Term Rewriting System R:

   [X, XS]
   zeros -> cons(0, n__zeros)
   zeros -> n__zeros
   tail(cons(X, XS)) -> activate(XS)
   activate(n__zeros) -> zeros
   activate(X) -> X

Termination of R to be shown.


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

   zeros -> cons(0, n__zeros)
   zeros -> n__zeros
   activate(X) -> X

where the Polynomial interpretation:
POL(n__zeros) = 0
POL(tail(x_1)) = 1 + x_1
POL(activate(x_1)) = 1 + x_1
POL(zeros) = 1
POL(0) = 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: 

   tail(cons(X, XS)) -> activate(XS)

where the Polynomial interpretation:
POL(n__zeros) = 0
POL(activate(x_1)) = x_1
POL(tail(x_1)) = 1 + x_1
POL(zeros) = 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: 

   activate(n__zeros) -> zeros

where the Polynomial interpretation:
POL(n__zeros) = 0
POL(activate(x_1)) = 1 + x_1
POL(zeros) = 0
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.377 seconds.