Term Rewriting System R:

   [ls, a, x, k]
   rev(ls) -> r1(ls, empty)
   r1(empty, a) -> a
   r1(cons(x, k), a) -> r1(k, cons(x, a))

Termination of R to be shown.


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

   rev(ls) -> r1(ls, empty)

where the Polynomial interpretation:
POL(r1(x_1, x_2)) = x_1 + x_2
POL(rev(x_1)) = 1 + x_1
POL(empty) = 0
POL(cons(x_1, x_2)) = x_1 + 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: 

   r1(empty, a) -> a

where the Polynomial interpretation:
POL(r1(x_1, x_2)) = 1 + x_1 + x_2
POL(empty) = 0
POL(cons(x_1, x_2)) = x_1 + 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: 

   r1(cons(x, k), a) -> r1(k, cons(x, a))

where the Polynomial interpretation:
POL(r1(x_1, x_2)) = 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: 0.387 seconds.