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)
Innermost 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:
21, 22, 23, 24, 25, 26, 27, 28
Node 21 is start node and node 22 is final node.
Those nodes are connect through the following edges:
- 22 to 22 labelled #(0)
- 21 to 23 labelled u(0)
- 23 to 22 labelled v(0)
- 21 to 22 labelled b(0)
- 21 to 24 labelled u(0)
- 24 to 22 labelled w(0)
- 21 to 25 labelled u(0)
- 25 to 26 labelled b(0)
- 26 to 22 labelled d(0)
- 21 to 22 labelled c(0)
- 23 to 27 labelled u(1)
- 27 to 28 labelled b(1)
- 28 to 22 labelled d(1)
- 23 to 22 labelled b(1)
- 27 to 22 labelled v(1)
- 24 to 22 labelled b(1)
- 24 to 27 labelled u(1)
- 27 to 22 labelled w(1)
- 21 to 22 labelled b(1)
- 27 to 22 labelled b(1)
- 27 to 27 labelled u(1)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes