Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
Q is empty.
Termination of the TRS R could be shown with a Match Bound [6,7] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 7, 6, 5, 4, 3, 12, 11, 10, 9, 8, 17, 16, 15, 14, 13, 22, 21, 20, 19, 18, 27, 26, 25, 24, 23, 32, 31, 30, 29, 28, 37, 36, 35, 34, 33, 42, 41, 40, 39, 38
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled s0_1(0)
- 2 to 2 labelled #_1(0)
- 7 to 2 labelled s1_1(0)
- 7 to 8 labelled s0_1(1)
- 6 to 7 labelled s1_1(0)
- 6 to 8 labelled s0_1(1)
- 5 to 6 labelled s1_1(0)
- 5 to 13 labelled s0_1(1)
- 4 to 5 labelled s0_1(0)
- 3 to 4 labelled s0_1(0)
- 12 to 2 labelled s1_1(1)
- 12 to 8 labelled s0_1(1)
- 11 to 12 labelled s1_1(1)
- 11 to 8 labelled s0_1(1)
- 10 to 11 labelled s1_1(1)
- 10 to 18 labelled s0_1(2)
- 9 to 10 labelled s0_1(1)
- 8 to 9 labelled s0_1(1)
- 17 to 9 labelled s1_1(1)
- 16 to 17 labelled s1_1(1)
- 16 to 23 labelled s0_1(2)
- 15 to 16 labelled s1_1(1)
- 14 to 15 labelled s0_1(1)
- 13 to 14 labelled s0_1(1)
- 22 to 9 labelled s1_1(2)
- 21 to 22 labelled s1_1(2)
- 21 to 23 labelled s0_1(2)
- 20 to 21 labelled s1_1(2)
- 19 to 20 labelled s0_1(2)
- 18 to 19 labelled s0_1(2)
- 27 to 18 labelled s1_1(2)
- 26 to 27 labelled s1_1(2)
- 26 to 28 labelled s0_1(3)
- 25 to 26 labelled s1_1(2)
- 24 to 25 labelled s0_1(2)
- 23 to 24 labelled s0_1(2)
- 32 to 20 labelled s1_1(3)
- 32 to 33 labelled s0_1(3)
- 31 to 32 labelled s1_1(3)
- 30 to 31 labelled s1_1(3)
- 30 to 38 labelled s0_1(4)
- 29 to 30 labelled s0_1(3)
- 28 to 29 labelled s0_1(3)
- 37 to 24 labelled s1_1(3)
- 36 to 37 labelled s1_1(3)
- 35 to 36 labelled s1_1(3)
- 34 to 35 labelled s0_1(3)
- 33 to 34 labelled s0_1(3)
- 42 to 34 labelled s1_1(4)
- 41 to 42 labelled s1_1(4)
- 40 to 41 labelled s1_1(4)
- 39 to 40 labelled s0_1(4)
- 38 to 39 labelled s0_1(4)