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, x + y) | x > 0 /\ x > y

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

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