Term Rewriting System R:

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

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: 


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

Furthermore, R contains one SCC.


SCC1:

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

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

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


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

The transformation is resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.406 seconds.