Term Rewriting System R:

   [y, u, v, w, z]
   concat(leaf, y) -> y
   concat(cons(u, v), y) -> cons(u, concat(v, y))
   less_leaves(x, leaf) -> false
   less_leaves(leaf, cons(w, z)) -> true
   less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))

Termination of R to be shown.


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

   concat(leaf, y) -> y
   less_leaves(x, leaf) -> false
   less_leaves(leaf, cons(w, z)) -> true

where the Polynomial interpretation:
POL(concat(x_1, x_2)) = x_1 + x_2
POL(x) = 0
POL(true) = 0
POL(less_leaves(x_1, x_2)) = x_1 + x_2
POL(leaf) = 1
POL(false) = 0
POL(cons(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: 

   concat(cons(u, v), y) -> cons(u, concat(v, y))
   less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))

where the Polynomial interpretation:
POL(concat(x_1, x_2)) = 2*x_1 + x_2
POL(less_leaves(x_1, x_2)) = 2 + x_1 + x_2
POL(cons(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: 0.408 seconds.