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) filter#(J, cons(X1, Y1)) => filter#(J, Y1)
      (2) filter#(J, cons(X1, Y1)) => consif#(J(X1), X1, filter(J, Y1))

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

There is only one SCC, so all DPs not inside the SCC can be removed:

  P2. (1) filter#(J, cons(X1, Y1)) => filter#(J, Y1)

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

We use the following projection function:

  nu(filter#) = 2

We thus have:

  (1) cons(X1, Y1) |>| Y1

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