Term Rewriting System R:

   [x, y, z]
   *(i(x), x) -> 1
   *(1, y) -> y
   *(x, 0) -> 0
   *(*(x, y), z) -> *(x, *(y, z))

Termination of R to be shown.


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

   *(i(x), x) -> 1

where the Polynomial interpretation:
POL(*(x_1, x_2)) = x_1 + x_2
POL(1) = 0
POL(i(x_1)) = 1 + x_1
POL(0) = 0
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: 

   *(1, y) -> y

where the Polynomial interpretation:
POL(*(x_1, x_2)) = x_1 + x_2
POL(1) = 1
POL(0) = 0
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: 

   *(x, 0) -> 0

where the Polynomial interpretation:
POL(*(x_1, x_2)) = 1 + x_1 + x_2
POL(0) = 0
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: 

   *(*(x, y), z) -> *(x, *(y, z))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.391 seconds.