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) => minusNat#(y >= 0 /\ x = y + 1, x, y)
      (2) minusNat#(true, x, y) => round#(y)
      (3) minusNat#(true, x, y) => minus#(x, round(y))
      (4) round#(x) => if#(x % 2 = 0, x, x + 1)

***** 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) => minusNat#(y >= 0 /\ x = y + 1, x, y)
      (2) minusNat#(true, x, y) => minus#(x, round(y))

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

We use the following theory arguments function:

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

This yields the following new DP problems:

  P3. (1) minus#(x, y) => minusNat#(y >= 0 /\ x = y + 1, x, y)
      (2) minusNat#(true, x, y) => minus#(x, round(y)) { x, y }

  P4. (1) minusNat#(true, x, y) => minus#(x, round(y))

***** No progress could be made on DP problem P3.