Term Rewriting System R:

   [x, y, z]
   implies(not(x), y) -> or(x, y)
   implies(not(x), or(y, z)) -> implies(y, or(x, z))
   implies(x, or(y, z)) -> or(y, implies(x, z))

Termination of R to be shown.


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

   implies(not(x), y) -> or(x, y)
   implies(not(x), or(y, z)) -> implies(y, or(x, z))

where the Polynomial interpretation:
POL(not(x_1)) = 1 + x_1
POL(implies(x_1, x_2)) = x_1 + x_2
POL(or(x_1, x_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: 

   implies(x, or(y, z)) -> or(y, implies(x, z))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.384 seconds.