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

Termination of R to be shown. 



   TRS
     ↳Reversing
     ↳Rev
     ↳DPs




Rule(s) before reversing:

f(x) -> f(f(x))


Rule(s) after reversing:

f'(x) -> f'(f'(x))




Trying another alternative: 
   TRS
     ↳Rev
     ↳Reversing
     ↳DPs




Rule(s) before reversing:

f(x) -> f(f(x))


Rule(s) after reversing:

f'(x) -> f'(f'(x))




Trying another alternative: 
   TRS
     ↳Rev
     ↳Rev
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(x) -> F(f(x))
F(x) -> F(x)

Furthermore, R contains one SCC. 


   TRS
     ↳Rev
     ↳Rev
     ↳DPs
       →DP Problem 1
         ↳Non Termination


Dependency Pairs:

F(x) -> F(x)
F(x) -> F(f(x))


Rule:


f(x) -> f(f(x))





Found an infinite P-chain over R:
P =

F(x) -> F(x)
F(x) -> F(f(x))

R =

f(x) -> f(f(x))

s = F(x')
evaluates to t =F(x')

Thus, s starts an infinite chain.

Non-Termination of R could be shown.
Duration:
0:00 minutes