Term Rewriting System R:

   [x]
   fib(0) -> 0
   fib(s(0)) -> s(0)
   fib(s(s(x))) -> +(fib(s(x)), fib(x))

Termination of R to be shown.


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

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

where the Polynomial interpretation:
POL(s(x_1)) = 2*x_1
POL(fib(x_1)) = 2*x_1
POL(+(x_1, x_2)) = x_1 + x_2
POL(0) = 1
was used. 



Not all Rules of R can be deleted, so we still have to regard a part of R.


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(s(x_1)) = 1 + 2*x_1
POL(fib(x_1)) = x_1
POL(+(x_1, x_2)) = x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.397 seconds.