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) takeWhile#(J, cons(X1, Y1)) => takeWhile#(J, Y1)
      (2) takeWhile#(J, cons(X1, Y1)) => if#(J(X1), cons(X1, takeWhile(J, Y1)), nil)
      (3) dropWhile#(H1, cons(W1, P1)) => dropWhile#(H1, P1)
      (4) dropWhile#(H1, cons(W1, P1)) => if#(H1(W1), dropWhile(H1, P1), cons(W1, P1))

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

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

  P2. (1) takeWhile#(J, cons(X1, Y1)) => takeWhile#(J, Y1)

  P3. (1) dropWhile#(H1, cons(W1, P1)) => dropWhile#(H1, P1)

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

We use the following projection function:

  nu(takeWhile#) = 2

We thus have:

  (1) cons(X1, Y1) |>| Y1

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(dropWhile#) = 2

We thus have:

  (1) cons(W1, P1) |>| P1

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