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#(F, cons(x, xs)) => map#(F, xs)
      (2) double#(s(x)) => double#(x)

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

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

  P2. (1) map#(F, cons(x, xs)) => map#(F, xs)

  P3. (1) double#(s(x)) => double#(x)

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

We use the following projection function:

  nu(map#) = 2

We thus have:

  (1) cons(x, xs) |>| xs

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(double#) = 1

We thus have:

  (1) s(x) |>| x

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