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

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

  Rules: map(F, nil) -> nil
         map(Z, cons(U, V)) -> cons(Z(U), map(Z, V))

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#(Z, cons(U, V)) => map#(Z, V)

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

We use the following projection function:

  nu(map#) = 2

We thus have:

  (1) cons(U, V) |>| V

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

Processor output: { }.