Term Rewriting System R:

   [X, Y]
   f(0, 1, X) -> h(X, X)
   h(0, X) -> f(0, 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) -> H(X, X)
   H(0, X) -> F(0, X, X)

Furthermore, R contains one SCC.


SCC1:

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

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

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


   F(0, 1, 1) -> H(1, 1)

The transformation is resulting in no subcycles.




Innermost Termination of R successfully shown.


Duration: 0.389 seconds.