Term Rewriting System R:
[x, y, z]
and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Instantiation Transformation


Dependency Pair:

AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)


Rule:


and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)





On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule

AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)
one new Dependency Pair is created:

AND(not(not(x0)), band(x''', z'''), not(z'')) -> AND(band(x''', z'''), band(x0, z''), x0)

The transformation is resulting in no new DP problems.


Termination of R successfully shown.
Duration:
0:00 minutes