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

  Signature: cons   :: (a -> a) -> listf -> listf
             dapply :: a -> (a -> a) -> (a -> a) -> a
             lapply :: a -> listf -> a
             nil    :: listf

  Rules: dapply(x, F, G) -> F(G(x))
         lapply(x, nil) -> x
         lapply(x, cons(F, lf)) -> F(lapply(x, lf))

The system is accessible function passing by a sort ordering with listf ≻ a.

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

  P1. (1) lapply#(x, cons(F, lf)) => lapply#(x, lf)

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

We use the following projection function:

  nu(lapply#) = 2

We thus have:

  (1) cons(F, lf) |>| lf

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

Processor output: { }.