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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pairs:

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


Rule:


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





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

A(b(x)) -> A(a(x))
one new Dependency Pair is created:

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

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 2
             ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

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


Rule:


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




Termination of R could not be shown.
Duration:
0:00 minutes