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) times#(s(W), P) => times#(W, P)
      (3) times#(s(W), P) => plus#(times(W, P), P)
      (4) inc#(X1) => plus#(s(0), X{12})
      (5) inc#(X1) => map#(plus(s(0)), X1)
      (6) double#(Y1) => times#(s(s(0)), X{13})
      (7) double#(Y1) => map#(times(s(s(0))), Y1)
      (8) map#(H1, cons(W1, P1)) => map#(H1, P1)

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

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

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

  P3. (1) times#(s(W), P) => times#(W, P)

  P4. (1) map#(H1, cons(W1, P1)) => map#(H1, P1)

***** 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(times#) = 1

We thus have:

  (1) s(W) |>| W

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#) = 2

We thus have:

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

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