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Is there a text that goes through some explicit examples of converting tree automata to tree regular expressions?

I'm working through Comon's "Tree Automata Techniques and Applications", and I'm trying to work out some examples of regular expressions from tree automata. I'm convinced that the procedure given in the text works, but when I try to apply it to an automaton as simple as "are there an odd number of nodes labeled 'a'?" the resulting expressions are quite complicated. I'd appreciate a reference to improve my intuition and confidence that I've applied the technique correctly.

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Here is a master's thesis and an arXiv paper on the topic, which contains some examples.

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