Term Rewriting System R:

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

Termination of R to be shown.


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

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

where the Polynomial interpretation:
POL(g(x_1)) = 1 + x_1
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.


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

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

where the Polynomial interpretation:
POL(g(x_1)) = x_1
POL(f(x_1)) = 1 + x_1
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 2.902 seconds.