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) append#(cons(X, Y), U) => append#(Y, U)
      (2) shuffle#(cons(X, Y)) => reverse#(Y)
      (3) shuffle#(cons(X, Y)) => shuffle#(reverse(Y))
      (4) mirror#(cons(X, Y)) => mirror#(Y)
      (5) mirror#(cons(X, Y)) => append#(cons(X, mirror(Y)), cons(X, nil))
      (6) map#(H, cons(X, Y)) => map#(H, Y)

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

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

  P2. (1) append#(cons(X, Y), U) => append#(Y, U)

  P3. (1) shuffle#(cons(X, Y)) => shuffle#(reverse(Y))

  P4. (1) mirror#(cons(X, Y)) => mirror#(Y)

  P5. (1) map#(H, cons(X, Y)) => map#(H, Y)

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

We use the following projection function:

  nu(append#) = 1

We thus have:

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

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

***** No progress could be made on DP problem P3.