Term Rewriting System R:

   [X]
   a__c -> a__f(g(c))
   a__c -> c
   a__f(g(X)) -> g(X)
   a__f(X) -> f(X)
   mark(c) -> a__c
   mark(f(X)) -> a__f(X)
   mark(g(X)) -> g(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

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__f(0)
* 3 to 4 labelled g(0)
* 4 to 2 labelled c(0)
* 1 to 2 labelled c(0)
* 1 to 2 labelled g(0)
* 1 to 2 labelled f(0)
* 1 to 2 labelled a__c(0)
* 1 to 2 labelled a__f(0)
* 1 to 2 labelled f(1)
* 1 to 3 labelled f(1)
* 1 to 2 labelled c(1)
* 1 to 5 labelled a__f(1)
* 5 to 6 labelled g(1)
* 6 to 2 labelled c(1)
* 1 to 2 labelled g(1)
* 1 to 4 labelled g(1)
* 1 to 5 labelled f(2)
* 1 to 6 labelled g(2)




Termination of R successfully shown.


Duration: 0.326 seconds.