...

The same loop:

for I1 = 0 to 3 do

  for I2 = 0 to 3 do

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

For humans the easy way to understand this loop nest is to draw the iteration space showing the iteration-to-iteration dependences:

S⁰⁰

0

$\rightarrow$
$\delta$

S⁰¹

0

$\rightarrow$
$\delta$

S⁰²

0

$\rightarrow$
$\delta$

S⁰³

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

S¹⁰

0

$\rightarrow$
$\delta$

S¹¹

0

$\rightarrow$
$\delta$

S¹²

0

$\rightarrow$
$\delta$

S¹³

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

S²⁰

0

$\rightarrow$
$\delta$

S²¹

0

$\rightarrow$
$\delta$

S²²

0

$\rightarrow$
$\delta$

S²³

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

$\delta$ $\downarrow$

S³⁰

0

$\rightarrow$
$\delta$

S³¹

0

$\rightarrow$
$\delta$

S³²

0

$\rightarrow$
$\delta$

S³³

The diagram shows an arrow for each solution of each dependence equation.