Term Rewriting System R:

   []
   f(a) -> f(a)
   a -> b

Termination of R to be shown.


Removing the following rules from R which fullfill a polynomial ordering: 

   a -> b

where the Polynomial interpretation:
POL(b) = 0
POL(a) = 1
POL(f(x_1)) = 2 + x_1
was used. 



Not all Rules of R can be deleted, so we still have to regard a part of R.


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


R contains the following Dependency Pairs: 


   F(a) -> F(a)

Furthermore, R contains one SCC.


SCC1:

F(a) -> F(a)

Found an infinite P-chain over R:
P = F(a) -> F(a)
R = []
s = F(a) evaluates to t = F(a)
Thus, s starts an infinite reduction.


Non-Termination of R could be shown.

Duration: 0.681 seconds.