{\rm Ack}(m,n)=\begin{cases} n+1, & \mbox{if}~m=0\\ {\rm Ack}(m-1,1), & \mbox{if}~n=0\\ {\rm Ack}(m-1,{\rm Ack}(m, n-1)), & \mbox{otherwise}\\ \end{cases}
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