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

Innermost Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

A(b(a(b(x)))) -> A(b(a(a(b(x)))))
A(b(a(b(x)))) -> A(a(b(x)))

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Narrowing Transformation


Dependency Pair:

A(b(a(b(x)))) -> A(b(a(a(b(x)))))


Rule:


a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))


Strategy:

innermost




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

A(b(a(b(x)))) -> A(b(a(a(b(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