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) add#(s(Y), U) => add#(Y, U)
      (2) mult#(s(W), P) => mult#(W, P)
      (3) mult#(s(W), P) => add#(mult(W, P), P)
      (4) rec#(G1, V1, s(W1)) => rec#(G1, V1, W1)
      (5) fact#(X{11}) => mult#(X{12}, X{13})
      (6) fact#(X{11}) => rec#(mult, s(0), X{11})

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

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

  P2. (1) add#(s(Y), U) => add#(Y, U)

  P3. (1) mult#(s(W), P) => mult#(W, P)

  P4. (1) rec#(G1, V1, s(W1)) => rec#(G1, V1, W1)

***** We apply the Subterm Criterion Processor on P2.

We use the following projection function:

  nu(add#) = 1

We thus have:

  (1) s(Y) |>| Y

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

***** We apply the Subterm Criterion Processor on P3.

We use the following projection function:

  nu(mult#) = 1

We thus have:

  (1) s(W) |>| W

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

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

We use the following projection function:

  nu(rec#) = 3

We thus have:

  (1) s(W1) |>| W1

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