Term Rewriting System R:
[x, y]
f(g(x), y, y) -> g(f(x, x, y))

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Instantiation Transformation


Dependency Pair:

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


Rule:


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


Strategy:

innermost




On this DP problem, an 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 new DP problems.


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