Term Rewriting System R:

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

Termination of R to be shown.


Termination could be shown with a Match Bound of 1.
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8

Node 1 is start node and node 2 is final node.

Those nodes are connect through the following edges:

* 2 to 2 labelled #(0)
* 1 to 3 labelled g(0)
* 3 to 4 labelled g(0)
* 4 to 2 labelled f(0)
* 1 to 5 labelled g(0)
* 5 to 6 labelled g(0)
* 6 to 2 labelled g(0)
* 4 to 7 labelled g(1)
* 7 to 8 labelled g(1)
* 8 to 2 labelled g(1)
* 8 to 2 labelled f(1)
* 8 to 7 labelled g(1)




Termination of R successfully shown.


Duration: 0.320 seconds.