Term Rewriting System R:
[X]
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

C(b(a(X))) -> A(a(b(b(c(c(X))))))
C(b(a(X))) -> A(b(b(c(c(X)))))
C(b(a(X))) -> B(b(c(c(X))))
C(b(a(X))) -> B(c(c(X)))
C(b(a(X))) -> C(c(X))
C(b(a(X))) -> C(X)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pairs:

C(b(a(X))) -> C(X)
C(b(a(X))) -> C(c(X))


Rules:


c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e





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

C(b(a(X))) -> C(c(X))
two new Dependency Pairs are created:

C(b(a(b(a(X''))))) -> C(a(a(b(b(c(c(X'')))))))
C(b(a(X''))) -> C(e)

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:

C(b(a(b(a(X''))))) -> C(a(a(b(b(c(c(X'')))))))
C(b(a(X))) -> C(X)


Rules:


c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e




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