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#(s(Y), U) => plus#(Y, U)
      (2) inc#(V) => plus#(s(0), X{8})
      (3) inc#(V) => map#(plus(s(0)), V)
      (4) map#(J, cons(X1, Y1)) => map#(J, Y1)

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

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

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

  P3. (1) map#(J, cons(X1, Y1)) => map#(J, Y1)

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

We use the following projection function:

  nu(plus#) = 1

We thus have:

  (1) s(Y) |>| Y

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

We thus have:

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

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