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) nthtail#(n, l) => length#(l)
      (2) nthtail#(n, l) => cond#(n >= length(l), n, l)
      (3) cond#(false, n, l) => nthtail#(n + 1, l)
      (4) cond#(false, n, l) => tail#(nthtail(n + 1, l))
      (5) length#(cons(x, l)) => length#(l)

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

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

  P2. (1) length#(cons(x, l)) => length#(l)

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

We use the following projection function:

  nu(length#) = 1

We thus have:

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

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