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) sum#(x, y) => sif#(x >= y, x, y)
      (2) sif#(true, x, y) => sum#(x, y + 1)

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

We use the following theory arguments function:

  sif# : [1, 2, 3]
  sum# : [1, 2]

This yields the following new DP problems:

  P2. (1) sum#(x, y) => sif#(x >= y, x, y)
      (2) sif#(true, x, y) => sum#(x, y + 1) { x, y }

  P3. (1) sif#(true, x, y) => sum#(x, y + 1)

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

We use the following theory arguments function:

  sif# : [1, 2, 3]
  sum# : [1, 2]

This yields the following new DP problems:

  P4. (1) sum#(x, y) => sif#(x >= y, x, y) { x, y }
      (2) sif#(true, x, y) => sum#(x, y + 1) { x, y }

  P5. (1) sum#(x, y) => sif#(x >= y, 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.