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) *#(*(U1, V1), W1) => *#(V1, W1)
      (2) *#(*(U1, V1), W1) => *#(U1, *(V1, W1))
      (3) i#(*(X2, Y2)) => i#(Y2)
      (4) i#(*(X2, Y2)) => i#(X2)
      (5) i#(*(X2, Y2)) => *#(i(Y2), i(X2))
      (6) map#(H2, cons(W2, P2)) => map#(H2, P2)
      (7) filter#(Z3, cons(U3, V3)) => filter2#(Z3(U3), Z3, U3, V3)
      (8) filter2#(true, I3, P3, X4) => filter#(I3, X4)
      (9) filter2#(false, Z4, U4, V4) => filter#(Z4, V4)

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

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

  P2. (1) *#(*(U1, V1), W1) => *#(V1, W1)
      (2) *#(*(U1, V1), W1) => *#(U1, *(V1, W1))

  P3. (1) i#(*(X2, Y2)) => i#(Y2)
      (2) i#(*(X2, Y2)) => i#(X2)

  P4. (1) map#(H2, cons(W2, P2)) => map#(H2, P2)

  P5. (1) filter#(Z3, cons(U3, V3)) => filter2#(Z3(U3), Z3, U3, V3)
      (2) filter2#(true, I3, P3, X4) => filter#(I3, X4)
      (3) filter2#(false, Z4, U4, V4) => filter#(Z4, V4)

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

We use the following projection function:

  nu(*#) = 1

We thus have:

  (1) *(U1, V1) |>| V1
  (2) *(U1, V1) |>| U1

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(i#) = 1

We thus have:

  (1) *(X2, Y2) |>| Y2
  (2) *(X2, Y2) |>| X2

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(map#) = 2

We thus have:

  (1) cons(W2, P2) |>| P2

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

***** We apply the Subterm Criterion Processor on P5.

We use the following projection function:

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

We thus have:

  (1) cons(U3, V3) |>|  V3
  (2) X4           |>=| X4
  (3) V4           |>=| V4

We may remove the strictly oriented DPs, which yields:

  P6. (1) filter2#(true, I3, P3, X4) => filter#(I3, X4)
      (2) filter2#(false, Z4, U4, V4) => filter#(Z4, V4)

***** We apply the Graph Processor on P6.

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