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#(n, m) => gcd#(-n, m) | n < 0
      (2) gcd#(n, m) => gcd#(n, -m) | m < 0
      (3) gcd#(n, m) => gcd#(m, n % m) | n >= 0 /\ m > 0
      (4) fold#(F, n, cons(x, y)) => fold#(F, n, y)
      (5) gcdlist#(l) => gcd#(X{14}, X{15})
      (6) gcdlist#(l) => fold#(gcd, 0, l)

***** We apply the Graph Processor on P1.

Considering the 3 SCCs, this DP problem is split into the following new problems.

  P2. (1) gcd#(n, m) => gcd#(m, n % m) | n >= 0 /\ m > 0

  P3. (1) gcd#(n, m) => gcd#(-n, m) | n < 0
      (2) gcd#(n, m) => gcd#(n, -m) | m < 0

  P4. (1) fold#(F, n, cons(x, y)) => fold#(F, n, y)

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

We use the following integer mapping:

  J(gcd#) = arg_2 - 1

We thus have:

  (1) n >= 0 /\ m > 0 |= m - 1 > n % m - 1 (and m - 1 >= 0)

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

***** We apply the Theory Arguments Processor on P3.

We use the following theory arguments function:

  gcd# : [1]

This yields the following new DP problems:

  P5. (1) gcd#(n, m) => gcd#(-n, m) | n < 0
      (2) gcd#(n, m) => gcd#(n, -m) | m < 0 { n, m }

  P6. (1) gcd#(n, m) => gcd#(n, -m) | m < 0

***** We apply the Subterm Criterion Processor on P4.

We use the following projection function:

  nu(fold#) = 3

We thus have:

  (1) cons(x, y) |>| y

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

***** We apply the Integer Function Processor on P5.

We use the following integer mapping:

  J(gcd#) = 0 - arg_1

We thus have:

  (1) n < 0 |= 0 - n >  0 - -n (and 0 - n >= 0)
  (2) m < 0 |= 0 - n >= 0 - n

We may remove the strictly oriented DPs, which yields:

  P7. (1) gcd#(n, m) => gcd#(n, -m) | m < 0 { n, m }

***** We apply the Graph Processor on P6.

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

***** We apply the Graph Processor on P7.

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