The system is accessible function passing by a sort ordering that equates all sorts.

We start by computing the following initial DP problem:

  P1. (1) div#(x, y) => div#(x - y, y) | x > y /\ y > 0

***** We apply the Integer Function Processor on P1.

We use the following integer mapping:

  J(div#) = arg_1 - 1

We thus have:

  (1) x > y /\ y > 0 |= x - 1 > x - y - 1 (and x - 1 >= 0)

All DPs are strictly oriented, and may be removed.  Hence, this DP problem is finite.