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)
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, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32
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 22 labelled f(0)
- 22 to 23 labelled d(0)
- 23 to 2 labelled f(0)
- 1 to 2 labelled c(0)
- 1 to 24 labelled g(0)
- 24 to 25 labelled d(0)
- 25 to 2 labelled 1(0)
- 7 to 26 labelled f(1)
- 26 to 27 labelled d(1)
- 27 to 2 labelled f(1)
- 7 to 28 labelled f(1)
- 28 to 29 labelled c(1)
- 29 to 2 labelled f(1)
- 23 to 26 labelled f(1)
- 23 to 28 labelled f(1)
- 1 to 30 labelled g(1)
- 30 to 31 labelled d(1)
- 31 to 32 labelled h(1)
- 32 to 2 labelled 0(1)
- 1 to 2 labelled 0(1)
- 1 to 2 labelled f(1)
- 1 to 2 labelled g(1)
- 31 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)
- 1 to 26 labelled f(1)
- 1 to 28 labelled f(1)
- 1 to 5 labelled h(1)
- 27 to 26 labelled f(1)
- 27 to 28 labelled f(1)
- 29 to 26 labelled f(1)
- 29 to 28 labelled f(1)
- 1 to 2 labelled 1(2)
- 1 to 32 labelled h(2)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes