Term Rewriting System R:
[X]
f(a) -> f(c(a))
f(c(X)) -> X
f(c(a)) -> f(d(b))
f(a) -> f(d(a))
f(d(X)) -> X
f(c(b)) -> f(d(a))
e(g(X)) -> e(X)
Innermost Termination of R to be shown.
TRS
↳RFC Match Bounds
Termination could be shown with a Match Bound of 3.
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
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 f(0)
- 3 to 4 labelled d(0)
- 4 to 2 labelled a(0)
- 1 to 2 labelled c(0)
- 1 to 2 labelled g(0)
- 1 to 5 labelled f(0)
- 5 to 6 labelled c(0)
- 6 to 2 labelled a(0)
- 1 to 2 labelled a(0)
- 1 to 2 labelled f(0)
- 1 to 2 labelled e(0)
- 1 to 2 labelled d(0)
- 1 to 2 labelled b(0)
- 1 to 7 labelled f(0)
- 7 to 8 labelled d(0)
- 8 to 2 labelled b(0)
- 1 to 2 labelled c(1)
- 1 to 2 labelled e(1)
- 1 to 2 labelled b(1)
- 1 to 2 labelled g(1)
- 1 to 2 labelled a(1)
- 1 to 9 labelled f(1)
- 9 to 10 labelled c(1)
- 10 to 2 labelled a(1)
- 1 to 2 labelled d(1)
- 1 to 11 labelled f(1)
- 11 to 12 labelled d(1)
- 12 to 2 labelled b(1)
- 12 to 2 labelled a(1)
- 1 to 2 labelled f(1)
- 1 to 2 labelled b(2)
- 1 to 2 labelled a(2)
- 1 to 13 labelled f(2)
- 13 to 14 labelled d(2)
- 14 to 2 labelled b(2)
- 1 to 2 labelled b(3)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes