Term Rewriting System R:

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

Termination of R to be shown.


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

   f(x) -> g(x)

where the Polynomial interpretation:
POL(b) = 0
POL(g(x_1)) = x_1
POL(a) = 0
POL(f(x_1)) = 1 + 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(b)
   G(b) -> G(a)

R contains no SCCs.




Termination of R successfully shown.


Duration: 0.846 seconds.