(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(x)))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58
Node 33 is start node and node 34 is final node.
Those nodes are connected through the following edges:
- 33 to 35 labelled b_1(0)
- 34 to 34 labelled #_1(0)
- 35 to 36 labelled a_1(0)
- 36 to 37 labelled a_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 47 labelled b_1(1)
- 40 to 34 labelled a_1(0)
- 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 45 labelled b_1(1)
- 45 to 46 labelled a_1(1)
- 45 to 53 labelled b_1(2)
- 46 to 34 labelled a_1(1)
- 46 to 41 labelled b_1(1)
- 47 to 48 labelled a_1(1)
- 48 to 49 labelled a_1(1)
- 49 to 50 labelled b_1(1)
- 50 to 51 labelled b_1(1)
- 51 to 52 labelled a_1(1)
- 51 to 53 labelled b_1(2)
- 52 to 44 labelled a_1(1)
- 52 to 41 labelled b_1(1)
- 53 to 54 labelled a_1(2)
- 54 to 55 labelled a_1(2)
- 55 to 56 labelled b_1(2)
- 56 to 57 labelled b_1(2)
- 57 to 58 labelled a_1(2)
- 57 to 53 labelled b_1(2)
- 58 to 44 labelled a_1(2)
- 58 to 41 labelled b_1(1)