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) plus#(Y, s(U)) => plus#(Y, U)
      (2) f#(0, s(0), V) => plus#(V, V)
      (3) f#(0, s(0), V) => f#(V, plus(V, V), V)
      (4) map#(H1, cons(W1, P1)) => map#(H1, P1)
      (5) filter#(Z2, cons(U2, V2)) => filter2#(Z2(U2), Z2, U2, V2)
      (6) filter2#(true, I2, P2, X3) => filter#(I2, X3)
      (7) filter2#(false, Z3, U3, V3) => filter#(Z3, V3)

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

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

  P2. (1) plus#(Y, s(U)) => plus#(Y, U)

  P3. (1) f#(0, s(0), V) => f#(V, plus(V, V), V)

  P4. (1) map#(H1, cons(W1, P1)) => map#(H1, P1)

  P5. (1) filter#(Z2, cons(U2, V2)) => filter2#(Z2(U2), Z2, U2, V2)
      (2) filter2#(true, I2, P2, X3) => filter#(I2, X3)
      (3) filter2#(false, Z3, U3, V3) => filter#(Z3, V3)

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

We use the following projection function:

  nu(plus#) = 2

We thus have:

  (1) s(U) |>| U

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

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