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{11}) | n > 0
      (2) fact#(n, k) => fact#(n - 1, comp(k, [*](n))) | n > 0
      (3) fact1#(n) => id#(X{12})
      (4) fact1#(n) => fact#(n, id)
      (5) fact2#(n) => fact2#(n - 1) | n > 0

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

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

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

  P3. (1) fact2#(n) => fact2#(n - 1) | 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.

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

We use the following integer mapping:

  J(fact2#) = 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.