The system is accessible function passing by a sort ordering with b = c ≻ a.

We start by computing the following initial DP problem:

  P1. (1) append#(cons(Y, U), V) => append#(U, V)
      (2) flatwith#(F1, node(Y1)) => flatwithsub#(F1, Y1)
      (3) flatwithsub#(H1, cons(W1, P1)) => flatwith#(H1, W1)
      (4) flatwithsub#(H1, cons(W1, P1)) => flatwithsub#(H1, P1)
      (5) flatwithsub#(H1, cons(W1, P1)) => append#(flatwith(H1, W1), flatwithsub(H1, P1))

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

Considering the 2 SCCs, this DP problem is split into the following new problems.

  P2. (1) append#(cons(Y, U), V) => append#(U, V)

  P3. (1) flatwith#(F1, node(Y1)) => flatwithsub#(F1, Y1)
      (2) flatwithsub#(H1, cons(W1, P1)) => flatwith#(H1, W1)
      (3) flatwithsub#(H1, cons(W1, P1)) => flatwithsub#(H1, P1)

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

We use the following projection function:

  nu(append#) = 1

We thus have:

  (1) cons(Y, U) |>| U

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(flatwith#)    = 2
  nu(flatwithsub#) = 2

We thus have:

  (1) node(Y1)     |>| Y1
  (2) cons(W1, P1) |>| W1
  (3) cons(W1, P1) |>| P1

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