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) lt#(s(X), s(Y)) => lt#(X, Y)
      (2) member#(U1, fork(V1, W1, P1)) => lt#(U1, W1)
      (3) member#(U1, fork(V1, W1, P1)) => member#(U1, V1)
      (4) member#(U1, fork(V1, W1, P1)) => eq#(U1, W1)
      (5) member#(U1, fork(V1, W1, P1)) => member#(U1, P1)

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

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

  P2. (1) lt#(s(X), s(Y)) => lt#(X, Y)

  P3. (1) member#(U1, fork(V1, W1, P1)) => member#(U1, V1)
      (2) member#(U1, fork(V1, W1, P1)) => member#(U1, P1)

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

We use the following projection function:

  nu(lt#) = 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(member#) = 2

We thus have:

  (1) fork(V1, W1, P1) |>| V1
  (2) fork(V1, W1, P1) |>| P1

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