Term Rewriting System R:

   [x, y]
   minus(minus(x)) -> x
   minux(+(x, y)) -> +(minus(y), minus(x))
   +(minus(x), +(x, y)) -> y
   +(+(x, y), minus(y)) -> x

Termination of R to be shown.


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

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

where the Polynomial interpretation:
POL(minux(x_1)) = 2 + x_1
POL(minus(x_1)) = 1 + x_1
POL(+(x_1, x_2)) = x_1 + x_2
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: 

   minux(+(x, y)) -> +(minus(y), minus(x))

where the Polynomial interpretation:
POL(minux(x_1)) = 1 + x_1
POL(minus(x_1)) = x_1
POL(+(x_1, x_2)) = x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.383 seconds.