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_1#(x, y) => eval_2#(x, y) | x = y /\ x > 0
      (2) eval_2#(x, y) => eval_2#(x - 1, y - 1) | y > 0
      (3) eval_2#(x, y) => eval_1#(x, y) | 0 >= y

***** We apply the Graph Processor on P1.

There is only one SCC, so all DPs not inside the SCC can be removed:

  P2. (1) eval_2#(x, y) => eval_2#(x - 1, y - 1) | y > 0

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

We use the following integer mapping:

  J(eval_2#) = arg_2

We thus have:

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

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