Is this system causal or not?
Note that in this case you can see that the system is causal only from the given implementation. It's important to understand that you can't see it from the difference equation (if no initial conditions are given), and in general you can't see it from the transfer function either (if no region of convergence is given). The only case for which the expression of the transfer function is sufficient to conclude that the corresponding system is non-causal is if the transfer function is not proper, i.e., if the degree of the numerator (as a function of $z$, not $z^{-1}$!) is greater than the degree of the denominator. Also take a look at this related answer.
Let's look at an example:
$$y[n]=ay[n-1]+bx[n]\tag{1}$$
Does $(1)$ describe a causal system? Well, it can describe a causal system, but it can also be read as
$$y[n-1]=\frac{1}{a}\big(y[n]-bx[n]\big),\qquad a\neq 0\tag{2}$$
which can clearly describe a non-causal system if interpreted as &quot;at time instant $n-1$, compute $y[n-1]$ from $y[n]$ and $x[n]$ according to the equation&quot;.
The corresponding transfer function
$$H(z)=\frac{b}{1-az^{-1}}\tag{3}$$
just conveys the same information as the difference equation $(1)$. Consequently, the expression $(3)$ doesn't reveal the system's causality either. Only if we know the region of convergence (ROC) of $(3)$ can we judge whether the system is causal or not. If the ROC is $|z|&gt;a$, the corresponding system is causal, and and if the ROC is $|z|&lt;a$, the system is non-causal.