Term Rewriting System R:

   [y, x]
   +(0, y) -> y
   +(s(x), 0) -> s(x)
   +(s(x), s(y)) -> s(+(s(x), +(y, 0)))

Termination of R to be shown.


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

   +(0, y) -> y
   +(s(x), 0) -> s(x)

where the Polynomial interpretation:
POL(s(x_1)) = 2 + x_1
POL(+(x_1, x_2)) = 1 + x_1 + 2*x_2
POL(0) = 0
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: 

   +(s(x), s(y)) -> s(+(s(x), +(y, 0)))

where the Polynomial interpretation:
POL(s(x_1)) = 1 + x_1
POL(+(x_1, x_2)) = x_1 + 2*x_2
POL(0) = 0
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.409 seconds.