Term Rewriting System R:

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

Termination of R to be shown.


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

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

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.357 seconds.