Bit Blasting Algorithm

Question

I found a pseudo algorithm which describes bit blasting: click (page 156,157). I am trying to implement it in C, but I don't understand it yet completely. Let's make an example:

Assume our bit-vectors have only a length of 2 bits (for simplicity) and they are unsigned and out bit-vector formula looks as follows: $\phi = x \,\,\,\wedge\,\,\, y\mid 2 = z \,\,\,\wedge\,\,\, 1 < 3$.

Let's describe Boolean variables with $b_0, b_1,...$ ($x,y$ and $z$ are bit vectors).

The set of atoms would be $At(\phi) = \{ x,\,\,\, y\mid2=z,\,\,\, 1<3 \}$ and therefore the initially $\beta = e(\phi) = b_0 \,\,\,\wedge\,\,\, b_1 \,\,\,\wedge\,\,\, b_2$.

The set of terms would be $T(\phi) = \{ x,\,\,\, y, \,\,\, 2,\,\,\, z,\,\,\ 1,\,\,\,3 \}$.

Algorithm

Line 2: $\beta$ is already set.

Line 3-5: We set the $t \in T(\phi)$ to Boolean variables, hence $x \rightarrow b_3, b_4\,$ - (because we said our bit-vectors only have a length of 2 bits), the same with $y$ and $z$, but what happens with constants? I would guess: $2 \rightarrow 1,0$ or more precise $2 \rightarrow b_7=1, \, b_8=0$.

So after line 5, our $T(\phi) = \{ b_3, b_4,..., b_{14}\}$.

Then I stuck, how does it go on? And how would the equisatisfiable Boolean formula $\beta$ look like after the algorithm? Other references to other algorithms would be also nice.