Term Rewriting System R:
[x]
s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))
Innermost Termination of R to be shown.
TRS
↳RFC Match Bounds
Termination could be shown with a Match Bound of 4.
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, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48
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 s0(0)
- 3 to 4 labelled s0(0)
- 4 to 5 labelled s0(0)
- 5 to 6 labelled s1(0)
- 6 to 7 labelled s1(0)
- 7 to 2 labelled s1(0)
- 7 to 8 labelled s0(1)
- 8 to 9 labelled s0(1)
- 9 to 10 labelled s0(1)
- 10 to 11 labelled s1(1)
- 11 to 12 labelled s1(1)
- 12 to 2 labelled s1(1)
- 6 to 8 labelled s0(1)
- 12 to 8 labelled s0(1)
- 11 to 8 labelled s0(1)
- 5 to 19 labelled s0(1)
- 19 to 20 labelled s0(1)
- 20 to 21 labelled s0(1)
- 21 to 22 labelled s1(1)
- 22 to 23 labelled s1(1)
- 23 to 9 labelled s1(1)
- 10 to 24 labelled s0(2)
- 24 to 25 labelled s0(2)
- 25 to 26 labelled s0(2)
- 26 to 27 labelled s1(2)
- 27 to 28 labelled s1(2)
- 28 to 9 labelled s1(2)
- 22 to 29 labelled s0(2)
- 29 to 30 labelled s0(2)
- 30 to 31 labelled s0(2)
- 31 to 32 labelled s1(2)
- 32 to 33 labelled s1(2)
- 33 to 24 labelled s1(2)
- 27 to 29 labelled s0(2)
- 32 to 34 labelled s0(3)
- 34 to 35 labelled s0(3)
- 35 to 36 labelled s0(3)
- 36 to 37 labelled s1(3)
- 37 to 38 labelled s1(3)
- 38 to 26 labelled s1(3)
- 38 to 39 labelled s0(3)
- 39 to 40 labelled s0(3)
- 40 to 41 labelled s0(3)
- 41 to 42 labelled s1(3)
- 42 to 43 labelled s1(3)
- 43 to 30 labelled s1(3)
- 36 to 44 labelled s0(4)
- 44 to 45 labelled s0(4)
- 45 to 46 labelled s0(4)
- 46 to 47 labelled s1(4)
- 47 to 48 labelled s1(4)
- 48 to 40 labelled s1(4)
Innermost Termination of R successfully shown.
Duration:
0:00 minutes