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

Termination of R to be shown.



   TRS
Removing Redundant Rules



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

g(g(x)) -> f(x)

where the Polynomial interpretation:
  POL(g(x1))=  1 + x1  
  POL(f(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
Removing Redundant Rules



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

f(f(x)) -> g(f(x))

where the Polynomial interpretation:
  POL(g(x1))=  x1  
  POL(f(x1))=  1 + x1  
was used.

All Rules of R can be deleted.


   TRS
RRRPolo
       →TRS2
RRRPolo
           →TRS3
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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