Term Rewriting System R:

   [x, y, z, u, v]
   f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
   f(x, y, y) -> y
   f(x, y, g(y)) -> x
   f(x, x, y) -> x
   f(g(x), x, y) -> y

Termination of R to be shown.


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

   f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
   f(x, y, y) -> y
   f(x, y, g(y)) -> x
   f(x, x, y) -> x
   f(g(x), x, y) -> y

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.380 seconds.