Term Rewriting System R:
[X]
f(X) -> g(nh(nf(X)))
f(X) -> nf(X)
h(X) -> nh(X)
activate(nh(X)) -> h(activate(X))
activate(nf(X)) -> f(activate(X))
activate(X) -> X
Innermost 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 2 labelled n__f(0)
- 1 to 2 labelled g(0)
- 1 to 3 labelled f(0)
- 3 to 2 labelled activate(0)
- 1 to 3 labelled h(0)
- 1 to 4 labelled g(0)
- 4 to 5 labelled n__h(0)
- 5 to 2 labelled n__f(0)
- 1 to 2 labelled n__h(0)
- 1 to 2 labelled activate(0)
- 1 to 2 labelled h(0)
- 1 to 2 labelled f(0)
- 1 to 2 labelled n__h(1)
- 1 to 3 labelled n__h(1)
- 1 to 6 labelled g(1)
- 6 to 7 labelled n__h(1)
- 7 to 3 labelled n__f(1)
- 1 to 3 labelled n__f(1)
- 7 to 2 labelled n__f(1)
- 1 to 2 labelled n__f(1)
- 3 to 8 labelled h(1)
- 8 to 2 labelled activate(1)
- 3 to 8 labelled f(1)
- 3 to 2 labelled n__f(1)
- 3 to 2 labelled g(1)
- 3 to 2 labelled n__h(1)
- 3 to 2 labelled activate(1)
- 3 to 2 labelled f(1)
- 3 to 2 labelled h(1)
- 1 to 8 labelled h(1)
- 1 to 8 labelled f(1)
- 1 to 2 labelled g(1)
- 1 to 2 labelled activate(1)
- 1 to 2 labelled f(1)
- 1 to 2 labelled h(1)
- 1 to 9 labelled g(2)
- 9 to 10 labelled n__h(2)
- 10 to 8 labelled n__f(2)
- 1 to 8 labelled n__f(2)
- 1 to 2 labelled n__h(2)
- 10 to 2 labelled n__f(2)
- 1 to 2 labelled n__f(2)
- 3 to 8 labelled n__h(2)
- 3 to 2 labelled n__h(2)
- 3 to 9 labelled g(2)
- 3 to 8 labelled n__f(2)
- 1 to 8 labelled n__h(2)
- 3 to 2 labelled n__f(2)
- 8 to 8 labelled h(1)
- 8 to 8 labelled f(1)
- 8 to 2 labelled n__f(1)
- 8 to 2 labelled g(1)
- 8 to 2 labelled n__h(1)
- 8 to 2 labelled f(1)
- 8 to 2 labelled h(1)
- 8 to 9 labelled g(2)
- 8 to 8 labelled n__f(2)
- 8 to 2 labelled n__h(2)
- 8 to 8 labelled n__h(2)
- 8 to 2 labelled n__f(2)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes