(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:
a(b(a(a(b(x))))) → b(a(a(b(b(a(a(b(a(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 24, 25, 26, 27, 28, 37, 38, 39, 40, 41, 42, 43, 44, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 5 labelled b_1(0)
- 2 to 2 labelled #_1(0)
- 5 to 6 labelled a_1(0)
- 6 to 7 labelled a_1(0)
- 7 to 8 labelled b_1(0)
- 8 to 9 labelled b_1(0)
- 9 to 10 labelled a_1(0)
- 9 to 37 labelled b_1(1)
- 10 to 11 labelled a_1(0)
- 10 to 21 labelled b_1(1)
- 11 to 12 labelled b_1(0)
- 12 to 2 labelled a_1(0)
- 12 to 21 labelled b_1(1)
- 21 to 22 labelled a_1(1)
- 22 to 23 labelled a_1(1)
- 23 to 24 labelled b_1(1)
- 24 to 25 labelled b_1(1)
- 25 to 26 labelled a_1(1)
- 25 to 61 labelled b_1(2)
- 26 to 27 labelled a_1(1)
- 26 to 21 labelled b_1(1)
- 27 to 28 labelled b_1(1)
- 28 to 2 labelled a_1(1)
- 28 to 21 labelled b_1(1)
- 37 to 38 labelled a_1(1)
- 38 to 39 labelled a_1(1)
- 39 to 40 labelled b_1(1)
- 40 to 41 labelled b_1(1)
- 41 to 42 labelled a_1(1)
- 42 to 43 labelled a_1(1)
- 43 to 44 labelled b_1(1)
- 44 to 24 labelled a_1(1)
- 44 to 69 labelled b_1(2)
- 61 to 62 labelled a_1(2)
- 62 to 63 labelled a_1(2)
- 63 to 64 labelled b_1(2)
- 64 to 65 labelled b_1(2)
- 65 to 66 labelled a_1(2)
- 66 to 67 labelled a_1(2)
- 67 to 68 labelled b_1(2)
- 68 to 24 labelled a_1(2)
- 68 to 69 labelled b_1(2)
- 69 to 70 labelled a_1(2)
- 70 to 71 labelled a_1(2)
- 71 to 72 labelled b_1(2)
- 72 to 73 labelled b_1(2)
- 73 to 74 labelled a_1(2)
- 73 to 61 labelled b_1(2)
- 74 to 75 labelled a_1(2)
- 74 to 21 labelled b_1(1)
- 75 to 76 labelled b_1(2)
- 76 to 28 labelled a_1(2)
- 76 to 61 labelled b_1(2)