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) half#(s(s(X))) => half#(X)
      (2) bits#(s(Y)) => half#(s(Y))
      (3) bits#(s(Y)) => bits#(half(s(Y)))
      (4) map#(H, cons(W, P)) => map#(H, P)
      (5) filter#(Z1, cons(U1, V1)) => filter2#(Z1(U1), Z1, U1, V1)
      (6) filter2#(true, I1, P1, X2) => filter#(I1, X2)
      (7) filter2#(false, Z2, U2, V2) => filter#(Z2, V2)

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

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

  P2. (1) half#(s(s(X))) => half#(X)

  P3. (1) bits#(s(Y)) => bits#(half(s(Y)))

  P4. (1) map#(H, cons(W, P)) => map#(H, P)

  P5. (1) filter#(Z1, cons(U1, V1)) => filter2#(Z1(U1), Z1, U1, V1)
      (2) filter2#(true, I1, P1, X2) => filter#(I1, X2)
      (3) filter2#(false, Z2, U2, V2) => filter#(Z2, V2)

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

We use the following projection function:

  nu(half#) = 1

We thus have:

  (1) s(s(X)) |>| X

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

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