Term Rewriting System R:

   [X]
   a -> g(c)
   g(a) -> b
   f(g(X), b) -> f(a, X)

Termination of R to be shown.


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

   a -> g(c)

where the Polynomial interpretation:
POL(g(x_1)) = x_1
POL(b) = 1
POL(a) = 1
POL(f(x_1, x_2)) = 2 + x_1 + x_2
POL(c) = 0
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(a) -> b
   f(g(X), b) -> f(a, X)

where the Polynomial interpretation:
POL(g(x_1)) = 1 + x_1
POL(b) = 0
POL(a) = 0
POL(f(x_1, x_2)) = 2 + x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.367 seconds.