(1) 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(a(a(b(b(b(x)))))) → b(b(b(b(a(a(a(a(x))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 40, 41, 42, 43, 44, 45, 46, 47, 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
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 40 labelled b_1(0)
- 3 to 3 labelled #_1(0)
- 40 to 41 labelled b_1(0)
- 41 to 42 labelled b_1(0)
- 42 to 43 labelled b_1(0)
- 43 to 44 labelled a_1(0)
- 43 to 54 labelled b_1(1)
- 44 to 45 labelled a_1(0)
- 44 to 47 labelled b_1(1)
- 45 to 46 labelled a_1(0)
- 45 to 47 labelled b_1(1)
- 46 to 3 labelled a_1(0)
- 46 to 47 labelled b_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 61 labelled b_1(2)
- 51 to 52 labelled a_1(1)
- 51 to 47 labelled b_1(1)
- 52 to 53 labelled a_1(1)
- 52 to 47 labelled b_1(1)
- 53 to 3 labelled a_1(1)
- 53 to 47 labelled b_1(1)
- 54 to 55 labelled b_1(1)
- 55 to 56 labelled b_1(1)
- 56 to 57 labelled b_1(1)
- 57 to 58 labelled a_1(1)
- 58 to 59 labelled a_1(1)
- 58 to 68 labelled b_1(2)
- 59 to 60 labelled a_1(1)
- 60 to 49 labelled a_1(1)
- 61 to 62 labelled b_1(2)
- 62 to 63 labelled b_1(2)
- 63 to 64 labelled b_1(2)
- 64 to 65 labelled a_1(2)
- 65 to 66 labelled a_1(2)
- 65 to 68 labelled b_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 49 labelled a_1(2)
- 68 to 69 labelled b_1(2)
- 69 to 70 labelled b_1(2)
- 70 to 71 labelled b_1(2)
- 71 to 72 labelled a_1(2)
- 72 to 73 labelled a_1(2)
- 73 to 74 labelled a_1(2)
- 74 to 62 labelled a_1(2)