(3) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
b(a(b(a(a(b(x)))))) → a(b(a(b(a(b(a(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 6, 7, 8, 9, 10, 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
Node 2 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 2 to 5 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 5 to 6 labelled b_1(0)
- 5 to 59 labelled a_1(1)
- 6 to 7 labelled a_1(0)
- 7 to 8 labelled b_1(0)
- 7 to 53 labelled a_1(1)
- 8 to 9 labelled a_1(0)
- 9 to 10 labelled b_1(0)
- 9 to 53 labelled a_1(1)
- 10 to 4 labelled a_1(0)
- 53 to 54 labelled b_1(1)
- 53 to 65 labelled a_1(2)
- 54 to 55 labelled a_1(1)
- 55 to 56 labelled b_1(1)
- 55 to 53 labelled a_1(1)
- 56 to 57 labelled a_1(1)
- 57 to 58 labelled b_1(1)
- 57 to 53 labelled a_1(1)
- 58 to 4 labelled a_1(1)
- 59 to 60 labelled b_1(1)
- 60 to 61 labelled a_1(1)
- 61 to 62 labelled b_1(1)
- 61 to 71 labelled a_1(2)
- 62 to 63 labelled a_1(1)
- 63 to 64 labelled b_1(1)
- 64 to 54 labelled a_1(1)
- 65 to 66 labelled b_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 68 labelled b_1(2)
- 67 to 71 labelled a_1(2)
- 68 to 69 labelled a_1(2)
- 69 to 70 labelled b_1(2)
- 70 to 54 labelled a_1(2)
- 71 to 72 labelled b_1(2)
- 72 to 73 labelled a_1(2)
- 73 to 74 labelled b_1(2)
- 73 to 77 labelled a_1(2)
- 74 to 75 labelled a_1(2)
- 75 to 76 labelled b_1(2)
- 76 to 56 labelled a_1(2)
- 77 to 78 labelled b_1(2)
- 78 to 79 labelled a_1(2)
- 79 to 80 labelled b_1(2)
- 79 to 53 labelled a_1(1)
- 80 to 81 labelled a_1(2)
- 81 to 82 labelled b_1(2)
- 82 to 58 labelled a_1(2)