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:
a(a(a(b(b(x1))))) → b(b(b(b(b(a(a(a(a(a(x1))))))))))
Q is empty.
↳ QTRS
↳ RFCMatchBoundsTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(b(b(x1))))) → b(b(b(b(b(a(a(a(a(a(x1))))))))))
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:
a(a(a(b(b(x1))))) → b(b(b(b(b(a(a(a(a(a(x1))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 6, 7, 5, 4, 3, 11, 10, 9, 8, 15, 16, 14, 13, 12, 20, 19, 18, 17, 24, 25, 23, 22, 21, 29, 28, 27, 26, 33, 34, 32, 31, 30, 38, 37, 36, 35, 42, 43, 41, 40, 39, 47, 46, 45, 44, 51, 52, 50, 49, 48, 56, 55, 54, 53, 60, 61, 59, 58, 57, 65, 64, 63, 62, 69, 70, 68, 67, 66, 74, 73, 72, 71, 78, 79, 77, 76, 75, 83, 82, 81, 80, 92, 91, 90, 89, 88, 87, 86, 85, 84, 96, 97, 95, 94, 93, 101, 100, 99, 98, 115, 114, 113, 112, 111, 110, 109, 108, 107
Node 1 is start node and node 2 is final node.
Those nodes are connect through the following edges:
- 1 to 3 labelled b_1(0)
- 2 to 2 labelled #_1(0)
- 6 to 7 labelled b_1(0)
- 7 to 8 labelled a_1(0)
- 7 to 21 labelled b_1(1)
- 5 to 6 labelled b_1(0)
- 4 to 5 labelled b_1(0)
- 3 to 4 labelled b_1(0)
- 11 to 2 labelled a_1(0)
- 11 to 12 labelled b_1(1)
- 10 to 11 labelled a_1(0)
- 10 to 12 labelled b_1(1)
- 9 to 10 labelled a_1(0)
- 9 to 12 labelled b_1(1)
- 8 to 9 labelled a_1(0)
- 8 to 21 labelled b_1(1)
- 15 to 16 labelled b_1(1)
- 16 to 17 labelled a_1(1)
- 16 to 30 labelled b_1(2)
- 14 to 15 labelled b_1(1)
- 13 to 14 labelled b_1(1)
- 12 to 13 labelled b_1(1)
- 20 to 2 labelled a_1(1)
- 20 to 12 labelled b_1(1)
- 19 to 20 labelled a_1(1)
- 19 to 12 labelled b_1(1)
- 18 to 19 labelled a_1(1)
- 18 to 12 labelled b_1(1)
- 17 to 18 labelled a_1(1)
- 17 to 30 labelled b_1(2)
- 24 to 25 labelled b_1(1)
- 25 to 26 labelled a_1(1)
- 23 to 24 labelled b_1(1)
- 22 to 23 labelled b_1(1)
- 21 to 22 labelled b_1(1)
- 29 to 13 labelled a_1(1)
- 28 to 29 labelled a_1(1)
- 27 to 28 labelled a_1(1)
- 27 to 39 labelled b_1(2)
- 26 to 27 labelled a_1(1)
- 33 to 34 labelled b_1(2)
- 34 to 35 labelled a_1(2)
- 32 to 33 labelled b_1(2)
- 31 to 32 labelled b_1(2)
- 30 to 31 labelled b_1(2)
- 38 to 13 labelled a_1(2)
- 37 to 38 labelled a_1(2)
- 36 to 37 labelled a_1(2)
- 36 to 39 labelled b_1(2)
- 35 to 36 labelled a_1(2)
- 42 to 43 labelled b_1(2)
- 43 to 44 labelled a_1(2)
- 41 to 42 labelled b_1(2)
- 40 to 41 labelled b_1(2)
- 39 to 40 labelled b_1(2)
- 47 to 15 labelled a_1(2)
- 46 to 47 labelled a_1(2)
- 45 to 46 labelled a_1(2)
- 45 to 48 labelled b_1(2)
- 44 to 45 labelled a_1(2)
- 51 to 52 labelled b_1(2)
- 52 to 53 labelled a_1(2)
- 50 to 51 labelled b_1(2)
- 49 to 50 labelled b_1(2)
- 48 to 49 labelled b_1(2)
- 56 to 30 labelled a_1(2)
- 55 to 56 labelled a_1(2)
- 54 to 55 labelled a_1(2)
- 54 to 57 labelled b_1(3)
- 53 to 54 labelled a_1(2)
- 60 to 61 labelled b_1(3)
- 61 to 62 labelled a_1(3)
- 59 to 60 labelled b_1(3)
- 58 to 59 labelled b_1(3)
- 57 to 58 labelled b_1(3)
- 65 to 32 labelled a_1(3)
- 64 to 65 labelled a_1(3)
- 63 to 64 labelled a_1(3)
- 63 to 66 labelled b_1(3)
- 62 to 63 labelled a_1(3)
- 69 to 70 labelled b_1(3)
- 70 to 71 labelled a_1(3)
- 68 to 69 labelled b_1(3)
- 67 to 68 labelled b_1(3)
- 66 to 67 labelled b_1(3)
- 74 to 34 labelled a_1(3)
- 74 to 75 labelled b_1(3)
- 73 to 74 labelled a_1(3)
- 72 to 73 labelled a_1(3)
- 71 to 72 labelled a_1(3)
- 71 to 84 labelled b_1(4)
- 78 to 79 labelled b_1(3)
- 79 to 80 labelled a_1(3)
- 77 to 78 labelled b_1(3)
- 76 to 77 labelled b_1(3)
- 75 to 76 labelled b_1(3)
- 83 to 40 labelled a_1(3)
- 82 to 83 labelled a_1(3)
- 81 to 82 labelled a_1(3)
- 81 to 93 labelled b_1(3)
- 80 to 81 labelled a_1(3)
- 92 to 76 labelled a_1(4)
- 91 to 92 labelled a_1(4)
- 90 to 91 labelled a_1(4)
- 90 to 107 labelled b_1(4)
- 89 to 90 labelled a_1(4)
- 88 to 89 labelled a_1(4)
- 87 to 88 labelled b_1(4)
- 86 to 87 labelled b_1(4)
- 85 to 86 labelled b_1(4)
- 84 to 85 labelled b_1(4)
- 96 to 97 labelled b_1(3)
- 97 to 98 labelled a_1(3)
- 95 to 96 labelled b_1(3)
- 94 to 95 labelled b_1(3)
- 93 to 94 labelled b_1(3)
- 101 to 42 labelled a_1(3)
- 100 to 101 labelled a_1(3)
- 99 to 100 labelled a_1(3)
- 98 to 99 labelled a_1(3)
- 115 to 78 labelled a_1(4)
- 114 to 115 labelled a_1(4)
- 113 to 114 labelled a_1(4)
- 112 to 113 labelled a_1(4)
- 111 to 112 labelled a_1(4)
- 110 to 111 labelled b_1(4)
- 109 to 110 labelled b_1(4)
- 108 to 109 labelled b_1(4)
- 107 to 108 labelled b_1(4)