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) gcd#(x, y) => gcd#(x - y, y) | x >= y /\ y > 0
      (2) gcd#(x, y) => gcd#(y - x, x) | y > x /\ x > 0

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

We use the following integer mapping:

  J(gcd#) = arg_2

We thus have:

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

We may remove the strictly oriented DPs, which yields:

  P2. (1) gcd#(x, y) => gcd#(x - y, y) | x >= y /\ y > 0

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

We use the following integer mapping:

  J(gcd#) = arg_1 - arg_2

We thus have:

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

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