Termination Proof using AProVE

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.

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

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

Termination of R successfully shown.
Duration:
0:00 minutes