Term Rewriting System R:

   [y]
   f(a, y) -> f(y, g(y))
   g(a) -> b
   g(b) -> b

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(a, y) -> F(y, g(y))
   F(a, y) -> G(y)

Furthermore, R contains one SCC.


SCC1:

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

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

   F(a, y) -> F(y, g(y))
two new Dependency Pairs
are created:


   F(a, b) -> F(b, b)
   F(a, a) -> F(a, b)

The transformation is resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.427 seconds.