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) f#(true, x, y, z) => g#(x > y, x, y, z)
      (2) g#(true, x, y, z) => f#(x > z, x, y + 1, z)
      (3) g#(true, x, y, z) => f#(x > z, x, y, z + 1)

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

We use the following theory arguments function:

  f# : [1, 2, 3, 4]
  g# : [1, 2, 3, 4]

This yields the following new DP problems:

  P2. (1) f#(true, x, y, z) => g#(x > y, x, y, z)
      (2) g#(true, x, y, z) => f#(x > z, x, y + 1, z) { x, y, z }
      (3) g#(true, x, y, z) => f#(x > z, x, y, z + 1) { x, y, z }

  P3. (1) g#(true, x, y, z) => f#(x > z, x, y + 1, z)
      (2) g#(true, x, y, z) => f#(x > z, x, y, z + 1)

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

We use the following theory arguments function:

  f# : [1, 2, 3, 4]
  g# : [1, 2, 3, 4]

This yields the following new DP problems:

  P4. (1) f#(true, x, y, z) => g#(x > y, x, y, z) { x, y, z }
      (2) g#(true, x, y, z) => f#(x > z, x, y + 1, z) { x, y, z }
      (3) g#(true, x, y, z) => f#(x > z, x, y, z + 1) { x, y, z }

  P5. (1) f#(true, x, y, z) => g#(x > y, x, y, z)

***** 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.