(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:
b(a(a(b(b(x))))) → a(a(b(b(b(a(a(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46
Node 1 is start node and node 3 is final node.
Those nodes are connected through the following edges:
- 1 to 5 labelled a_1(0)
- 3 to 3 labelled #_1(0)
- 5 to 6 labelled a_1(0)
- 6 to 7 labelled b_1(0)
- 6 to 29 labelled a_1(1)
- 7 to 8 labelled b_1(0)
- 7 to 23 labelled a_1(1)
- 8 to 9 labelled b_1(0)
- 8 to 17 labelled a_1(1)
- 9 to 10 labelled a_1(0)
- 10 to 3 labelled a_1(0)
- 17 to 18 labelled a_1(1)
- 18 to 19 labelled b_1(1)
- 18 to 41 labelled a_1(2)
- 19 to 20 labelled b_1(1)
- 19 to 35 labelled a_1(2)
- 20 to 21 labelled b_1(1)
- 20 to 17 labelled a_1(1)
- 21 to 22 labelled a_1(1)
- 22 to 3 labelled a_1(1)
- 23 to 24 labelled a_1(1)
- 24 to 25 labelled b_1(1)
- 25 to 26 labelled b_1(1)
- 26 to 27 labelled b_1(1)
- 27 to 28 labelled a_1(1)
- 28 to 20 labelled a_1(1)
- 29 to 30 labelled a_1(1)
- 30 to 31 labelled b_1(1)
- 31 to 32 labelled b_1(1)
- 32 to 33 labelled b_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 26 labelled a_1(1)
- 35 to 36 labelled a_1(2)
- 36 to 37 labelled b_1(2)
- 37 to 38 labelled b_1(2)
- 38 to 39 labelled b_1(2)
- 39 to 40 labelled a_1(2)
- 40 to 20 labelled a_1(2)
- 41 to 42 labelled a_1(2)
- 42 to 43 labelled b_1(2)
- 43 to 44 labelled b_1(2)
- 44 to 45 labelled b_1(2)
- 45 to 46 labelled a_1(2)
- 46 to 38 labelled a_1(2)