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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

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


Rule:


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




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