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

Termination of R to be shown.



   TRS
Removing Redundant Rules



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

f(x) -> g(x)

where the Polynomial interpretation:
  POL(g(x1))=  x1  
  POL(b)=  0  
  POL(a)=  0  
  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
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(a) -> F(b)
G(b) -> G(a)

R contains no SCCs.

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