Termination Proof using AProVE

Term Rewriting System R:
[X]
a_{_g}(X) -> a_{_h}(X)
a_{_g}(X) -> g(X)
a_{_c} -> d
a_{_c} -> c
a_{_h}(d) -> a_{_g}(c)
a_{_h}(X) -> h(X)
mark(g(X)) -> a_{_g}(X)
mark(h(X)) -> a_{_h}(X)
mark(c) -> a_{_c}
mark(d) -> d

Termination of R to be shown.

TRS

     ↳RFC Match Bounds

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

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 a__h(0)
1 to 2 labelled h(0)
1 to 2 labelled c(0)
1 to 1 labelled a__g(0)
1 to 2 labelled d(0)
1 to 2 labelled g(0)
1 to 2 labelled a__c(0)
1 to 2 labelled a__g(0)
1 to 2 labelled a__h(1)
1 to 2 labelled g(1)
1 to 1 labelled a__h(1)
1 to 1 labelled g(1)
1 to 2 labelled h(1)
1 to 2 labelled c(1)
1 to 2 labelled d(1)
1 to 1 labelled a__g(1)
1 to 1 labelled a__h(2)
1 to 1 labelled g(2)
1 to 2 labelled h(2)
1 to 1 labelled h(2)
1 to 3 labelled a__g(2)
3 to 2 labelled c(2)
1 to 1 labelled h(3)
1 to 3 labelled a__h(3)
1 to 3 labelled g(3)
1 to 3 labelled h(4)

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