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) app#(cons(Y, U), V) => app#(U, V)
      (2) reverse#(cons(W, P)) => reverse#(P)
      (3) reverse#(cons(W, P)) => app#(reverse(P), cons(W, nil))
      (4) shuffle#(cons(X1, Y1)) => reverse#(Y1)
      (5) shuffle#(cons(X1, Y1)) => shuffle#(reverse(Y1))
      (6) map#(H1, cons(W1, P1)) => map#(H1, P1)

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

Considering the 4 SCCs, this DP problem is split into the following new problems.

  P2. (1) app#(cons(Y, U), V) => app#(U, V)

  P3. (1) reverse#(cons(W, P)) => reverse#(P)

  P4. (1) shuffle#(cons(X1, Y1)) => shuffle#(reverse(Y1))

  P5. (1) map#(H1, cons(W1, P1)) => map#(H1, P1)

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

We use the following projection function:

  nu(app#) = 1

We thus have:

  (1) cons(Y, U) |>| U

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(reverse#) = 1

We thus have:

  (1) cons(W, P) |>| P

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

***** No progress could be made on DP problem P4.