Term Rewriting System R:
[X, XS]
zeros -> cons(0, nzeros)
zeros -> nzeros
tail(cons(X, XS)) -> activate(XS)
activate(nzeros) -> zeros
activate(X) -> X

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

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

where the Polynomial interpretation:
  POL(activate(x1))=  1 + x1  
  POL(n__zeros)=  0  
  POL(0)=  0  
  POL(cons(x1, x2))=  x1 + x2  
  POL(tail(x1))=  1 + x1  
  POL(zeros)=  1  
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.


   R
RRRPolo
       →TRS2
Removing Redundant Rules



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

activate(nzeros) -> zeros

where the Polynomial interpretation:
  POL(activate(x1))=  x1  
  POL(n__zeros)=  1  
  POL(cons(x1, x2))=  x1 + x2  
  POL(tail(x1))=  x1  
  POL(zeros)=  0  
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.


   R
RRRPolo
       →TRS2
RRRPolo
           →TRS3
Removing Redundant Rules



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

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

where the Polynomial interpretation:
  POL(activate(x1))=  x1  
  POL(cons(x1, x2))=  x1 + x2  
  POL(tail(x1))=  1 + x1  
was used.

All Rules of R can be deleted.


   R
RRRPolo
       →TRS2
RRRPolo
           →TRS3
RRRPolo
             ...
               →TRS4
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

Innermost Termination of R successfully shown.
Duration:
0:00 minutes