Term Rewriting System R:

   [x]
   s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))

Termination of R to be shown.


Termination could be shown with a Match Bound of 4.
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, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42

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 s0(0)
* 3 to 4 labelled s0(0)
* 4 to 5 labelled s0(0)
* 5 to 6 labelled s1(0)
* 6 to 7 labelled s1(0)
* 7 to 2 labelled s1(0)
* 7 to 8 labelled s0(1)
* 8 to 9 labelled s0(1)
* 9 to 10 labelled s0(1)
* 10 to 11 labelled s1(1)
* 11 to 12 labelled s1(1)
* 12 to 2 labelled s1(1)
* 6 to 8 labelled s0(1)
* 12 to 8 labelled s0(1)
* 11 to 8 labelled s0(1)
* 5 to 13 labelled s0(1)
* 13 to 14 labelled s0(1)
* 14 to 15 labelled s0(1)
* 15 to 16 labelled s1(1)
* 16 to 17 labelled s1(1)
* 17 to 9 labelled s1(1)
* 10 to 18 labelled s0(2)
* 18 to 19 labelled s0(2)
* 19 to 20 labelled s0(2)
* 20 to 21 labelled s1(2)
* 21 to 22 labelled s1(2)
* 22 to 9 labelled s1(2)
* 21 to 23 labelled s0(2)
* 23 to 24 labelled s0(2)
* 24 to 25 labelled s0(2)
* 25 to 26 labelled s1(2)
* 26 to 27 labelled s1(2)
* 27 to 18 labelled s1(2)
* 16 to 23 labelled s0(2)
* 26 to 28 labelled s0(3)
* 28 to 29 labelled s0(3)
* 29 to 30 labelled s0(3)
* 30 to 31 labelled s1(3)
* 31 to 32 labelled s1(3)
* 32 to 20 labelled s1(3)
* 32 to 33 labelled s0(3)
* 33 to 34 labelled s0(3)
* 34 to 35 labelled s0(3)
* 35 to 36 labelled s1(3)
* 36 to 37 labelled s1(3)
* 37 to 24 labelled s1(3)
* 30 to 38 labelled s0(4)
* 38 to 39 labelled s0(4)
* 39 to 40 labelled s0(4)
* 40 to 41 labelled s1(4)
* 41 to 42 labelled s1(4)
* 42 to 34 labelled s1(4)




Termination of R successfully shown.


Duration: 0.402 seconds.