Term Rewriting System R:
[x]
w(r(x)) -> r(w(x))
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))

Termination of R to be shown.



   TRS
Removing Redundant Rules



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

b(w(x)) -> w(b(x))

where the Polynomial interpretation:
  POL(b(x1))=  2·x1  
  POL(w(x1))=  1 + x1  
  POL(r(x1))=  x1  
was used.

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


   TRS
RRRPolo
       →TRS2
Removing Redundant Rules



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

b(r(x)) -> r(b(x))

where the Polynomial interpretation:
  POL(b(x1))=  2·x1  
  POL(w(x1))=  x1  
  POL(r(x1))=  1 + x1  
was used.

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


   TRS
RRRPolo
       →TRS2
RRRPolo
           →TRS3
Removing Redundant Rules



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

w(r(x)) -> r(w(x))

where the Polynomial interpretation:
  POL(w(x1))=  2·x1  
  POL(r(x1))=  1 + x1  
was used.

All Rules of R can be deleted.


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



R contains no Dependency Pairs and therefore no SCCs.

Termination of R successfully shown.
Duration:
0:01 minutes