Term Rewriting System R:
[x]
g(s(x)) -> f(x)
g(0) -> 0
f(0) -> s(0)
f(s(x)) -> s(s(g(x)))
Termination of R to be shown.
TRS
↳RFC Match Bounds
Termination could be shown with a Match Bound of 1.
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7
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 s(0)
- 3 to 2 labelled 0(0)
- 1 to 2 labelled f(0)
- 1 to 2 labelled 0(0)
- 1 to 4 labelled s(0)
- 4 to 5 labelled s(0)
- 5 to 2 labelled g(0)
- 5 to 2 labelled 0(1)
- 5 to 2 labelled f(1)
- 1 to 6 labelled s(1)
- 6 to 7 labelled s(1)
- 7 to 2 labelled g(1)
- 1 to 5 labelled s(1)
- 5 to 6 labelled s(1)
- 5 to 5 labelled s(1)
- 7 to 2 labelled 0(1)
- 7 to 2 labelled f(1)
- 7 to 6 labelled s(1)
- 7 to 5 labelled s(1)
Termination of R successfully shown.
Duration:
0:00 minutes