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) map_1#(F, cons(Y, U)) => map_1#(F, U)
      (2) map_2#(I, V, cons(P, X1)) => map_2#(I, V, X1)
      (3) map_3#(G1, g, Y1, cons(V1, W1)) => map_3#(G1, g, Y1, W1)

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

Considering the 3 SCCs, this DP problem is split into the following new problems.

  P2. (1) map_1#(F, cons(Y, U)) => map_1#(F, U)

  P3. (1) map_2#(I, V, cons(P, X1)) => map_2#(I, V, X1)

  P4. (1) map_3#(G1, g, Y1, cons(V1, W1)) => map_3#(G1, g, Y1, W1)

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

We use the following projection function:

  nu(map_1#) = 2

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(map_2#) = 3

We thus have:

  (1) cons(P, 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(map_3#) = 4

We thus have:

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

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