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Equation [*] has solutions for

\begin{eqnarray*}((I_1^1, I_2^1), (I_1^2, I_2^2)) & = & ((0,0), (1,0)), \\
& =...
...3), (1,3)), \\
& = & ((1,3), (2,3)), \\
& = & ((2,3), (3,3))
\end{eqnarray*}


We can summarise this by saying that the dependence distance vector for this dependence is

(I12-I11, I22-I21)

that is, (1,0).

This corresponds to a dependence direction vector (<,.): there is a loop-carried data dependence in the outer loop.