Term Rewriting System R:

   [x, y, z]
   f(x, y, z) -> g(x, y, z)
   g(0, 1, x) -> f(x, x, x)

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


   G(0, 1, x) -> F(x, x, x)
   F(x, y, z) -> G(x, y, z)

Furthermore, R contains one SCC.


SCC1:

F(x, y, z) -> G(x, y, z)
G(0, 1, x) -> F(x, x, x)

On this Scc, a Instantiation SCC transformation can be performed.
 
As a result of transforming the rule 

   F(x, y, z) -> G(x, y, z)
one new Dependency Pair
is created:


   F(z', z', z') -> G(z', z', z')

The transformation is resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.430 seconds.