Term Rewriting System R:

   [X, Y]
   f(0, 1, X) -> f(g(X, X), X, X)
   g(X, Y) -> X
   g(X, Y) -> Y

Innermost Termination of R to be shown.


R contains the following Dependency Pairs: 


   F(0, 1, X) -> F(g(X, X), X, X)
   F(0, 1, X) -> G(X, X)

Furthermore, R contains one SCC.


SCC1:

F(0, 1, X) -> F(g(X, X), X, X)

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

   F(0, 1, X) -> F(g(X, X), X, X)
one new Dependency Pair
is created:


   F(0, 1, X'') -> F(X'', X'', X'')

The transformation is resulting in no subcycles.




Innermost Termination of R successfully shown.


Duration: 0.383 seconds.