Term Rewriting System R:
[x]
g(x, a, b) -> g(b, b, a)

Termination of R to be shown.



   R
Removing Redundant Rules



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

g(x, a, b) -> g(b, b, a)

where the Polynomial interpretation:
  POL(g(x1, x2, x3))=  x1 + 2·x2 + x3  
  POL(b)=  0  
  POL(a)=  1  
was used.

All Rules of R can be deleted.


   R
RRRPolo
       →TRS2
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
OC
           →TRS3
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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