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
     ↳Dependency Pair Analysis



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. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

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


Rules:


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


Strategy:

innermost




On this DP problem, 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 new DP problems.


Innermost Termination of R successfully shown.
Duration:
0:00 minutes