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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pairs:

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


Rule:


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





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

F(x, f(a, y)) -> F(y, f(f(a, a), a))
no new Dependency Pairs are created.
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 Pair:

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


Rule:


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




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