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) mult#(x, y) => mult#(x - 1, y) | x > 0
      (2) mult#(x, y) => mult#(-x, y) | 0 > x

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

There is only one SCC, so all DPs not inside the SCC can be removed:

  P2. (1) mult#(x, y) => mult#(x - 1, y) | x > 0

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

We use the following integer mapping:

  J(mult#) = 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.