Term Rewriting System R:

   [x, y]
   app(id, x) -> x
   app(plus, 0) -> id
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

Termination of R to be shown.


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

   app(id, x) -> x

where the Polynomial interpretation:
POL(plus) = 0
POL(id) = 1
POL(s) = 0
POL(app(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: 

   app(plus, 0) -> id

where the Polynomial interpretation:
POL(plus) = 0
POL(s) = 0
POL(id) = 0
POL(app(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: 

   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.407 seconds.