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) eval#(i, j) => eval#(i - nat, j + pos) | i - j >= 1 /\ nat >= 0 /\ pos > 0

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

We use the following integer mapping:

  J(eval#) = arg_1 - arg_2 - 1

We thus have:

  (1) i - j >= 1 /\ nat >= 0 /\ pos > 0 |= i - j - 1 > i - nat - (j + pos) - 1 (and i - j - 1 >= 0)

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