Term Rewriting System R:

   [x, y]
   merge(x, nil) -> x
   merge(nil, y) -> y
   merge(++(x, y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))
   merge(++(x, y), ++(u, v)) -> ++(u, merge(++(x, y), v))

Termination of R to be shown.


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

   merge(x, nil) -> x
   merge(nil, y) -> y

where the Polynomial interpretation:
POL(nil) = 1
POL(++(x_1, x_2)) = x_1 + x_2
POL(merge(x_1, x_2)) = x_1 + x_2
POL(v) = 0
POL(u) = 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: 

   merge(++(x, y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))

where the Polynomial interpretation:
POL(++(x_1, x_2)) = 1 + x_1 + x_2
POL(merge(x_1, x_2)) = 2*x_1 + x_2
POL(v) = 0
POL(u) = 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: 

   merge(++(x, y), ++(u, v)) -> ++(u, merge(++(x, y), v))

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



All Rules of R can be deleted.



Termination of R successfully shown.


Duration: 0.464 seconds.