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Consider the following ZX graph:

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If you perform tensor contraction on this graph, you get the zero tensor. Therefore it should be equivalent to this graph:

enter image description here

How do you rewrite the graph, axiom by axiom, to get from the attached loop to the independent node?

What I do know how to do is to pump a $\pi$ node and some scalar factors out of the loop. This is enough to e.g. make PyZX simplify the graph into different results depending on which rewrites I've applied to the graph:

enter image description here

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The trick is to setup a situation where the hopf law disconnects the pi part from the line part.

enter image description here

enter image description here

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