Term Rewriting System R:

   [x]
   a(a(x)) -> b(b(x))
   b(b(a(x))) -> a(b(b(x)))

Termination of R to be shown.



Rule(s) before reversing: 

   a(a(x)) -> b(b(x))
   b(b(a(x))) -> a(b(b(x)))


Rule(s) after reversing: 

   a(a(x)) -> b(b(x))
   a(b(b(x))) -> b(b(a(x)))


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:
13, 14, 15, 16, 17, 18, 19

Node 13 is start node and node 14 is final node.

Those nodes are connect through the following edges:

* 14 to 14 labelled #(0)
* 13 to 15 labelled b(0)
* 15 to 14 labelled b(0)
* 13 to 16 labelled b(0)
* 16 to 17 labelled b(0)
* 17 to 14 labelled a(0)
* 17 to 18 labelled b(1)
* 18 to 19 labelled b(1)
* 19 to 14 labelled a(1)
* 18 to 14 labelled b(1)
* 19 to 18 labelled b(1)




Termination of R successfully shown.


Duration: 1.888 seconds.