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#(x) => g#(x - 1)
      (2) g#(x) => f#(x) | x > 0

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

We use the following theory arguments function:

  f# : [1]
  g# : [1]

This yields the following new DP problems:

  P2. (1) f#(x) => g#(x - 1) { x }
      (2) g#(x) => f#(x) | x > 0

  P3. (1) f#(x) => g#(x - 1)

***** We apply the Integer Function Processor on P2.

We use the following integer mapping:

  J(f#) = arg_1 - 1
  J(g#) = arg_1

We thus have:

  (1) true  |= x - 1 >= x - 1
  (2) x > 0 |= x     >  x - 1 (and x >= 0)

We may remove the strictly oriented DPs, which yields:

  P4. (1) f#(x) => g#(x - 1) { x }

***** We apply the Graph Processor on P3.

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

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

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