Term Rewriting System R:
[x]
f(a, f(b, f(a, x))) -> f(a, f(b, f(b, f(a, x))))
f(b, f(b, f(b, x))) -> f(b, f(b, x))

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

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


Rules:


f(a, f(b, f(a, x))) -> f(a, f(b, f(b, f(a, x))))
f(b, f(b, f(b, x))) -> f(b, f(b, x))


Strategy:

innermost




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

F(a, f(b, f(a, x))) -> F(a, f(b, f(b, f(a, x))))
no new Dependency Pairs are created.
The transformation is resulting in no new DP problems.


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