Term Rewriting System R:

   [X, Y, Z]
   div(X, e) -> i(X)
   div(div(X, Y), Z) -> div(Y, div(i(X), Z))
   i(div(X, Y)) -> div(Y, X)

Termination of R to be shown.


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

   div(X, e) -> i(X)

where the Polynomial interpretation:
POL(e) = 1
POL(i(x_1)) = x_1
POL(div(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: 

   div(div(X, Y), Z) -> div(Y, div(i(X), Z))
   i(div(X, Y)) -> div(Y, X)

where the Polynomial interpretation:
POL(i(x_1)) = 2*x_1
POL(div(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: 0.384 seconds.