Term Rewriting System R:

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

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 a(0)
* 4 to 5 labelled b(0)
* 5 to 2 labelled f(0)
* 1 to 2 labelled b(0)
* 1 to 2 labelled a(0)
* 4 to 5 labelled a(1)
* 1 to 2 labelled a(1)
* 5 to 6 labelled f(1)
* 6 to 7 labelled a(1)
* 7 to 8 labelled b(1)
* 8 to 2 labelled f(1)
* 5 to 2 labelled b(1)
* 7 to 8 labelled a(2)
* 5 to 2 labelled a(2)
* 8 to 6 labelled f(1)
* 8 to 2 labelled b(1)
* 8 to 2 labelled a(2)




Termination of R successfully shown.


Duration: 0.330 seconds.