Term Rewriting System R:

   [x, y]
   rev(a) -> a
   rev(b) -> b
   rev(++(x, y)) -> ++(rev(y), rev(x))
   rev(++(x, x)) -> rev(x)

Termination of R to be shown.


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

   rev(a) -> a

where the Polynomial interpretation:
POL(b) = 0
POL(++(x_1, x_2)) = x_1 + x_2
POL(a) = 1
POL(rev(x_1)) = 2*x_1
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: 

   rev(b) -> b

where the Polynomial interpretation:
POL(b) = 1
POL(++(x_1, x_2)) = x_1 + x_2
POL(rev(x_1)) = 2*x_1
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: 

   rev(++(x, y)) -> ++(rev(y), rev(x))
   rev(++(x, x)) -> rev(x)

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.400 seconds.