Term Rewriting System R:

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

Innermost Termination of R to be shown.


R contains the following Dependency Pairs: 


   QUOT(x, 0, s(z)) -> QUOT(x, s(z), s(z))
   QUOT(s(x), s(y), z) -> QUOT(x, y, z)

Furthermore, R contains one SCC.


SCC1:

QUOT(s(x), s(y), z) -> QUOT(x, y, z)
QUOT(x, 0, s(z)) -> QUOT(x, s(z), s(z))

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(QUOT(x_1, x_2, x_3)) = x_1
POL(0) = 0

 resulting in no subcycles.




Innermost Termination of R successfully shown.


Duration: 0.503 seconds.