Term Rewriting System R:
[x, y]
*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

*'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)
*'(x, *(minus(y), y)) -> *'(y, y)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Instantiation Transformation


Dependency Pair:

*'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)


Rule:


*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)


Strategy:

innermost




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

*'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)
one new Dependency Pair is created:

*'(minus(x'''), *(minus(y'), y')) -> *'(minus(*(y', y')), minus(x'''))

The transformation is resulting in no new DP problems.


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