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) fact#(n, k) => comp#(k, [*](n), X{9}) | n > 0
      (2) fact#(n, k) => fact#(n - 1, comp(k, [*](n))) | n > 0

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

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

  P2. (1) fact#(n, k) => fact#(n - 1, comp(k, [*](n))) | n > 0

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

We use the following integer mapping:

  J(fact#) = arg_1

We thus have:

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

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