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) map#(Z, cons(U, V)) => map#(Z, V)
      (2) minus#(s(P), s(X1)) => minus#(P, X1)
      (3) div#(s(U1), s(V1)) => minus#(U1, V1)
      (4) div#(s(U1), s(V1)) => div#(minus(U1, V1), s(V1))

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

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

  P2. (1) map#(Z, cons(U, V)) => map#(Z, V)

  P3. (1) minus#(s(P), s(X1)) => minus#(P, X1)

  P4. (1) div#(s(U1), s(V1)) => div#(minus(U1, V1), s(V1))

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

We use the following projection function:

  nu(map#) = 2

We thus have:

  (1) cons(U, V) |>| V

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(minus#) = 1

We thus have:

  (1) s(P) |>| P

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

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