Term Rewriting System R:

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

Termination of R to be shown.


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

   b -> a

where the Polynomial interpretation:
POL(g(x_1)) = x_1
POL(b) = 1
POL(a) = 0
POL(f(x_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: 

   g(b) -> f(b)

where the Polynomial interpretation:
POL(g(x_1)) = 2*x_1
POL(b) = 1
POL(a) = 0
POL(f(x_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(a) -> g(a)

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.872 seconds.