An all-pass filter by definition has poles in the left and zeros in the right half plane. Assuming that the op-amp can be regarded as an ideal op-amp, it will reverse the response, so you get zeros in the left and poles in the right half plane. Circuits with poles in the right half plane are unstable, depending on whether it is a single pole or a pole pair they can either be latches / Schmitt triggers or oscillators.
So all in all, your circuit will be a latch, a Schmitt trigger or an oscillator.
So all in all, your circuit will be a latch, a Schmitt trigger or an oscillator.
How do I know its one of those If I simulate in circuitslab Online circuit simulator & schematic editor - CircuitLab
If there is a transient analysis available, run a transient analysis and apply a small step at the input. If the output doesn't show oscillations but just goes close to a supply rail and stays there, do a second run where you slowly ramp the input voltage from the negative to the positive supply rail and back.
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