YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(b(b(x1))))) -> b(b(b(b(b(a(a(a(a(a(x1)))))))))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(a(a(a(x1))))) -> a(a(a(a(a(b(b(b(b(b(x1)))))))))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) 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(x1))))) -> a(a(a(a(a(b(b(b(b(b(x1)))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 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, 152, 153, 154, 155, 156, 157, 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, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211 Node 111 is start node and node 112 is final node. Those nodes are connected through the following edges: * 111 to 113 labelled a_1(0)* 112 to 112 labelled #_1(0)* 113 to 114 labelled a_1(0)* 114 to 115 labelled a_1(0)* 115 to 116 labelled a_1(0)* 116 to 117 labelled a_1(0)* 117 to 118 labelled b_1(0)* 117 to 140 labelled a_1(1)* 118 to 119 labelled b_1(0)* 118 to 131 labelled a_1(1)* 119 to 120 labelled b_1(0)* 119 to 131 labelled a_1(1)* 120 to 121 labelled b_1(0)* 120 to 122 labelled a_1(1)* 121 to 112 labelled b_1(0)* 121 to 122 labelled a_1(1)* 122 to 123 labelled a_1(1)* 123 to 124 labelled a_1(1)* 124 to 125 labelled a_1(1)* 125 to 126 labelled a_1(1)* 126 to 127 labelled b_1(1)* 126 to 158 labelled a_1(2)* 127 to 128 labelled b_1(1)* 127 to 149 labelled a_1(2)* 128 to 129 labelled b_1(1)* 128 to 149 labelled a_1(2)* 129 to 130 labelled b_1(1)* 129 to 122 labelled a_1(1)* 130 to 112 labelled b_1(1)* 130 to 122 labelled a_1(1)* 131 to 132 labelled a_1(1)* 132 to 133 labelled a_1(1)* 133 to 134 labelled a_1(1)* 134 to 135 labelled a_1(1)* 135 to 136 labelled b_1(1)* 136 to 137 labelled b_1(1)* 136 to 176 labelled a_1(2)* 137 to 138 labelled b_1(1)* 138 to 139 labelled b_1(1)* 138 to 167 labelled a_1(2)* 139 to 124 labelled b_1(1)* 140 to 141 labelled a_1(1)* 141 to 142 labelled a_1(1)* 142 to 143 labelled a_1(1)* 143 to 144 labelled a_1(1)* 144 to 145 labelled b_1(1)* 145 to 146 labelled b_1(1)* 146 to 147 labelled b_1(1)* 147 to 148 labelled b_1(1)* 148 to 133 labelled b_1(1)* 149 to 150 labelled a_1(2)* 150 to 151 labelled a_1(2)* 151 to 152 labelled a_1(2)* 152 to 153 labelled a_1(2)* 153 to 154 labelled b_1(2)* 154 to 155 labelled b_1(2)* 154 to 185 labelled a_1(3)* 155 to 156 labelled b_1(2)* 156 to 157 labelled b_1(2)* 156 to 167 labelled a_1(2)* 157 to 124 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)* 164 to 165 labelled b_1(2)* 165 to 166 labelled b_1(2)* 166 to 151 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)* 172 to 203 labelled a_1(3)* 173 to 174 labelled b_1(2)* 174 to 175 labelled b_1(2)* 174 to 194 labelled a_1(3)* 175 to 158 labelled b_1(2)* 176 to 177 labelled a_1(2)* 177 to 178 labelled a_1(2)* 178 to 179 labelled a_1(2)* 179 to 180 labelled a_1(2)* 180 to 181 labelled b_1(2)* 181 to 182 labelled b_1(2)* 182 to 183 labelled b_1(2)* 183 to 184 labelled b_1(2)* 184 to 169 labelled b_1(2)* 185 to 186 labelled a_1(3)* 186 to 187 labelled a_1(3)* 187 to 188 labelled a_1(3)* 188 to 189 labelled a_1(3)* 189 to 190 labelled b_1(3)* 190 to 191 labelled b_1(3)* 191 to 192 labelled b_1(3)* 192 to 193 labelled b_1(3)* 193 to 169 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 161 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) ---------------------------------------- (4) YES