Undecidability in Mathematica

In choosing functions to build into Mathematica I tried to avoid ones that would often encounter undecidability. And this is why for example there is no built-in function in Mathematica that tries to predict whether a given program will terminate. But inevitably functions like FixedPoint

FixedPoint, ReplaceRepeated

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ReplaceRepeated and FullSimplify

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FullSimplify can run into undecidability—so that ultimately they have to be limited by constructs such as $IterationLimit

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$IterationLimit and TimeConstraint

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TimeConstraint.