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

  Signature: cons :: nat -> list -> list
             nil  :: list
             suc  :: nat -> nat
             take :: nat -> list -> list
             zero :: nat

  Rules: take(zero, l) -> nil
         take(n, nil) -> nil
         take(suc(n), cons(x, l)) -> cons(x, take(n, l))

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_?, f, c), where:

  P1. (1) take#(suc(n), cons(x, l)) => take#(n, l)

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

We use the following projection function:

  nu(take#) = 1

We thus have:

  (1) suc(n) |>| n

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

Processor output: { }.