Term Rewriting System R:

   [l, x, k, a, b, c]
   f(empty, l) -> l
   f(cons(x, k), l) -> g(k, l, cons(x, k))
   g(a, b, c) -> f(a, cons(b, c))

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


   G(a, b, c) -> F(a, cons(b, c))
   F(cons(x, k), l) -> G(k, l, cons(x, k))

Furthermore, R contains one SCC.


SCC1:

F(cons(x, k), l) -> G(k, l, cons(x, k))
G(a, b, c) -> F(a, cons(b, c))

By using a polynomial ordering, at least one Dependency Pair of this SCC can be strictly oriented.

No rules need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
POL(G(x_1, x_2, x_3)) = x_1
POL(F(x_1, x_2)) = x_1
POL(cons(x_1, x_2)) = 1 + x_2

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.522 seconds.