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A few notes on the computational class:
- There is a difference between something being a push-down automaton and being able to emulate any push-down automaton. The latter is strictly more powerful, since there are no universal push-down automata.
- Conditional branches can take many forms. While I don't know how to prove this language's computational class, the core idea of the language seems like a potentially valid conditional. The value at the top of the stack determines the next instruction, which is a conditional branch except that it checks every value rather than a single condition.
- The conditional branch doesn't check all data; it doesn't care about the value of any element other than the top, so it may be possible to specialize a conditional to a finite amount of values (this may require unbounded stack elements (a 32-bit/64-bit integer won't cut it, only an arbitrary-precision integer)).