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, z) => f#(x, y + 1, z) | x > y /\ x > z
      (2) f#(x, y, z) => f#(x, y, z + 1) | x > y /\ x > z

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

We use the following integer mapping:

  J(f#) = arg_1 - arg_3 - 1

We thus have:

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

We may remove the strictly oriented DPs, which yields:

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

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

We use the following integer mapping:

  J(f#) = arg_1 - arg_2 - 1

We thus have:

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

All DPs are strictly oriented, and may be removed.  Hence, this DP problem is finite.