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) rand#(s(X)) => rand#(X)
      (2) filter#(F, cons(H, T)) => filter#(F, T)
      (3) filter#(F, cons(H, T)) => consif#(F(H), H, filter(F, T))

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

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

  P2. (1) rand#(s(X)) => rand#(X)

  P3. (1) filter#(F, cons(H, T)) => filter#(F, T)

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

We use the following projection function:

  nu(rand#) = 1

We thus have:

  (1) s(X) |>| X

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(filter#) = 2

We thus have:

  (1) cons(H, T) |>| T

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