Polynomial-time conjecture for quadrilateral-to-standard solution set conversion

Let $n$ be the number of tetrahedra and let $k'$ denote the size of the standard solution set produced by Algorithm~ for converting a quadrilateral solution set to a standard solution set. Polynomial-time conjecture. The time complexity of Algorithm~ is at worst polynomial in the size of the output; equivalently, its running time is at most a polynomial function of $n$ and $k'$. This proposal is motivated by empirical evidence that the algorithm's intermediate lists do not undergo the combinatorial explosion seen in general double description methods, and that conversion is negligible compared with enumeration. The statement remains unproved in the supplied text.