Term Rewriting System R:

   [X, Y, Z]
   plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
   times(X, s(Y)) -> plus(X, times(Y, X))

Termination of R to be shown.


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

   times(X, s(Y)) -> plus(X, times(Y, X))

where the Polynomial interpretation:
POL(plus(x_1, x_2)) = x_1 + x_2
POL(s(x_1)) = 1 + 2*x_1
POL(times(x_1, x_2)) = 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: 

   plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))

where the Polynomial interpretation:
POL(plus(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: 0.383 seconds.