We consider termination of the LCTRS with only rule scheme Calc:

  Signature: f :: Int -> o

  Rules: f(x) -> f(x) | x * x < 0

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) f#(x) => f#(x) | x * x < 0

***** 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: { }.