(5) 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:
a(b(b(a(b(a(b(b(b(x))))))))) → b(a(b(a(b(b(b(a(b(a(b(b(x))))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88
Node 31 is start node and node 32 is final node.
Those nodes are connected through the following edges:
- 31 to 33 labelled b_1(0)
- 32 to 32 labelled #_1(0)
- 33 to 34 labelled a_1(0)
- 34 to 35 labelled b_1(0)
- 35 to 36 labelled a_1(0)
- 36 to 37 labelled b_1(0)
- 37 to 38 labelled b_1(0)
- 38 to 39 labelled b_1(0)
- 39 to 40 labelled a_1(0)
- 39 to 67 labelled b_1(1)
- 40 to 41 labelled b_1(0)
- 41 to 42 labelled a_1(0)
- 41 to 44 labelled b_1(1)
- 42 to 43 labelled b_1(0)
- 43 to 32 labelled b_1(0)
- 44 to 45 labelled a_1(1)
- 45 to 46 labelled b_1(1)
- 46 to 47 labelled a_1(1)
- 47 to 48 labelled b_1(1)
- 48 to 49 labelled b_1(1)
- 49 to 50 labelled b_1(1)
- 50 to 51 labelled a_1(1)
- 50 to 78 labelled b_1(2)
- 51 to 52 labelled b_1(1)
- 52 to 53 labelled a_1(1)
- 52 to 44 labelled b_1(1)
- 53 to 54 labelled b_1(1)
- 54 to 32 labelled b_1(1)
- 67 to 68 labelled a_1(1)
- 68 to 69 labelled b_1(1)
- 69 to 70 labelled a_1(1)
- 70 to 71 labelled b_1(1)
- 71 to 72 labelled b_1(1)
- 72 to 73 labelled b_1(1)
- 73 to 74 labelled a_1(1)
- 73 to 78 labelled b_1(2)
- 74 to 75 labelled b_1(1)
- 75 to 76 labelled a_1(1)
- 75 to 44 labelled b_1(1)
- 76 to 77 labelled b_1(1)
- 77 to 50 labelled b_1(1)
- 78 to 79 labelled a_1(2)
- 79 to 80 labelled b_1(2)
- 80 to 81 labelled a_1(2)
- 81 to 82 labelled b_1(2)
- 82 to 83 labelled b_1(2)
- 83 to 84 labelled b_1(2)
- 84 to 85 labelled a_1(2)
- 84 to 78 labelled b_1(2)
- 85 to 86 labelled b_1(2)
- 86 to 87 labelled a_1(2)
- 86 to 44 labelled b_1(1)
- 87 to 88 labelled b_1(2)
- 88 to 50 labelled b_1(2)