(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
b(a(a(b(a(b(a(x))))))) → a(a(b(a(b(b(a(a(b(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 3, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92
Node 2 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 2 to 21 labelled a_1(0)
- 3 to 3 labelled #_1(0)
- 21 to 22 labelled a_1(0)
- 22 to 23 labelled b_1(0)
- 23 to 24 labelled a_1(0)
- 24 to 25 labelled b_1(0)
- 24 to 53 labelled a_1(1)
- 25 to 26 labelled b_1(0)
- 25 to 29 labelled a_1(1)
- 26 to 27 labelled a_1(0)
- 27 to 28 labelled a_1(0)
- 28 to 3 labelled b_1(0)
- 28 to 29 labelled a_1(1)
- 29 to 30 labelled a_1(1)
- 30 to 31 labelled b_1(1)
- 31 to 48 labelled a_1(1)
- 48 to 49 labelled b_1(1)
- 48 to 61 labelled a_1(2)
- 49 to 50 labelled b_1(1)
- 49 to 29 labelled a_1(1)
- 50 to 51 labelled a_1(1)
- 51 to 52 labelled a_1(1)
- 52 to 3 labelled b_1(1)
- 52 to 29 labelled a_1(1)
- 53 to 54 labelled a_1(1)
- 54 to 55 labelled b_1(1)
- 55 to 56 labelled a_1(1)
- 56 to 57 labelled b_1(1)
- 57 to 58 labelled b_1(1)
- 57 to 69 labelled a_1(2)
- 58 to 59 labelled a_1(1)
- 59 to 60 labelled a_1(1)
- 60 to 29 labelled b_1(1)
- 61 to 62 labelled a_1(2)
- 62 to 63 labelled b_1(2)
- 63 to 64 labelled a_1(2)
- 64 to 65 labelled b_1(2)
- 65 to 66 labelled b_1(2)
- 65 to 69 labelled a_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 68 labelled a_1(2)
- 68 to 29 labelled b_1(2)
- 69 to 70 labelled a_1(2)
- 70 to 71 labelled b_1(2)
- 71 to 72 labelled a_1(2)
- 72 to 73 labelled b_1(2)
- 73 to 74 labelled b_1(2)
- 74 to 75 labelled a_1(2)
- 75 to 76 labelled a_1(2)
- 76 to 48 labelled b_1(2)
- 76 to 77 labelled a_1(3)
- 77 to 78 labelled a_1(3)
- 78 to 79 labelled b_1(3)
- 79 to 80 labelled a_1(3)
- 80 to 81 labelled b_1(3)
- 81 to 82 labelled b_1(3)
- 81 to 85 labelled a_1(3)
- 82 to 83 labelled a_1(3)
- 83 to 84 labelled a_1(3)
- 84 to 69 labelled b_1(3)
- 85 to 86 labelled a_1(3)
- 86 to 87 labelled b_1(3)
- 87 to 88 labelled a_1(3)
- 88 to 89 labelled b_1(3)
- 89 to 90 labelled b_1(3)
- 90 to 91 labelled a_1(3)
- 91 to 92 labelled a_1(3)
- 92 to 72 labelled b_1(3)