Term Rewriting System R:

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

Termination of R to be shown.


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

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

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

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

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.376 seconds.