This is a sequential circuit (whose output depends not only on the present value of its input signals but on the sequence of past inputs) not a combinational one (whose output depends only on the present inputs), therefore solving using just input variable does not yields correct output.
First we need to simplify the circuit.
The two $\textsf{NOT}$ gates at the input end of the $\textsf{NOR}$ gate can be combined with the gate to get: $(A'+B')' = AB$
Now, since we have two variables we will have $4$ combinations $00\; 01\; 10\; 11.$
On analyzing each we will see that for every combination where
- $A = 0$ we have the stable output of $0$
- $A=1$ we will have a RACE condition