YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) 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: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 153, 155, 157, 159, 161, 163, 165, 167, 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 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled 1_1(0)* 1 to 12 labelled 1_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled 2_1(0)* 4 to 5 labelled 1_1(0)* 5 to 6 labelled 1_1(0)* 6 to 7 labelled 0_1(0)* 6 to 47 labelled 1_1(1)* 6 to 65 labelled 1_1(1)* 7 to 8 labelled 1_1(0)* 8 to 9 labelled 2_1(0)* 9 to 10 labelled 0_1(0)* 9 to 24 labelled 1_1(1)* 9 to 33 labelled 1_1(1)* 10 to 11 labelled 1_1(0)* 11 to 2 labelled 2_1(0)* 12 to 13 labelled 2_1(0)* 13 to 14 labelled 1_1(0)* 14 to 15 labelled 1_1(0)* 15 to 16 labelled 0_1(0)* 15 to 110 labelled 1_1(1)* 15 to 119 labelled 1_1(1)* 16 to 17 labelled 1_1(0)* 17 to 18 labelled 2_1(0)* 18 to 19 labelled 0_1(0)* 18 to 47 labelled 1_1(1)* 18 to 65 labelled 1_1(1)* 19 to 20 labelled 1_1(0)* 20 to 21 labelled 2_1(0)* 21 to 22 labelled 0_1(0)* 21 to 24 labelled 1_1(1)* 21 to 33 labelled 1_1(1)* 22 to 23 labelled 1_1(0)* 23 to 2 labelled 2_1(0)* 24 to 25 labelled 2_1(1)* 25 to 26 labelled 1_1(1)* 26 to 27 labelled 1_1(1)* 27 to 28 labelled 0_1(1)* 27 to 132 labelled 1_1(2)* 27 to 153 labelled 1_1(2)* 28 to 29 labelled 1_1(1)* 29 to 30 labelled 2_1(1)* 30 to 31 labelled 0_1(1)* 30 to 24 labelled 1_1(1)* 30 to 33 labelled 1_1(1)* 31 to 32 labelled 1_1(1)* 32 to 2 labelled 2_1(1)* 33 to 34 labelled 2_1(1)* 34 to 35 labelled 1_1(1)* 35 to 36 labelled 1_1(1)* 36 to 37 labelled 0_1(1)* 36 to 173 labelled 1_1(2)* 36 to 182 labelled 1_1(2)* 37 to 38 labelled 1_1(1)* 38 to 39 labelled 2_1(1)* 39 to 40 labelled 0_1(1)* 39 to 132 labelled 1_1(2)* 39 to 153 labelled 1_1(2)* 40 to 41 labelled 1_1(1)* 41 to 42 labelled 2_1(1)* 42 to 43 labelled 0_1(1)* 42 to 24 labelled 1_1(1)* 42 to 33 labelled 1_1(1)* 43 to 44 labelled 1_1(1)* 44 to 2 labelled 2_1(1)* 47 to 48 labelled 2_1(1)* 48 to 49 labelled 1_1(1)* 49 to 50 labelled 1_1(1)* 50 to 51 labelled 0_1(1)* 51 to 52 labelled 1_1(1)* 52 to 53 labelled 2_1(1)* 53 to 54 labelled 0_1(1)* 54 to 55 labelled 1_1(1)* 55 to 24 labelled 2_1(1)* 55 to 33 labelled 2_1(1)* 65 to 66 labelled 2_1(1)* 66 to 67 labelled 1_1(1)* 67 to 68 labelled 1_1(1)* 68 to 69 labelled 0_1(1)* 69 to 70 labelled 1_1(1)* 70 to 71 labelled 2_1(1)* 71 to 72 labelled 0_1(1)* 72 to 73 labelled 1_1(1)* 73 to 74 labelled 2_1(1)* 74 to 75 labelled 0_1(1)* 75 to 76 labelled 1_1(1)* 76 to 24 labelled 2_1(1)* 76 to 33 labelled 2_1(1)* 110 to 111 labelled 2_1(1)* 111 to 112 labelled 1_1(1)* 112 to 113 labelled 1_1(1)* 113 to 114 labelled 0_1(1)* 114 to 115 labelled 1_1(1)* 115 to 116 labelled 2_1(1)* 116 to 117 labelled 0_1(1)* 117 to 118 labelled 1_1(1)* 118 to 47 labelled 2_1(1)* 118 to 65 labelled 2_1(1)* 119 to 120 labelled 2_1(1)* 120 to 121 labelled 1_1(1)* 121 to 122 labelled 1_1(1)* 122 to 123 labelled 0_1(1)* 123 to 124 labelled 1_1(1)* 124 to 125 labelled 2_1(1)* 125 to 126 labelled 0_1(1)* 126 to 127 labelled 1_1(1)* 127 to 128 labelled 2_1(1)* 128 to 129 labelled 0_1(1)* 129 to 130 labelled 1_1(1)* 130 to 47 labelled 2_1(1)* 130 to 65 labelled 2_1(1)* 132 to 134 labelled 2_1(2)* 134 to 136 labelled 1_1(2)* 136 to 138 labelled 1_1(2)* 138 to 140 labelled 0_1(2)* 140 to 142 labelled 1_1(2)* 142 to 144 labelled 2_1(2)* 144 to 146 labelled 0_1(2)* 146 to 148 labelled 1_1(2)* 148 to 24 labelled 2_1(2)* 148 to 33 labelled 2_1(2)* 153 to 155 labelled 2_1(2)* 155 to 157 labelled 1_1(2)* 157 to 159 labelled 1_1(2)* 159 to 161 labelled 0_1(2)* 161 to 163 labelled 1_1(2)* 163 to 165 labelled 2_1(2)* 165 to 167 labelled 0_1(2)* 167 to 169 labelled 1_1(2)* 169 to 170 labelled 2_1(2)* 170 to 171 labelled 0_1(2)* 171 to 172 labelled 1_1(2)* 172 to 24 labelled 2_1(2)* 172 to 33 labelled 2_1(2)* 173 to 174 labelled 2_1(2)* 174 to 175 labelled 1_1(2)* 175 to 176 labelled 1_1(2)* 176 to 177 labelled 0_1(2)* 177 to 178 labelled 1_1(2)* 178 to 179 labelled 2_1(2)* 179 to 180 labelled 0_1(2)* 180 to 181 labelled 1_1(2)* 181 to 132 labelled 2_1(2)* 181 to 153 labelled 2_1(2)* 182 to 183 labelled 2_1(2)* 183 to 184 labelled 1_1(2)* 184 to 185 labelled 1_1(2)* 185 to 186 labelled 0_1(2)* 186 to 187 labelled 1_1(2)* 187 to 188 labelled 2_1(2)* 188 to 189 labelled 0_1(2)* 189 to 190 labelled 1_1(2)* 190 to 191 labelled 2_1(2)* 191 to 192 labelled 0_1(2)* 192 to 193 labelled 1_1(2)* 193 to 132 labelled 2_1(2)* 193 to 153 labelled 2_1(2) ---------------------------------------- (2) YES