Term Rewriting System R:

   [x]
   f(x, x) -> f(g(x), x)
   g(x) -> s(x)

Innermost Termination of R to be shown.


R contains the following Dependency Pairs: 


   F(x, x) -> F(g(x), x)
   F(x, x) -> G(x)

Furthermore, R contains one SCC.


SCC1:

F(x, x) -> F(g(x), x)

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

   F(x, x) -> F(g(x), x)
one new Dependency Pair
is created:


   F(x, x) -> F(s(x), x)

The transformation is resulting in no subcycles.




Innermost Termination of R successfully shown.


Duration: 0.404 seconds.