Term Rewriting System R:

   [x, y]
   g(x, y) -> x
   g(x, y) -> y
   f(s(x), y, y) -> f(y, x, s(x))

Termination of R to be shown.


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

   g(x, y) -> x
   g(x, y) -> y

where the Polynomial interpretation:
POL(g(x_1, x_2)) = 1 + x_1 + x_2
POL(s(x_1)) = x_1
POL(f(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + x_3
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: 

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

where the Polynomial interpretation:
POL(s(x_1)) = 1 + x_1
POL(f(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + x_3
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.375 seconds.