Term Rewriting System R:

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

Termination of R to be shown.


Termination could be shown with a Match Bound of 2.
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, 9, 10, 11, 12, 13

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 f(0)
* 3 to 4 labelled g(0)
* 4 to 5 labelled f(0)
* 5 to 6 labelled g(0)
* 6 to 2 labelled f(0)
* 1 to 7 labelled f(0)
* 7 to 2 labelled g(0)
* 6 to 8 labelled f(1)
* 8 to 9 labelled g(1)
* 9 to 10 labelled f(1)
* 10 to 11 labelled g(1)
* 11 to 2 labelled f(1)
* 8 to 2 labelled g(1)
* 1 to 8 labelled f(1)
* 4 to 8 labelled f(1)
* 8 to 5 labelled g(1)
* 11 to 8 labelled f(1)
* 8 to 8 labelled g(1)
* 9 to 12 labelled f(2)
* 12 to 2 labelled g(2)
* 1 to 13 labelled f(2)
* 13 to 10 labelled g(2)
* 6 to 13 labelled f(2)
* 4 to 13 labelled f(2)
* 12 to 8 labelled g(2)
* 9 to 8 labelled f(1)
* 8 to 13 labelled g(1)
* 11 to 13 labelled f(2)
* 13 to 12 labelled g(2)
* 1 to 12 labelled f(2)
* 11 to 12 labelled f(2)
* 6 to 12 labelled f(2)
* 4 to 12 labelled f(2)
* 9 to 13 labelled f(2)
* 12 to 13 labelled g(2)
* 8 to 12 labelled g(1)




Termination of R successfully shown.


Duration: 0.440 seconds.