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, z) => eval_2#(x, y, z) | x > y
      (2) eval_2#(x, y, z) => eval_1#(x, y + 1, z) | x > z
      (3) eval_2#(x, y, z) => eval_1#(x, y, z + 1) | x > z
      (4) eval_2#(x, y, z) => eval_1#(x - 1, y, z) | z >= x

***** We apply the Theory Arguments Processor on P1.

We use the following theory arguments function:

  eval_1# : [1, 2, 3]
  eval_2# : [1, 2, 3]

This yields the following new DP problems:

  P2. (1) eval_1#(x, y, z) => eval_2#(x, y, z) | x > y
      (2) eval_2#(x, y, z) => eval_1#(x, y + 1, z) | x > z { x, y, z }
      (3) eval_2#(x, y, z) => eval_1#(x, y, z + 1) | x > z { x, y, z }
      (4) eval_2#(x, y, z) => eval_1#(x - 1, y, z) | z >= x { x, y, z }

  P3. (1) eval_2#(x, y, z) => eval_1#(x, y + 1, z) | x > z
      (2) eval_2#(x, y, z) => eval_1#(x, y, z + 1) | x > z
      (3) eval_2#(x, y, z) => eval_1#(x - 1, y, z) | z >= x

***** We apply the Theory Arguments Processor on P2.

We use the following theory arguments function:

  eval_1# : [1, 2, 3]
  eval_2# : [1, 2, 3]

This yields the following new DP problems:

  P4. (1) eval_1#(x, y, z) => eval_2#(x, y, z) | x > y { x, y, z }
      (2) eval_2#(x, y, z) => eval_1#(x, y + 1, z) | x > z { x, y, z }
      (3) eval_2#(x, y, z) => eval_1#(x, y, z + 1) | x > z { x, y, z }
      (4) eval_2#(x, y, z) => eval_1#(x - 1, y, z) | z >= x { x, y, z }

  P5. (1) eval_1#(x, y, z) => eval_2#(x, y, z) | x > y

***** We apply the Graph Processor on P3.

As there are no SCCs, this DP problem is removed.

***** No progress could be made on DP problem P4.