Term Rewriting System R:

   [x, y, z]
   f(0, 1, x) -> f(s(x), x, x)
   f(x, y, s(z)) -> s(f(0, 1, z))

Termination of R to be shown.


R contains the following Dependency Pairs: 


   F(0, 1, x) -> F(s(x), x, x)
   F(x, y, s(z)) -> F(0, 1, z)

Furthermore, R contains one SCC.


SCC1:

F(x, y, s(z)) -> F(0, 1, z)
F(0, 1, x) -> F(s(x), x, x)

By using a polynomial ordering, at least one Dependency Pair of this SCC can be strictly oriented.

No rules need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
POL(s(x_1)) = 1 + x_1
POL(1) = 0
POL(F(x_1, x_2, x_3)) = x_3
POL(0) = 0

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.502 seconds.