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

  Signature: apply :: (a -> b) -> a -> b

  Rules: apply(F, Y) -> F(Y)

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, i, c), where:

  P1 [empty set of DPs]

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

We compute a graph approximation with the following edges:


As there are no SCCs, this DP problem is removed.

Processor output: { }.