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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

A(f, a(g, a(f, x))) -> A(f, a(g, a(g, a(f, x))))
A(f, a(g, a(f, x))) -> A(g, a(g, a(f, x)))
A(g, a(f, a(g, x))) -> A(g, a(f, a(f, a(g, x))))
A(g, a(f, a(g, x))) -> A(f, a(f, a(g, x)))

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

A(g, a(f, a(g, x))) -> A(f, a(f, a(g, x)))
A(g, a(f, a(g, x))) -> A(g, a(f, a(f, a(g, x))))
A(f, a(g, a(f, x))) -> A(g, a(g, a(f, x)))
A(f, a(g, a(f, x))) -> A(f, a(g, a(g, a(f, x))))


Rules:


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




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