Term Rewriting System R:

   [x, a, k, y]
   f(x, empty) -> x
   f(empty, cons(a, k)) -> f(cons(a, k), k)
   f(cons(a, k), y) -> f(y, k)

Termination of R to be shown.


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

   f(x, empty) -> x

where the Polynomial interpretation:
POL(f(x_1, x_2)) = 1 + x_1 + 2*x_2
POL(empty) = 0
POL(cons(x_1, x_2)) = x_1 + 2*x_2
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(empty, cons(a, k)) -> f(cons(a, k), k)

where the Polynomial interpretation:
POL(f(x_1, x_2)) = 2 + x_1 + 2*x_2
POL(empty) = 1
POL(cons(x_1, x_2)) = x_1 + 2*x_2
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(cons(a, k), y) -> f(y, k)

where the Polynomial interpretation:
POL(f(x_1, x_2)) = 2 + x_1 + x_2
POL(cons(x_1, x_2)) = 1 + x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.388 seconds.