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) rec#(F, x, y) => rec#(F, x - 1, y) | x > 0

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

We use the following integer mapping:

  J(rec#) = arg_2

We thus have:

  (1) x > 0 |= x > x - 1 (and x >= 0)

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