We consider universal computability of the STRS with no additional rule schemes:

  Signature: cons :: a -> list -> list
             map  :: list -> (a -> a) -> list
             nil  :: list

  Rules: map(nil, F) -> nil
         map(cons(x, l), F) -> cons(F(x), map(l, F))

The system is accessible function passing by a sort ordering that equates all sorts.

We start by computing the initial DP problem D1 = (P1, R UNION R_?, i, c), where:

  P1. (1) map#(cons(x, l), F) => map#(l, F)

***** We apply the Subterm Criterion Processor on D1 = (P1, R UNION R_?, i, c).

We use the following projection function:

  nu(map#) = 1

We thus have:

  (1) cons(x, l) |>| l

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

Processor output: { }.