(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(a(b(b(x)))) → b(b(b(a(a(a(x))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 40 labelled b_1(0)
- 2 to 2 labelled #_1(0)
- 40 to 41 labelled b_1(0)
- 41 to 42 labelled b_1(0)
- 42 to 43 labelled a_1(0)
- 42 to 50 labelled b_1(1)
- 43 to 44 labelled a_1(0)
- 43 to 45 labelled b_1(1)
- 44 to 2 labelled a_1(0)
- 44 to 45 labelled b_1(1)
- 45 to 46 labelled b_1(1)
- 46 to 47 labelled b_1(1)
- 47 to 48 labelled a_1(1)
- 47 to 55 labelled b_1(2)
- 48 to 49 labelled a_1(1)
- 48 to 45 labelled b_1(1)
- 49 to 2 labelled a_1(1)
- 49 to 45 labelled b_1(1)
- 50 to 51 labelled b_1(1)
- 51 to 52 labelled b_1(1)
- 52 to 53 labelled a_1(1)
- 53 to 54 labelled a_1(1)
- 53 to 65 labelled b_1(2)
- 54 to 46 labelled a_1(1)
- 55 to 56 labelled b_1(2)
- 56 to 57 labelled b_1(2)
- 57 to 58 labelled a_1(2)
- 58 to 59 labelled a_1(2)
- 58 to 65 labelled b_1(2)
- 59 to 46 labelled a_1(2)
- 65 to 66 labelled b_1(2)
- 66 to 67 labelled b_1(2)
- 67 to 68 labelled a_1(2)
- 68 to 69 labelled a_1(2)
- 68 to 70 labelled b_1(3)
- 69 to 55 labelled a_1(2)
- 70 to 71 labelled b_1(3)
- 71 to 72 labelled b_1(3)
- 72 to 73 labelled a_1(3)
- 72 to 80 labelled b_1(4)
- 73 to 74 labelled a_1(3)
- 74 to 57 labelled a_1(3)
- 74 to 75 labelled b_1(3)
- 75 to 76 labelled b_1(3)
- 76 to 77 labelled b_1(3)
- 77 to 78 labelled a_1(3)
- 78 to 79 labelled a_1(3)
- 79 to 66 labelled a_1(3)
- 80 to 81 labelled b_1(4)
- 81 to 82 labelled b_1(4)
- 82 to 83 labelled a_1(4)
- 83 to 84 labelled a_1(4)
- 84 to 76 labelled a_1(4)