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(0)) -> g(d(1))
g(c(1)) -> g(d(0))
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
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 1(0)
- 1 to 2 labelled g(0)
- 1 to 2 labelled 0(0)
- 1 to 2 labelled f(0)
- 1 to 3 labelled f(0)
- 3 to 4 labelled c(0)
- 4 to 2 labelled f(0)
- 1 to 2 labelled d(0)
- 1 to 5 labelled f(0)
- 5 to 6 labelled d(0)
- 6 to 2 labelled f(0)
- 1 to 7 labelled g(0)
- 7 to 8 labelled d(0)
- 8 to 2 labelled 0(0)
- 1 to 2 labelled c(0)
- 1 to 9 labelled g(0)
- 9 to 10 labelled d(0)
- 10 to 2 labelled 1(0)
- 4 to 11 labelled f(1)
- 11 to 12 labelled d(1)
- 12 to 2 labelled f(1)
- 4 to 13 labelled f(1)
- 13 to 14 labelled c(1)
- 14 to 2 labelled f(1)
- 1 to 11 labelled f(1)
- 1 to 13 labelled f(1)
- 6 to 11 labelled f(1)
- 6 to 13 labelled f(1)
- 1 to 15 labelled g(1)
- 15 to 16 labelled d(1)
- 16 to 2 labelled 0(1)
- 1 to 2 labelled 0(1)
- 1 to 2 labelled f(1)
- 1 to 2 labelled g(1)
- 16 to 2 labelled 1(1)
- 1 to 2 labelled 1(1)
- 1 to 2 labelled c(1)
- 1 to 2 labelled d(1)
- 12 to 11 labelled f(1)
- 12 to 13 labelled f(1)
- 14 to 11 labelled f(1)
- 14 to 13 labelled f(1)
- 1 to 2 labelled 0(2)
- 1 to 2 labelled 1(2)
Termination of R successfully shown.
Duration:
0:00 minutes