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) forall#(J, cons(X1, Y1)) => forall#(J, Y1)
      (2) forall#(J, cons(X1, Y1)) => and#(J(X1), forall(J, Y1))
      (3) forsome#(H1, cons(W1, P1)) => forsome#(H1, P1)
      (4) forsome#(H1, cons(W1, P1)) => or#(H1(W1), forsome(H1, P1))

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

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

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

  P3. (1) forsome#(H1, cons(W1, P1)) => forsome#(H1, P1)

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

We use the following projection function:

  nu(forall#) = 2

We thus have:

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

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(forsome#) = 2

We thus have:

  (1) cons(W1, P1) |>| P1

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