...

Consider the dependence equations:

for I1 = 0 to 3 do

  for I2 = 0 to 3 do

S:   A[I1,I2] := A[I1 - 1,I2] + A[I1,I2 - 1] 

There are two potential dependences arising from the three references to A.

Therefore two systems of dependence equations to solve:

1.

 Between A[I₁¹,I₂¹] and A[I₁² - 1,I₂²]:

$$\left\{ \begin{array}{ccc} I_1^1 & = & I_1^2-1 \\ I_2^1 & = & I_2^2 \end{array} \right.$$

2.

  Between A[I₁¹,I₂¹] and A[I₁²,I₂² - 1]:

$$\left\{ \begin{array}{ccc} I_1^1 = I_1^2 \\ I_2^1 = I_2^2-1 \end{array} \right.$$

((strictly we should also consider output dependences between A[I₁¹,I₂¹] and A[I₁²,I₂²], but this is obviously absent)).