Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r.

The output variable y is given by the negation of x xor r.

The register evaluation r changes according to the circuit function next_r = x OR r.

Note that once the register evaluation is [r = 1], r keeps that value.

Model the circuit behaviour with a transition system where each state corresponds to an evaluation of x and r, and the initial valuation of r is 0.

There are two initial states:
S1: x=0, r=0
S2: x=1, r=0


Write an LTL property that checks that the output bit y is set infinitely often. You may use auxiliary variables.

Use the variable names x, y and r.
