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)  h#(Y, e(X)) => d#(Y, X)
      (2)  h#(Y, e(X)) => h#(c(Y), d(Y, X))
      (3)  d#(P, g(V, W)) => d#(P, W)
      (4)  d#(P, g(V, W)) => g#(e(V), d(P, W))
      (5)  d#(c(U1), g(g(X1, Y1), 0)) => g#(X1, Y1)
      (6)  d#(c(U1), g(g(X1, Y1), 0)) => d#(c(U1), g(X1, Y1))
      (7)  d#(c(U1), g(g(X1, Y1), 0)) => g#(X1, Y1)
      (8)  d#(c(U1), g(g(X1, Y1), 0)) => d#(U1, g(X1, Y1))
      (9)  d#(c(U1), g(g(X1, Y1), 0)) => g#(d(c(U1), g(X1, Y1)), d(U1, g(X1, Y1)))
      (10) g#(e(V1), e(W1)) => g#(V1, W1)
      (11) map#(F2, cons(Y2, U2)) => map#(F2, U2)
      (12) filter#(I2, cons(P2, X3)) => filter2#(I2(P2), I2, P2, X3)
      (13) filter2#(true, Z3, U3, V3) => filter#(Z3, V3)
      (14) filter2#(false, I3, P3, X4) => filter#(I3, X4)

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

Considering the 5 SCCs, this DP problem is split into the following new problems.

  P2. (1) g#(e(V1), e(W1)) => g#(V1, W1)

  P3. (1) d#(P, g(V, W)) => d#(P, W)
      (2) d#(c(U1), g(g(X1, Y1), 0)) => d#(c(U1), g(X1, Y1))
      (3) d#(c(U1), g(g(X1, Y1), 0)) => d#(U1, g(X1, Y1))

  P4. (1) h#(Y, e(X)) => h#(c(Y), d(Y, X))

  P5. (1) map#(F2, cons(Y2, U2)) => map#(F2, U2)

  P6. (1) filter#(I2, cons(P2, X3)) => filter2#(I2(P2), I2, P2, X3)
      (2) filter2#(true, Z3, U3, V3) => filter#(Z3, V3)
      (3) filter2#(false, I3, P3, X4) => filter#(I3, X4)

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

We use the following projection function:

  nu(g#) = 1

We thus have:

  (1) e(V1) |>| V1

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(d#) = 1

We thus have:

  (1) P     |>=| P
  (2) c(U1) |>=| c(U1)
  (3) c(U1) |>|  U1

We may remove the strictly oriented DPs, which yields:

  P7. (1) d#(P, g(V, W)) => d#(P, W)
      (2) d#(c(U1), g(g(X1, Y1), 0)) => d#(c(U1), g(X1, Y1))

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