Slitherlink - A0, B1, C2, D3

Question

The standard Slitherlink rules apply. However, first replace $A_1$, $A_2$, $B_1$, $B_2$, $C_1$, $C_2$, $D_1$, and $D_2$; such that the Slitherlink is uniquely solvable.
Moreover, these equations must also be correct:

$A_1 + A_2 = 0$
$B_1 + B_2 = 1$
$C_1 + C_2 = 2$
$D_1 + D_2 = 3$

Stiv · Accepted Answer

The solution is:

Step 1:

Step 2:

Step 3:

Step 4:

Remarks on setting the initial values:
Here I explain the thought processes that actually led me to settle on this combination of starting numbers. However, please also read @Retudin's answer as I think they've done a nice job of explaining this part diagrammatically...

Retudin · Answer

OK too late.. (except that I handled the meta uniqueness)

Slitherlink - A0, B1, C2, D3

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