Term Rewriting System R:

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

Termination of R to be shown.


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

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

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

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

where the Polynomial interpretation:
POL(g(x_1, x_2)) = x_1 + 2*x_2
POL(h(x_1, x_2)) = 1 + x_1 + x_2
was used. 



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.394 seconds.