left(2,0\right) & = & 4\\
G\left(3,0\right) & = & 5\\
G\left(4,0\right) & = & 6
\end{eqnarray*}

,

\begin{eqnarray*}
G\left(0,1\right) & = & G\left(1,0\right)=3\\
G\left(1,1\right) & = & G\left(G\left(0,1\right),0\right)=G\left(0,1\right)+2=3+2=5\\
G\left(2,1\right) & = & G\left(G\left(1,1\right),0\right)=G\left(1,1\right)+2=5+2=7\\
G\left(3,1\right) & = & G\left(G\left(2,1\right),0\right)=G\left(2,1\right)+2=7+2=9\\
 & \vdots\\
G\left(x,1\right) & = & 2x+3
\end{eqnarray*}

,

\begin{eqnarray*}
G\left(0,2\right) & = & G\left(1,1\right)=5\\
G\left(1,2\right) & = & G\left(G\left(0,2\right),1\right)\\
 & = & G\left(5,1\right)\\
 & = & 2\left(5\right)+3\\
 & = & 13
\end{eqnarray*}

\begin{eqnarray*}
G\left(4,1\right) & = & 4\left(2\right)+3\\
 & = & 11
\end{eqnarray*}