Term Rewriting System R:

   [x, y, z, u, v]
   if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v))

Termination of R to be shown.


R contains the following Dependency Pairs: 


   IF(if(x, y, z), u, v) -> IF(x, if(y, u, v), if(z, u, v))
   IF(if(x, y, z), u, v) -> IF(y, u, v)
   IF(if(x, y, z), u, v) -> IF(z, u, v)

Furthermore, R contains one SCC.


SCC1:

IF(if(x, y, z), u, v) -> IF(z, u, v)
IF(if(x, y, z), u, v) -> IF(y, u, v)
IF(if(x, y, z), u, v) -> IF(x, if(y, u, v), if(z, u, v))

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(if(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
POL(IF(x_1, x_2, x_3)) = x_1

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.504 seconds.