Term Rewriting System R:

   [x, y]
   g(f(x), y) -> f(h(x, y))
   h(x, y) -> g(x, f(y))

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(f(x), y) -> H(x, y)
   H(x, y) -> G(x, f(y))

Furthermore, R contains one SCC.


SCC1:

H(x, y) -> G(x, f(y))
G(f(x), y) -> H(x, y)

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_1
POL(H(x_1, x_2)) = 1 + x_1
POL(f(x_1)) = 1 + x_1

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.476 seconds.