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, y) => g#(x, y - 1) | x = x /\ y >= 0
      (2) g#(x, y) => f#(x, y) | x = x /\ y = y

***** We apply the Integer Function Processor on P1.

We use the following integer mapping:

  J(f#) = arg_2
  J(g#) = arg_2

We thus have:

  (1) x = x /\ y >= 0 |= y >  y - 1 (and y >= 0)
  (2) x = x /\ y = y  |= y >= y

We may remove the strictly oriented DPs, which yields:

  P2. (1) g#(x, y) => f#(x, y) | x = x /\ y = y

***** We apply the Graph Processor on P2.

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