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You're positing some new notion of complexity, without a definition, where lists are somehow fundamentally different than trees. Sorry, but that kind of claim requires more than just just an appeal to intuitions about how they might be implemented on a typical CPU. They're both just initial algebras.

The fact that your grand ideas about machine and language models doesn't apply to the lambda calculus should be a hint. We know how lambda calculus relates to typed languages: it's a degenerate case with a single type. Any differences in the complexity of type-inference or checking are between language models. You can't (without wildly waving your hands) formulate a meaningfully comparable problem for TM states.




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