Term Rewriting System R:

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

Termination of R to be shown.


R contains the following Dependency Pairs: 


   G(g(x)) -> G(h(g(x)))
   G(g(x)) -> H(g(x))
   H(h(x)) -> H(f(h(x), x))

Furthermore, R contains one SCC.


SCC1:

G(g(x)) -> G(h(g(x)))

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

Additionally, the following rule can be oriented: 

   h(h(x)) -> h(f(h(x), x))


Used ordering: Polynomial ordering with Polynomial interpretation:
POL(g(x_1)) = 1
POL(G(x_1)) = x_1
POL(h(x_1)) = 0
POL(f(x_1, x_2)) = 0

 resulting in no subcycles.




Termination of R successfully shown.


Duration: 0.519 seconds.