We consider termination of the STRS with no additional rule schemes:

  Signature: cons  :: c -> d -> d
             fcons :: (b -> c) -> a -> a
             fmap  :: a -> b -> d
             fnil  :: a
             nil   :: d

  Rules: fmap(fnil, X) -> nil
         fmap(fcons(Z, U), V) -> cons(Z(V), fmap(U, V))

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

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

  P1. (1) fmap#(fcons(Z, U), V) => fmap#(U, V)

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

We use the following projection function:

  nu(fmap#) = 1

We thus have:

  (1) fcons(Z, U) |>| U

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

Processor output: { }.