Term Rewriting System R:
[x, y]
rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Termination of R to be shown. 



   R
     ↳Removing Redundant Rules



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

rev(a) -> a

where the Polynomial interpretation:
  POL(rev(x1))=  2·x1  
  POL(b)=  0  
  POL(++(x1, x2))=  x1 + x2  
  POL(a)=  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:

rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

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

rev(b) -> b

where the Polynomial interpretation:
  POL(rev(x1))=  1 + x1  
  POL(b)=  0  
was used.

All Rules of R can be deleted. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳RRRPolo
             ...
               →TRS4
                 ↳Overlay and local confluence Check



The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost. 


   R
     ↳RRRPolo
       →TRS2
         ↳RRRPolo
           →TRS3
             ↳RRRPolo
             ...
               →TRS5
                 ↳Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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