Term Rewriting System R:

   [X]
   a__f(X) -> g(h(f(X)))
   a__f(X) -> f(X)
   mark(f(X)) -> a__f(mark(X))
   mark(g(X)) -> g(X)
   mark(h(X)) -> h(mark(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, 7, 8, 9, 10

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 g(0)
* 3 to 4 labelled h(0)
* 4 to 2 labelled f(0)
* 1 to 2 labelled f(0)
* 1 to 5 labelled a__f(0)
* 5 to 2 labelled mark(0)
* 1 to 2 labelled g(0)
* 1 to 5 labelled h(0)
* 1 to 6 labelled g(1)
* 6 to 7 labelled h(1)
* 7 to 5 labelled f(1)
* 1 to 5 labelled f(1)
* 5 to 8 labelled a__f(1)
* 8 to 2 labelled mark(1)
* 5 to 8 labelled h(1)
* 5 to 2 labelled g(1)
* 5 to 9 labelled g(2)
* 9 to 10 labelled h(2)
* 10 to 8 labelled f(2)
* 5 to 8 labelled f(2)
* 8 to 8 labelled a__f(1)
* 8 to 8 labelled h(1)
* 8 to 2 labelled g(1)
* 8 to 9 labelled g(2)
* 8 to 8 labelled f(2)




Termination of R successfully shown.


Duration: 0.334 seconds.