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#(x, y) => eval#(x - 1, y + 1) | x > y

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

We use the following integer mapping:

  J(eval#) = arg_1 - arg_2

We thus have:

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

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