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) sumwith#(I, cons(P, X1)) => sumwith#(I, X1)
      (3) sumwith#(I, cons(P, X1)) => plus#(I(P), sumwith(I, X1))

***** 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) sumwith#(I, cons(P, X1)) => sumwith#(I, X1)

***** 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(sumwith#) = 2

We thus have:

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

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