Term Rewriting System R:
[x]
d(x) -> e(u(x))
d(u(x)) -> c(x)
c(u(x)) -> b(x)
v(e(x)) -> x
b(u(x)) -> a(e(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
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 d(0)
- 1 to 3 labelled a(0)
- 3 to 2 labelled e(0)
- 1 to 2 labelled c(0)
- 1 to 4 labelled e(0)
- 4 to 2 labelled u(0)
- 1 to 2 labelled e(0)
- 1 to 2 labelled b(0)
- 1 to 2 labelled a(0)
- 1 to 2 labelled u(0)
- 1 to 2 labelled v(0)
- 1 to 5 labelled e(1)
- 5 to 2 labelled u(1)
- 1 to 2 labelled e(1)
- 1 to 2 labelled b(1)
- 1 to 2 labelled c(1)
- 1 to 2 labelled u(1)
- 1 to 2 labelled d(1)
- 1 to 2 labelled v(1)
- 1 to 2 labelled a(1)
- 1 to 1 labelled a(1)
- 1 to 6 labelled e(2)
- 6 to 2 labelled u(2)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes