Term Rewriting System R:

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

Termination of R to be shown.


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

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

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

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

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.385 seconds.