Modelling of minimal NOR-circuit problem with CP I'm currently working on a Constraint Programming problem which I find difficult to model.

Here 's the definition of the problem :

" Given a specification of a Boolean function f(x1, ..., xn) in the form of a truth table, to find a NOR-circuit (meaning only NOR gates) satisfying the specification that minimizes depth (and, in case of a tie in depth, with minimum size).
In order to simplify the problem, several assumptions are made:

• Only NOR gates with 2 inputs and 1 output can be used: more general
NOR gates with more inputs are not allowed (i.e., the fan-in of NOR
gates is always 2).

• The output of a NOR gate can only be the input of a single gate:
outputs cannot be reused as inputs of more than one gate (i.e., the
fan-out of NOR gates is always 1).

• In addition to the input signals of the Boolean function to be implemented, constant 0 signals can also be used as inputs of NOR gates.
Constant 0 signals as well as input signals can be used as many times
as needed as inputs of NOR gates. On the other hand, the circuit does
not need to use all input signals. Similarly, the constant 0 signal does
not have to be used if it is not needed."

Source : https://www.cs.upc.edu/~erodri/webpage/cps/projects/Q2-16-17/proj.pdf

Since this is the first time that I'm confronted to this kind of problem, I'm having difficulties finding "good" decision variables. Maybe I'm missing something trivial ...

Do you have any idea/hint on how to model this problem ?
This is a logic synthesis problem.  Specifically, without the "fan-out of 1" limitation, this looks like the circuit minimization problem.  Circuit minimization is $\Sigma_2^P$-complete, so you should not expect any efficient algorithm for it.  There are many algorithms in the literature that you can explore, including Karnaugh Maps, Quine-McCluskey, Espresso, and others.  I wouldn't consider constraint programming the obvious first way to approach this problem.

If you have a requirement to use constraint programming for some homework exercise, well, you should do  your own exercise, but here is a hint: you should be able to tell whether there exists a circuit of depth $d$ and width $w$ by building a $d \times w$ grid of NOR gates, then using decision variables to represent which edges are used to connect these gates.  How could you use that to solve the original problem?

Limiting fan-out to 1 seems unrealistic, as gnasher729 explains.