3.57/1.64 YES 3.57/1.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.57/1.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.57/1.68 3.57/1.68 3.57/1.68 Termination w.r.t. Q of the given QTRS could be proven: 3.57/1.68 3.57/1.68 (0) QTRS 3.57/1.68 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.57/1.68 (2) QTRS 3.57/1.68 (3) RFCMatchBoundsTRSProof [EQUIVALENT, 12 ms] 3.57/1.68 (4) YES 3.57/1.68 3.57/1.68 3.57/1.68 ---------------------------------------- 3.57/1.68 3.57/1.68 (0) 3.57/1.68 Obligation: 3.57/1.68 Q restricted rewrite system: 3.57/1.68 The TRS R consists of the following rules: 3.57/1.68 3.57/1.68 a(a(a(b(b(x1))))) -> b(b(b(b(b(a(a(a(a(a(x1)))))))))) 3.57/1.68 3.57/1.68 Q is empty. 3.57/1.68 3.57/1.68 ---------------------------------------- 3.57/1.68 3.57/1.68 (1) QTRS Reverse (EQUIVALENT) 3.57/1.68 We applied the QTRS Reverse Processor [REVERSE]. 3.57/1.68 ---------------------------------------- 3.57/1.68 3.57/1.68 (2) 3.57/1.68 Obligation: 3.57/1.68 Q restricted rewrite system: 3.57/1.68 The TRS R consists of the following rules: 3.57/1.68 3.57/1.68 b(b(a(a(a(x1))))) -> a(a(a(a(a(b(b(b(b(b(x1)))))))))) 3.57/1.68 3.57/1.68 Q is empty. 3.57/1.68 3.57/1.68 ---------------------------------------- 3.57/1.68 3.57/1.68 (3) RFCMatchBoundsTRSProof (EQUIVALENT) 3.57/1.68 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 3.57/1.68 The following rules were used to construct the certificate: 3.57/1.68 3.57/1.68 b(b(a(a(a(x1))))) -> a(a(a(a(a(b(b(b(b(b(x1)))))))))) 3.57/1.68 3.57/1.68 The certificate found is represented by the following graph. 3.57/1.68 The certificate consists of the following enumerated nodes: 3.57/1.68 2, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 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, 203, 204, 205, 206, 207, 208, 209, 210, 211 3.57/1.68 3.57/1.68 Node 2 is start node and node 67 is final node. 3.57/1.68 3.57/1.68 Those nodes are connected through the following edges: 3.57/1.68 3.57/1.68 * 2 to 68 labelled a_1(0)* 67 to 67 labelled #_1(0)* 68 to 69 labelled a_1(0)* 69 to 70 labelled a_1(0)* 70 to 71 labelled a_1(0)* 71 to 72 labelled a_1(0)* 72 to 73 labelled b_1(0)* 72 to 104 labelled a_1(1)* 73 to 74 labelled b_1(0)* 73 to 95 labelled a_1(1)* 74 to 75 labelled b_1(0)* 74 to 95 labelled a_1(1)* 75 to 76 labelled b_1(0)* 75 to 86 labelled a_1(1)* 76 to 67 labelled b_1(0)* 76 to 86 labelled a_1(1)* 86 to 87 labelled a_1(1)* 87 to 88 labelled a_1(1)* 88 to 89 labelled a_1(1)* 89 to 90 labelled a_1(1)* 90 to 91 labelled b_1(1)* 90 to 131 labelled a_1(2)* 91 to 92 labelled b_1(1)* 91 to 114 labelled a_1(2)* 92 to 93 labelled b_1(1)* 92 to 114 labelled a_1(2)* 93 to 94 labelled b_1(1)* 93 to 86 labelled a_1(1)* 94 to 67 labelled b_1(1)* 94 to 86 labelled a_1(1)* 95 to 96 labelled a_1(1)* 96 to 97 labelled a_1(1)* 97 to 98 labelled a_1(1)* 98 to 99 labelled a_1(1)* 99 to 100 labelled b_1(1)* 100 to 101 labelled b_1(1)* 100 to 167 labelled a_1(2)* 101 to 102 labelled b_1(1)* 102 to 103 labelled b_1(1)* 102 to 140 labelled a_1(2)* 103 to 88 labelled b_1(1)* 104 to 105 labelled a_1(1)* 105 to 106 labelled a_1(1)* 106 to 107 labelled a_1(1)* 107 to 108 labelled a_1(1)* 108 to 109 labelled b_1(1)* 109 to 110 labelled b_1(1)* 110 to 111 labelled b_1(1)* 111 to 112 labelled b_1(1)* 112 to 97 labelled b_1(1)* 114 to 116 labelled a_1(2)* 116 to 118 labelled a_1(2)* 118 to 120 labelled a_1(2)* 120 to 122 labelled a_1(2)* 122 to 124 labelled b_1(2)* 124 to 126 labelled b_1(2)* 124 to 176 labelled a_1(3)* 126 to 128 labelled b_1(2)* 128 to 130 labelled b_1(2)* 128 to 140 labelled a_1(2)* 130 to 88 labelled b_1(2)* 131 to 132 labelled a_1(2)* 132 to 133 labelled a_1(2)* 133 to 134 labelled a_1(2)* 134 to 135 labelled a_1(2)* 135 to 136 labelled b_1(2)* 136 to 137 labelled b_1(2)* 137 to 138 labelled b_1(2)* 138 to 139 labelled b_1(2)* 139 to 118 labelled b_1(2)* 140 to 141 labelled a_1(2)* 141 to 142 labelled a_1(2)* 142 to 143 labelled a_1(2)* 143 to 144 labelled a_1(2)* 144 to 145 labelled b_1(2)* 145 to 146 labelled b_1(2)* 145 to 203 labelled a_1(3)* 146 to 147 labelled b_1(2)* 147 to 148 labelled b_1(2)* 147 to 185 labelled a_1(3)* 148 to 131 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 142 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 142 labelled b_1(3)* 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 134 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 187 labelled b_1(3) 3.57/1.68 3.57/1.68 3.57/1.68 ---------------------------------------- 3.57/1.68 3.57/1.68 (4) 3.57/1.68 YES 3.81/1.71 EOF