Term Rewriting System R:

   [x, y, z]
   *(x, +(y, z)) -> +(*(x, y), *(x, z))

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


   *'(x, +(y, z)) -> *'(x, y)
   *'(x, +(y, z)) -> *'(x, z)

Furthermore, R contains one SCC.


SCC1:

*'(x, +(y, z)) -> *'(x, z)
*'(x, +(y, z)) -> *'(x, y)

Removing rules from R by ordering and analyzing Dependency Pairs, Usable Rules, and Usable Equations.

This is possible by using the following (C_E-compatible) Polynomial ordering.

Polynomial interpretation:
POL(*'(x_1, x_2)) = 1 + x_1 + x_2
POL(+(x_1, x_2)) = 1 + x_1 + x_2

The following Dependency Pairs can be deleted:

   *'(x, +(y, z)) -> *'(x, z)
   *'(x, +(y, z)) -> *'(x, y)



 This transformation is resulting in no new subcycles.




Termination of R successfully shown.


Duration: 0.432 seconds.