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, z) => eval#(x, y, z + y) | x >= z /\ y > 0

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

We use the following integer mapping:

  J(eval#) = arg_1 - arg_3

We thus have:

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

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