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

Termination of R to be shown.



   TRS
Removing Redundant Rules



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

b -> a

where the Polynomial interpretation:
  POL(g(x1))=  x1  
  POL(b)=  1  
  POL(a)=  0  
  POL(f(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:

f(a) -> g(a)

where the Polynomial interpretation:
  POL(g(x1))=  x1  
  POL(b)=  0  
  POL(a)=  1  
  POL(f(x1))=  2·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:

g(b) -> f(b)

where the Polynomial interpretation:
  POL(g(x1))=  1 + x1  
  POL(b)=  0  
  POL(f(x1))=  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