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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(h(x)) -> F(i(x))
F(h(x)) -> I(x)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

F(h(x)) -> F(i(x))


Rules:


f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)





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

F(h(x)) -> F(i(x))
one new Dependency Pair is created:

F(h(x'')) -> F(h(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 Pair:

F(h(x'')) -> F(h(x''))


Rules:


f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)




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