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) div#(x, y) => if#(x >= y /\ y > 0, x, y)
      (2) if#(true, x, y) => div#(x - y, y)

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

We use the following theory arguments function:

  div# : [1, 2]
  if#  : [1, 2, 3]

This yields the following new DP problems:

  P2. (1) div#(x, y) => if#(x >= y /\ y > 0, x, y)
      (2) if#(true, x, y) => div#(x - y, y) { x, y }

  P3. (1) if#(true, x, y) => div#(x - y, y)

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

We use the following theory arguments function:

  div# : [1, 2]
  if#  : [1, 2, 3]

This yields the following new DP problems:

  P4. (1) div#(x, y) => if#(x >= y /\ y > 0, x, y) { x, y }
      (2) if#(true, x, y) => div#(x - y, y) { x, y }

  P5. (1) div#(x, y) => if#(x >= y /\ y > 0, 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.