(3) 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(b(a(a(a(x))))) → a(a(a(a(a(b(b(b(b(b(x))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 50, 51, 52, 53, 54, 57, 59, 62, 64, 77, 78, 79, 80, 81, 82, 83, 84, 85, 95, 96, 97, 98, 99, 100, 101, 102, 103, 113, 114, 115, 116, 117, 118, 119, 120, 121, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211
Node 3 is start node and node 4 is final node.
Those nodes are connected through the following edges:
- 3 to 14 labelled a_1(0)
- 4 to 4 labelled #_1(0)
- 14 to 15 labelled a_1(0)
- 15 to 16 labelled a_1(0)
- 16 to 17 labelled a_1(0)
- 17 to 18 labelled a_1(0)
- 18 to 19 labelled b_1(0)
- 18 to 77 labelled a_1(1)
- 19 to 20 labelled b_1(0)
- 19 to 50 labelled a_1(1)
- 20 to 21 labelled b_1(0)
- 20 to 50 labelled a_1(1)
- 21 to 22 labelled b_1(0)
- 21 to 32 labelled a_1(1)
- 22 to 4 labelled b_1(0)
- 22 to 32 labelled a_1(1)
- 32 to 33 labelled a_1(1)
- 33 to 34 labelled a_1(1)
- 34 to 35 labelled a_1(1)
- 35 to 36 labelled a_1(1)
- 36 to 37 labelled b_1(1)
- 36 to 113 labelled a_1(2)
- 37 to 38 labelled b_1(1)
- 37 to 95 labelled a_1(2)
- 38 to 39 labelled b_1(1)
- 38 to 95 labelled a_1(2)
- 39 to 40 labelled b_1(1)
- 39 to 32 labelled a_1(1)
- 40 to 4 labelled b_1(1)
- 40 to 32 labelled a_1(1)
- 50 to 51 labelled a_1(1)
- 51 to 52 labelled a_1(1)
- 52 to 53 labelled a_1(1)
- 53 to 54 labelled a_1(1)
- 54 to 57 labelled b_1(1)
- 57 to 59 labelled b_1(1)
- 57 to 167 labelled a_1(2)
- 59 to 62 labelled b_1(1)
- 62 to 64 labelled b_1(1)
- 62 to 158 labelled a_1(2)
- 64 to 34 labelled b_1(1)
- 77 to 78 labelled a_1(1)
- 78 to 79 labelled a_1(1)
- 79 to 80 labelled a_1(1)
- 80 to 81 labelled a_1(1)
- 81 to 82 labelled b_1(1)
- 82 to 83 labelled b_1(1)
- 83 to 84 labelled b_1(1)
- 84 to 85 labelled b_1(1)
- 85 to 52 labelled b_1(1)
- 95 to 96 labelled a_1(2)
- 96 to 97 labelled a_1(2)
- 97 to 98 labelled a_1(2)
- 98 to 99 labelled a_1(2)
- 99 to 100 labelled b_1(2)
- 100 to 101 labelled b_1(2)
- 100 to 176 labelled a_1(3)
- 101 to 102 labelled b_1(2)
- 102 to 103 labelled b_1(2)
- 102 to 158 labelled a_1(2)
- 103 to 34 labelled b_1(2)
- 113 to 114 labelled a_1(2)
- 114 to 115 labelled a_1(2)
- 115 to 116 labelled a_1(2)
- 116 to 117 labelled a_1(2)
- 117 to 118 labelled b_1(2)
- 118 to 119 labelled b_1(2)
- 119 to 120 labelled b_1(2)
- 120 to 121 labelled b_1(2)
- 121 to 97 labelled b_1(2)
- 158 to 159 labelled a_1(2)
- 159 to 160 labelled a_1(2)
- 160 to 161 labelled a_1(2)
- 161 to 162 labelled a_1(2)
- 162 to 163 labelled b_1(2)
- 163 to 164 labelled b_1(2)
- 163 to 203 labelled a_1(3)
- 164 to 165 labelled b_1(2)
- 165 to 166 labelled b_1(2)
- 165 to 194 labelled a_1(3)
- 166 to 113 labelled b_1(2)
- 167 to 168 labelled a_1(2)
- 168 to 169 labelled a_1(2)
- 169 to 170 labelled a_1(2)
- 170 to 171 labelled a_1(2)
- 171 to 172 labelled b_1(2)
- 172 to 173 labelled b_1(2)
- 173 to 174 labelled b_1(2)
- 174 to 175 labelled b_1(2)
- 175 to 160 labelled b_1(2)
- 176 to 177 labelled a_1(3)
- 177 to 178 labelled a_1(3)
- 178 to 179 labelled a_1(3)
- 179 to 180 labelled a_1(3)
- 180 to 181 labelled b_1(3)
- 181 to 182 labelled b_1(3)
- 182 to 183 labelled b_1(3)
- 183 to 184 labelled b_1(3)
- 184 to 160 labelled b_1(3)
- 194 to 195 labelled a_1(3)
- 195 to 196 labelled a_1(3)
- 196 to 197 labelled a_1(3)
- 197 to 198 labelled a_1(3)
- 198 to 199 labelled b_1(3)
- 199 to 200 labelled b_1(3)
- 200 to 201 labelled b_1(3)
- 201 to 202 labelled b_1(3)
- 202 to 116 labelled b_1(3)
- 203 to 204 labelled a_1(3)
- 204 to 205 labelled a_1(3)
- 205 to 206 labelled a_1(3)
- 206 to 207 labelled a_1(3)
- 207 to 208 labelled b_1(3)
- 208 to 209 labelled b_1(3)
- 209 to 210 labelled b_1(3)
- 210 to 211 labelled b_1(3)
- 211 to 196 labelled b_1(3)