Term Rewriting System R:

   [x]
   a(c(d(x))) -> c(x)
   u(b(d(d(x)))) -> b(x)
   v(a(a(x))) -> u(v(x))
   v(a(c(x))) -> u(b(d(x)))
   v(c(x)) -> b(x)
   w(a(a(x))) -> u(w(x))
   w(a(c(x))) -> u(b(d(x)))
   w(c(x)) -> b(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 2 labelled c(0)
* 1 to 2 labelled b(0)
* 1 to 3 labelled u(0)
* 3 to 2 labelled v(0)
* 1 to 4 labelled u(0)
* 4 to 5 labelled b(0)
* 5 to 2 labelled d(0)
* 1 to 6 labelled u(0)
* 6 to 2 labelled w(0)
* 3 to 7 labelled u(1)
* 7 to 8 labelled b(1)
* 8 to 2 labelled d(1)
* 3 to 2 labelled b(1)
* 7 to 2 labelled v(1)
* 6 to 2 labelled b(1)
* 6 to 7 labelled u(1)
* 7 to 2 labelled w(1)
* 1 to 2 labelled b(1)
* 7 to 2 labelled b(1)
* 7 to 7 labelled u(1)




Termination of R successfully shown.


Duration: 0.374 seconds.