Term Rewriting System R:

   [x, y, z]
   f(+(x, 0)) -> f(x)
   +(x, +(y, z)) -> +(+(x, y), z)

Termination of R to be shown.


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

   f(+(x, 0)) -> f(x)

where the Polynomial interpretation:
POL(+(x_1, x_2)) = x_1 + x_2
POL(f(x_1)) = 2 + x_1
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, +(y, z)) -> +(+(x, y), z)

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.368 seconds.