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

  Signature: f  :: a -> b -> c
             f1 :: a -> b -> c
             f2 :: a -> b -> c

  Rules: f(x) -> f1(x)
         f1(x, y) -> f2(x, 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, f, c), where:

  P1. (1) f#(x, arg2) => f1#(x, arg2)

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

We compute a graph approximation with the following edges:

  1:

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

Processor output: { }.