(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
The following rules were used to construct the certificate:
b(a(b(a(a(a(x)))))) → a(a(a(a(b(a(b(a(b(x)))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 13, 14, 15, 16, 17, 18, 19, 20, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108
Node 1 is start node and node 2 is final node.
Those nodes are connected through the following edges:
- 1 to 13 labelled a_1(0)
- 2 to 2 labelled #_1(0)
- 13 to 14 labelled a_1(0)
- 14 to 15 labelled a_1(0)
- 15 to 16 labelled a_1(0)
- 16 to 17 labelled b_1(0)
- 16 to 45 labelled a_1(1)
- 17 to 18 labelled a_1(0)
- 18 to 19 labelled b_1(0)
- 18 to 37 labelled a_1(1)
- 19 to 20 labelled a_1(0)
- 20 to 2 labelled b_1(0)
- 20 to 37 labelled a_1(1)
- 37 to 38 labelled a_1(1)
- 38 to 39 labelled a_1(1)
- 39 to 40 labelled a_1(1)
- 40 to 41 labelled b_1(1)
- 40 to 85 labelled a_1(2)
- 41 to 42 labelled a_1(1)
- 42 to 43 labelled b_1(1)
- 42 to 37 labelled a_1(1)
- 43 to 44 labelled a_1(1)
- 44 to 2 labelled b_1(1)
- 44 to 37 labelled a_1(1)
- 45 to 46 labelled a_1(1)
- 46 to 47 labelled a_1(1)
- 47 to 48 labelled a_1(1)
- 48 to 49 labelled b_1(1)
- 49 to 50 labelled a_1(1)
- 50 to 51 labelled b_1(1)
- 50 to 93 labelled a_1(2)
- 51 to 52 labelled a_1(1)
- 52 to 38 labelled b_1(1)
- 85 to 86 labelled a_1(2)
- 86 to 87 labelled a_1(2)
- 87 to 88 labelled a_1(2)
- 88 to 89 labelled b_1(2)
- 89 to 90 labelled a_1(2)
- 90 to 91 labelled b_1(2)
- 90 to 93 labelled a_1(2)
- 91 to 92 labelled a_1(2)
- 92 to 38 labelled b_1(2)
- 93 to 94 labelled a_1(2)
- 94 to 95 labelled a_1(2)
- 95 to 96 labelled a_1(2)
- 96 to 97 labelled b_1(2)
- 97 to 98 labelled a_1(2)
- 98 to 99 labelled b_1(2)
- 98 to 101 labelled a_1(3)
- 99 to 100 labelled a_1(2)
- 100 to 85 labelled b_1(2)
- 101 to 102 labelled a_1(3)
- 102 to 103 labelled a_1(3)
- 103 to 104 labelled a_1(3)
- 104 to 105 labelled b_1(3)
- 105 to 106 labelled a_1(3)
- 106 to 107 labelled b_1(3)
- 107 to 108 labelled a_1(3)
- 108 to 88 labelled b_1(3)