Term Rewriting System R:

   [x]
   f(x) -> f(f(x))

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


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

Furthermore, R contains one SCC.


SCC1:

F(x) -> F(x)
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 reduction.


Non-Termination of R could be shown.

Duration: 0.580 seconds.