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)  D#(+(X, Y)) => D#(X)
      (2)  D#(+(X, Y)) => D#(Y)
      (3)  D#(*(U, V)) => D#(U)
      (4)  D#(*(U, V)) => D#(V)
      (5)  D#(-(W, P)) => D#(W)
      (6)  D#(-(W, P)) => D#(P)
      (7)  map#(Z1, cons(U1, V1)) => map#(Z1, V1)
      (8)  filter#(J1, cons(X2, Y2)) => filter2#(J1(X2), J1, X2, Y2)
      (9)  filter2#(true, G2, V2, W2) => filter#(G2, W2)
      (10) filter2#(false, J2, X3, Y3) => filter#(J2, Y3)

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

Considering the 3 SCCs, this DP problem is split into the following new problems.

  P2. (1) D#(+(X, Y)) => D#(X)
      (2) D#(+(X, Y)) => D#(Y)
      (3) D#(*(U, V)) => D#(U)
      (4) D#(*(U, V)) => D#(V)
      (5) D#(-(W, P)) => D#(W)
      (6) D#(-(W, P)) => D#(P)

  P3. (1) map#(Z1, cons(U1, V1)) => map#(Z1, V1)

  P4. (1) filter#(J1, cons(X2, Y2)) => filter2#(J1(X2), J1, X2, Y2)
      (2) filter2#(true, G2, V2, W2) => filter#(G2, W2)
      (3) filter2#(false, J2, X3, Y3) => filter#(J2, Y3)

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

We use the following projection function:

  nu(D#) = 1

We thus have:

  (1) +(X, Y) |>| X
  (2) +(X, Y) |>| Y
  (3) *(U, V) |>| U
  (4) *(U, V) |>| V
  (5) -(W, P) |>| W
  (6) -(W, P) |>| P

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(map#) = 2

We thus have:

  (1) cons(U1, V1) |>| V1

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

***** We apply the Subterm Criterion Processor on P4.

We use the following projection function:

  nu(filter#)  = 2
  nu(filter2#) = 4

We thus have:

  (1) cons(X2, Y2) |>|  Y2
  (2) W2           |>=| W2
  (3) Y3           |>=| Y3

We may remove the strictly oriented DPs, which yields:

  P5. (1) filter2#(true, G2, V2, W2) => filter#(G2, W2)
      (2) filter2#(false, J2, X3, Y3) => filter#(J2, Y3)

***** We apply the Graph Processor on P5.

As there are no SCCs, this DP problem is removed.