I have read Convict Conditioning. The programming in that book (that is, the way the overall workout is structured) is honestly pretty bad. I highly recommend doing the reddit /r/bodyweightfitness recommended routine.
It's free.
It has videos for every exercise.
It is a clear and complete program that actually allows for progression (the convict conditioning progression standards are at best a waste of time) and keeps you working out in the proper intensity range for strength.
If you are doing the recommended routine you can ask questions at /r/bodyweightfitness.
The main weakness of the recommended routine is the relative focus of upper body vs. lower body. Training your lower body effectively with only bodyweight exercises is difficult though. If you do want to use Convict Conditioning, /r/bodyweightfitness has some recommended changes which will make it more effective.
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A counterexample to your claim: Ackermann(m,m) is a computable function, hence computable by a universal Turing machine. Yet it is designed to be not primitive recursive.
And indeed Kleene's normal form theorem requires one application of the μ-Operator. Which introduces unbounded search.
Yes, but the U() and the T() are primitive recursive. Unbounded search is necessary to get the encoding of the program, but not to execute it, that's why I said "if an angel gives you the encoding".
The normal form theorem indeed says that any partial recursive function is equivalent to two primitive recursive functions / relations, namely U and T, and one application of unbounded search.