We consider universal computability of the LCTRS with only rule scheme Calc:

  Signature: f :: Int -> Int -> Int -> A

  Rules: f(x, y, z) -> f(x, x + 1, x - 1) | y < z /\ x = x

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 UNION R_?, i, c), where:

  P1. (1) f#(x, y, z) => f#(x, x + 1, x - 1) | y < z /\ x = x

***** We apply the Graph Processor on D1 = (P1, R UNION 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: { }.