The two input presentations define the same polynomial-time class for the full Lax808846 instruction set, including indexed input and EOF tests. The checked buffering compiler preserves the source input and output tapes; the internal legacy compilers then convert between the two presentations.

If $T$ and $Q$ are the source time and sufficient-width polynomials, the composed arena-to-native witnesses are $1188*T + 2382*X + 3382$ and $Q + 14$. The native-to-arena witnesses are $324*T + 108*X + 603$ and $Q + 14$. Both directions can introduce a linear startup term. Each implication chooses its own witnesses; no equality of polynomial degrees is stated or used.