Term Rewriting System R:
[x, y]
average(s(x), y) -> average(x, s(y))
average(x, s(s(s(y)))) -> s(average(s(x), y))
average(0, 0) -> 0
average(0, s(0)) -> 0
average(0, s(s(0))) -> s(0)

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

average(s(x), y) -> average(x, s(y))
average(0, s(0)) -> 0
average(0, s(s(0))) -> s(0)

where the Polynomial interpretation:
  POL(0)=  0  
  POL(average(x1, x2))=  2·x1 + x2  
  POL(s(x1))=  1 + x1  
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:

average(0, 0) -> 0

where the Polynomial interpretation:
  POL(0)=  1  
  POL(average(x1, x2))=  x1 + x2  
  POL(s(x1))=  x1  
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:

average(x, s(s(s(y)))) -> s(average(s(x), y))

where the Polynomial interpretation:
  POL(average(x1, x2))=  x1 + x2  
  POL(s(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