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)  *#(X, +(Y, U)) => *#(X, Y)
      (2)  *#(X, +(Y, U)) => *#(X, U)
      (3)  *#(X, +(Y, U)) => +#(*(X, Y), *(X, U))
      (4)  *#(+(W, P), V) => *#(V, W)
      (5)  *#(+(W, P), V) => *#(V, P)
      (6)  *#(+(W, P), V) => +#(*(V, W), *(V, P))
      (7)  *#(*(X1, Y1), U1) => *#(Y1, U1)
      (8)  *#(*(X1, Y1), U1) => *#(X1, *(Y1, U1))
      (9)  +#(+(V1, W1), P1) => +#(W1, P1)
      (10) +#(+(V1, W1), P1) => +#(V1, +(W1, P1))
      (11) map#(Z2, cons(U2, V2)) => map#(Z2, V2)
      (12) filter#(J2, cons(X3, Y3)) => filter2#(J2(X3), J2, X3, Y3)
      (13) filter2#(true, G3, V3, W3) => filter#(G3, W3)
      (14) filter2#(false, J3, X4, Y4) => filter#(J3, Y4)

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

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

  P2. (1) +#(+(V1, W1), P1) => +#(W1, P1)
      (2) +#(+(V1, W1), P1) => +#(V1, +(W1, P1))

  P3. (1) *#(X, +(Y, U)) => *#(X, Y)
      (2) *#(X, +(Y, U)) => *#(X, U)
      (3) *#(+(W, P), V) => *#(V, W)
      (4) *#(+(W, P), V) => *#(V, P)
      (5) *#(*(X1, Y1), U1) => *#(Y1, U1)
      (6) *#(*(X1, Y1), U1) => *#(X1, *(Y1, U1))

  P4. (1) map#(Z2, cons(U2, V2)) => map#(Z2, V2)

  P5. (1) filter#(J2, cons(X3, Y3)) => filter2#(J2(X3), J2, X3, Y3)
      (2) filter2#(true, G3, V3, W3) => filter#(G3, W3)
      (3) filter2#(false, J3, X4, Y4) => filter#(J3, Y4)

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

We use the following projection function:

  nu(+#) = 1

We thus have:

  (1) +(V1, W1) |>| W1
  (2) +(V1, W1) |>| V1

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

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