Term Rewriting System R:

   [x, y]
   app(app(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, x), x) -> e
   app(app(/, x), e) -> x
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y

Termination of R to be shown.


Removing the following rules from R which fullfill a polynomial ordering: 

   app(app(\, x), x) -> e
   app(app(\, e), x) -> x
   app(app(\, x), app(app(., x), y)) -> y
   app(app(\, app(app(/, x), y)), x) -> y
   app(app(/, app(app(., y), x)), x) -> y
   app(app(/, x), app(app(\, y), x)) -> y
   app(app(., e), x) -> x
   app(app(., x), e) -> x
   app(app(., x), app(app(\, x), y)) -> y
   app(app(., app(app(/, y), x)), x) -> y

where the Polynomial interpretation:
POL(e) = 0
POL(/) = 0
POL(\) = 1
POL(app(x_1, x_2)) = x_1 + x_2
POL(.) = 1
was used. 



Not all Rules of R can be deleted, so we still have to regard a part of R.


Removing the following rules from R which fullfill a polynomial ordering: 

   app(app(/, x), x) -> e
   app(app(/, x), e) -> x

where the Polynomial interpretation:
POL(e) = 0
POL(/) = 1
POL(app(x_1, x_2)) = x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.415 seconds.