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

We start by computing the following initial DP problem:

  P1. (1) map#(Z, cons(U, V)) => map#(Z, V)
      (2) le#(s(X1), s(Y1)) => le#(X1, Y1)
      (3) maxlist#(U1, cons(V1, W1)) => le#(U1, V1)
      (4) maxlist#(U1, cons(V1, W1)) => maxlist#(V1, W1)
      (5) height#(node(X2, Y2)) => height#(X{14})
      (6) height#(node(X2, Y2)) => map#(height, Y2)
      (7) height#(node(X2, Y2)) => maxlist#(0, map(height, Y2))

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

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

  P2. (1) map#(Z, cons(U, V)) => map#(Z, V)

  P3. (1) le#(s(X1), s(Y1)) => le#(X1, Y1)

  P4. (1) maxlist#(U1, cons(V1, W1)) => maxlist#(V1, W1)

  P5. (1) height#(node(X2, Y2)) => height#(X{14})

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

We use the following projection function:

  nu(map#) = 2

We thus have:

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

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(le#) = 1

We thus have:

  (1) s(X1) |>| X1

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

***** We apply the Subterm Criterion Processor on P4.

We use the following projection function:

  nu(maxlist#) = 2

We thus have:

  (1) cons(V1, W1) |>| W1

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

***** No progress could be made on DP problem P5.