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

  Signature: comp  :: (a -> a) -> (a -> a) -> a -> a
             twice :: (a -> a) -> a -> a

  Rules: comp(F, Z, U) -> F(Z(U))
         twice(H) -> comp(H, H)

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. (1) twice#(H, arg2) => comp#(H, H, arg2)

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

We compute a graph approximation with the following edges:

  1:

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

Processor output: { }.