Term Rewriting System R:

   [YS, X, XS, Y, L]
   app(nil, YS) -> YS
   app(cons(X), YS) -> cons(X)
   from(X) -> cons(X)
   zWadr(nil, YS) -> nil
   zWadr(XS, nil) -> nil
   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
   prefix(L) -> cons(nil)

Termination of R to be shown.


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

   app(nil, YS) -> YS
   app(cons(X), YS) -> cons(X)
   zWadr(nil, YS) -> nil
   zWadr(XS, nil) -> nil

where the Polynomial interpretation:
POL(nil) = 0
POL(prefix(x_1)) = x_1
POL(from(x_1)) = x_1
POL(app(x_1, x_2)) = 1 + x_1 + x_2
POL(zWadr(x_1, x_2)) = 1 + x_1 + x_2
POL(cons(x_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: 

   from(X) -> cons(X)

where the Polynomial interpretation:
POL(prefix(x_1)) = x_1
POL(nil) = 0
POL(from(x_1)) = 1 + x_1
POL(zWadr(x_1, x_2)) = x_1 + x_2
POL(app(x_1, x_2)) = x_1 + x_2
POL(cons(x_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: 

   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))

where the Polynomial interpretation:
POL(prefix(x_1)) = x_1
POL(nil) = 0
POL(zWadr(x_1, x_2)) = 1 + x_1 + x_2
POL(app(x_1, x_2)) = x_1 + x_2
POL(cons(x_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: 

   prefix(L) -> cons(nil)

where the Polynomial interpretation:
POL(prefix(x_1)) = 1 + x_1
POL(nil) = 0
POL(cons(x_1)) = x_1
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.419 seconds.