Term Rewriting System R:
[X]
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e
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, 8, 9, 10, 11, 12
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 e(0)
- 1 to 3 labelled a(0)
- 3 to 4 labelled a(0)
- 4 to 5 labelled b(0)
- 5 to 6 labelled b(0)
- 6 to 7 labelled c(0)
- 7 to 2 labelled c(0)
- 6 to 7 labelled e(1)
- 7 to 2 labelled e(1)
- 5 to 6 labelled e(1)
- 4 to 5 labelled e(1)
- 1 to 3 labelled e(1)
- 3 to 4 labelled e(1)
- 7 to 8 labelled a(1)
- 8 to 9 labelled a(1)
- 9 to 10 labelled b(1)
- 10 to 11 labelled b(1)
- 11 to 12 labelled c(1)
- 12 to 2 labelled c(1)
- 11 to 12 labelled e(2)
- 9 to 10 labelled e(2)
- 7 to 8 labelled e(2)
- 10 to 11 labelled e(2)
- 12 to 2 labelled e(2)
- 8 to 9 labelled e(2)
- 12 to 8 labelled a(1)
- 12 to 8 labelled e(2)
Termination of R successfully shown.
Duration:
0:00 minutes