Term Rewriting System R:
[x]
f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(d(x)) -> x
g(c(h(0))) -> g(d(1))
g(c(1)) -> g(d(h(0)))
g(h(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, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
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 h(0)
- 1 to 2 labelled g(0)
- 1 to 2 labelled 1(0)
- 1 to 2 labelled 0(0)
- 1 to 2 labelled f(0)
- 1 to 3 labelled g(0)
- 3 to 4 labelled d(0)
- 4 to 5 labelled h(0)
- 5 to 2 labelled 0(0)
- 1 to 6 labelled f(0)
- 6 to 7 labelled c(0)
- 7 to 2 labelled f(0)
- 1 to 2 labelled d(0)
- 1 to 8 labelled f(0)
- 8 to 9 labelled d(0)
- 9 to 2 labelled f(0)
- 1 to 2 labelled c(0)
- 1 to 10 labelled g(0)
- 10 to 11 labelled d(0)
- 11 to 2 labelled 1(0)
- 7 to 12 labelled f(1)
- 12 to 13 labelled d(1)
- 13 to 2 labelled f(1)
- 7 to 14 labelled f(1)
- 14 to 15 labelled c(1)
- 15 to 2 labelled f(1)
- 1 to 16 labelled g(1)
- 16 to 17 labelled d(1)
- 17 to 18 labelled h(1)
- 18 to 2 labelled 0(1)
- 1 to 2 labelled 0(1)
- 1 to 2 labelled f(1)
- 1 to 2 labelled g(1)
- 17 to 2 labelled 1(1)
- 1 to 2 labelled h(1)
- 1 to 2 labelled 1(1)
- 1 to 2 labelled c(1)
- 1 to 2 labelled d(1)
- 9 to 12 labelled f(1)
- 9 to 14 labelled f(1)
- 1 to 12 labelled f(1)
- 1 to 14 labelled f(1)
- 1 to 5 labelled h(1)
- 15 to 12 labelled f(1)
- 15 to 14 labelled f(1)
- 13 to 12 labelled f(1)
- 13 to 14 labelled f(1)
- 1 to 18 labelled h(2)
- 1 to 2 labelled 1(2)
Termination of R successfully shown.
Duration:
0:00 minutes