(3) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
The following rules were used to construct the certificate:
a(a(b(a(b(x))))) → b(a(b(a(b(a(a(a(x))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 4, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 40, 41, 42, 43, 44, 45, 46, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151
Node 1 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 1 to 19 labelled b_1(0)
- 4 to 4 labelled #_1(0)
- 19 to 20 labelled a_1(0)
- 20 to 21 labelled b_1(0)
- 21 to 22 labelled a_1(0)
- 22 to 23 labelled b_1(0)
- 23 to 24 labelled a_1(0)
- 23 to 40 labelled b_1(1)
- 24 to 25 labelled a_1(0)
- 24 to 26 labelled b_1(1)
- 25 to 4 labelled a_1(0)
- 25 to 26 labelled b_1(1)
- 26 to 27 labelled a_1(1)
- 27 to 28 labelled b_1(1)
- 28 to 29 labelled a_1(1)
- 29 to 30 labelled b_1(1)
- 30 to 31 labelled a_1(1)
- 30 to 61 labelled b_1(2)
- 31 to 32 labelled a_1(1)
- 31 to 26 labelled b_1(1)
- 32 to 4 labelled a_1(1)
- 32 to 26 labelled b_1(1)
- 40 to 41 labelled a_1(1)
- 41 to 42 labelled b_1(1)
- 42 to 43 labelled a_1(1)
- 43 to 44 labelled b_1(1)
- 44 to 45 labelled a_1(1)
- 44 to 82 labelled b_1(2)
- 45 to 46 labelled a_1(1)
- 46 to 28 labelled a_1(1)
- 46 to 68 labelled b_1(2)
- 61 to 62 labelled a_1(2)
- 62 to 63 labelled b_1(2)
- 63 to 64 labelled a_1(2)
- 64 to 65 labelled b_1(2)
- 65 to 66 labelled a_1(2)
- 65 to 103 labelled b_1(3)
- 66 to 67 labelled a_1(2)
- 67 to 28 labelled a_1(2)
- 67 to 68 labelled b_1(2)
- 68 to 69 labelled a_1(2)
- 69 to 70 labelled b_1(2)
- 70 to 71 labelled a_1(2)
- 71 to 72 labelled b_1(2)
- 72 to 73 labelled a_1(2)
- 72 to 110 labelled b_1(3)
- 73 to 74 labelled a_1(2)
- 74 to 26 labelled a_1(2)
- 74 to 89 labelled b_1(2)
- 82 to 83 labelled a_1(2)
- 83 to 84 labelled b_1(2)
- 84 to 85 labelled a_1(2)
- 85 to 86 labelled b_1(2)
- 86 to 87 labelled a_1(2)
- 87 to 88 labelled a_1(2)
- 88 to 70 labelled a_1(2)
- 89 to 90 labelled a_1(2)
- 90 to 91 labelled b_1(2)
- 91 to 92 labelled a_1(2)
- 92 to 93 labelled b_1(2)
- 93 to 94 labelled a_1(2)
- 93 to 117 labelled b_1(3)
- 94 to 95 labelled a_1(2)
- 94 to 117 labelled b_1(3)
- 95 to 30 labelled a_1(2)
- 95 to 61 labelled b_1(2)
- 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 109 labelled a_1(3)
- 109 to 70 labelled a_1(3)
- 110 to 111 labelled a_1(3)
- 111 to 112 labelled b_1(3)
- 112 to 113 labelled a_1(3)
- 113 to 114 labelled b_1(3)
- 114 to 115 labelled a_1(3)
- 114 to 131 labelled b_1(4)
- 115 to 116 labelled a_1(3)
- 116 to 91 labelled a_1(3)
- 116 to 124 labelled b_1(3)
- 117 to 118 labelled a_1(3)
- 118 to 119 labelled b_1(3)
- 119 to 120 labelled a_1(3)
- 120 to 121 labelled b_1(3)
- 121 to 122 labelled a_1(3)
- 122 to 123 labelled a_1(3)
- 123 to 63 labelled a_1(3)
- 124 to 125 labelled a_1(3)
- 125 to 126 labelled b_1(3)
- 126 to 127 labelled a_1(3)
- 127 to 128 labelled b_1(3)
- 128 to 129 labelled a_1(3)
- 128 to 145 labelled b_1(4)
- 129 to 130 labelled a_1(3)
- 130 to 117 labelled a_1(3)
- 130 to 138 labelled b_1(4)
- 131 to 132 labelled a_1(4)
- 132 to 133 labelled b_1(4)
- 133 to 134 labelled a_1(4)
- 134 to 135 labelled b_1(4)
- 135 to 136 labelled a_1(4)
- 136 to 137 labelled a_1(4)
- 137 to 126 labelled a_1(4)
- 138 to 139 labelled a_1(4)
- 139 to 140 labelled b_1(4)
- 140 to 141 labelled a_1(4)
- 141 to 142 labelled b_1(4)
- 142 to 143 labelled a_1(4)
- 143 to 144 labelled a_1(4)
- 144 to 121 labelled a_1(4)
- 145 to 146 labelled a_1(4)
- 146 to 147 labelled b_1(4)
- 147 to 148 labelled a_1(4)
- 148 to 149 labelled b_1(4)
- 149 to 150 labelled a_1(4)
- 150 to 151 labelled a_1(4)
- 151 to 140 labelled a_1(4)