Termination Proof using AProVE

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.

TRS

     ↳RFC Match Bounds

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 5 labelled a__f(0)
5 to 2 labelled mark(0)
1 to 2 labelled f(0)
1 to 5 labelled h(0)
1 to 2 labelled g(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:
0:00 minutes