Term Rewriting System R:

   [X]
   c(b(a(X))) -> a(a(b(b(c(c(X))))))
   c(X) -> e
   a(X) -> e
   b(X) -> e

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

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 a(0)
* 3 to 4 labelled a(0)
* 4 to 5 labelled b(0)
* 5 to 6 labelled b(0)
* 6 to 7 labelled c(0)
* 7 to 2 labelled c(0)
* 1 to 2 labelled e(0)
* 5 to 6 labelled e(1)
* 3 to 4 labelled e(1)
* 6 to 7 labelled e(1)
* 4 to 5 labelled e(1)
* 1 to 3 labelled e(1)
* 7 to 2 labelled e(1)
* 7 to 8 labelled a(1)
* 8 to 9 labelled a(1)
* 9 to 10 labelled b(1)
* 10 to 11 labelled b(1)
* 11 to 12 labelled c(1)
* 12 to 2 labelled c(1)
* 8 to 9 labelled e(2)
* 7 to 8 labelled e(2)
* 9 to 10 labelled e(2)
* 12 to 2 labelled e(2)
* 11 to 12 labelled e(2)
* 10 to 11 labelled e(2)
* 12 to 8 labelled a(1)
* 12 to 8 labelled e(2)




Termination of R successfully shown.


Duration: 0.338 seconds.