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) sum#(x) => sum#(x - 1) | x != 0

***** We apply the Constraint Modification Processor on P1.

We replace sum#(x) => sum#(x - 1) | x != 0 by:

  sum#(x) => sum#(x - 1) | x > 0
  sum#(x) => sum#(x - 1) | x < 0

This yields:

  P2. (1) sum#(x) => sum#(x - 1) | x > 0
      (2) sum#(x) => sum#(x - 1) | x < 0

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

Considering the 2 SCCs, this DP problem is split into the following new problems.

  P3. (1) sum#(x) => sum#(x - 1) | x > 0

  P4. (1) sum#(x) => sum#(x - 1) | x < 0

***** We apply the Integer Function Processor on P3.

We use the following integer mapping:

  J(sum#) = arg_1

We thus have:

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

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

***** No progress could be made on DP problem P4.