Term Rewriting System R:
[x]
a(c(d(x))) -> c(x)
u(b(d(d(x)))) -> b(x)
v(a(a(x))) -> u(v(x))
v(a(c(x))) -> u(b(d(x)))
v(c(x)) -> b(x)
w(a(a(x))) -> u(w(x))
w(a(c(x))) -> u(b(d(x)))
w(c(x)) -> b(x)
Termination of R to be shown.
TRS
↳RFC Match Bounds
Termination could be shown with a Match Bound of 1.
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
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 u(0)
- 3 to 2 labelled v(0)
- 1 to 2 labelled b(0)
- 1 to 4 labelled u(0)
- 4 to 2 labelled w(0)
- 1 to 5 labelled u(0)
- 5 to 6 labelled b(0)
- 6 to 2 labelled d(0)
- 1 to 2 labelled c(0)
- 4 to 2 labelled b(1)
- 4 to 7 labelled u(1)
- 7 to 8 labelled b(1)
- 8 to 2 labelled d(1)
- 7 to 2 labelled w(1)
- 3 to 7 labelled u(1)
- 3 to 2 labelled b(1)
- 7 to 2 labelled v(1)
- 1 to 2 labelled b(1)
- 7 to 7 labelled u(1)
- 7 to 2 labelled b(1)
Termination of R successfully shown.
Duration:
0:00 minutes