Term Rewriting System R:

   [x]
   a(b(x)) -> b(a(x))
   a(c(x)) -> x

Termination of R to be shown.


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

   a(c(x)) -> x

where the Polynomial interpretation:
POL(b(x_1)) = x_1
POL(a(x_1)) = x_1
POL(c(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: 

   a(b(x)) -> b(a(x))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.388 seconds.