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) minus#(x, y) => min#(x, y)
      (2) minus#(x, y) => cond#(min(x, y), x, y)
      (3) cond#(y, x, y) => minus#(x, y + 1)
      (4) min#(u, v) => if#(u < v, u, v)

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

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

  P2. (1) minus#(x, y) => cond#(min(x, y), x, y)
      (2) cond#(y, x, y) => minus#(x, y + 1)

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

We use the following theory arguments function:

  cond#  : [2, 3]
  minus# : [1, 2]

This yields the following new DP problems:

  P3. (1) minus#(x, y) => cond#(min(x, y), x, y)
      (2) cond#(y, x, y) => minus#(x, y + 1) { y, x }

  P4. (1) cond#(y, x, y) => minus#(x, y + 1)

***** We apply the Theory Arguments Processor on P3.

We use the following theory arguments function:

  cond#  : [2, 3]
  minus# : [1, 2]

This yields the following new DP problems:

  P5. (1) minus#(x, y) => cond#(min(x, y), x, y) { x, y }
      (2) cond#(y, x, y) => minus#(x, y + 1) { y, x }

  P6. (1) minus#(x, y) => cond#(min(x, y), x, y)

***** We apply the Graph Processor on P4.

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

***** No progress could be made on DP problem P5.