Term Rewriting System R:
[X]
f(f(X)) -> f(g(f(g(f(X)))))
f(g(f(X))) -> f(g(X))
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, 13
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 2 labelled g(0)
- 1 to 4 labelled f(0)
- 4 to 5 labelled g(0)
- 5 to 6 labelled f(0)
- 6 to 7 labelled g(0)
- 7 to 2 labelled f(0)
- 7 to 8 labelled f(1)
- 8 to 9 labelled g(1)
- 9 to 10 labelled f(1)
- 10 to 11 labelled g(1)
- 11 to 2 labelled f(1)
- 8 to 2 labelled g(1)
- 1 to 8 labelled f(1)
- 8 to 6 labelled g(1)
- 5 to 8 labelled f(1)
- 11 to 8 labelled f(1)
- 8 to 8 labelled g(1)
- 9 to 12 labelled f(2)
- 12 to 2 labelled g(2)
- 1 to 13 labelled f(2)
- 13 to 10 labelled g(2)
- 5 to 13 labelled f(2)
- 7 to 13 labelled f(2)
- 8 to 13 labelled g(1)
- 9 to 8 labelled f(1)
- 12 to 8 labelled g(2)
- 13 to 12 labelled g(2)
- 11 to 13 labelled f(2)
- 12 to 13 labelled g(2)
- 1 to 12 labelled f(2)
- 11 to 12 labelled f(2)
- 5 to 12 labelled f(2)
- 7 to 12 labelled f(2)
- 9 to 13 labelled f(2)
- 8 to 12 labelled g(1)
Termination of R successfully shown.
Duration:
0:00 minutes