Term Rewriting System R:
[x]
fib(0) -> 0
fib(s(0)) -> s(0)
fib(s(s(x))) -> +(fib(s(x)), fib(x))

Innermost Termination of R to be shown.



   R
Removing Redundant Rules



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

fib(0) -> 0
fib(s(0)) -> s(0)

where the Polynomial interpretation:
  POL(0)=  1  
  POL(fib(x1))=  2·x1  
  POL(s(x1))=  2·x1  
  POL(+(x1, x2))=  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
Removing Redundant Rules



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

fib(s(s(x))) -> +(fib(s(x)), fib(x))

where the Polynomial interpretation:
  POL(fib(x1))=  x1  
  POL(s(x1))=  1 + 2·x1  
  POL(+(x1, x2))=  x1 + x2  
was used.

All Rules of R can be deleted.


   R
RRRPolo
       →TRS2
RRRPolo
           →TRS3
Dependency Pair Analysis



R contains no Dependency Pairs and therefore no SCCs.

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