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, z) | x > 0 /\ y > 0
      (2) eval#(x, y) => eval#(x, y - 1) | x > 0 /\ y > 0

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

We use the following integer mapping:

  J(eval#) = arg_1 - 1

We thus have:

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

We may remove the strictly oriented DPs, which yields:

  P2. (1) eval#(x, y) => eval#(x, y - 1) | x > 0 /\ y > 0

***** We apply the Integer Function Processor on P2.

We use the following integer mapping:

  J(eval#) = arg_2 - 1

We thus have:

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

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