/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 8 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: 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 95, 96, 97, 98, 99, 100, 101, 102, 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, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 Node 48 is start node and node 49 is final node. Those nodes are connected through the following edges: * 48 to 50 labelled a_1(0)* 49 to 49 labelled #_1(0)* 50 to 51 labelled a_1(0)* 51 to 52 labelled a_1(0)* 52 to 53 labelled a_1(0)* 53 to 54 labelled a_1(0)* 54 to 55 labelled b_1(0)* 54 to 95 labelled a_1(1)* 55 to 56 labelled b_1(0)* 55 to 68 labelled a_1(1)* 56 to 57 labelled b_1(0)* 56 to 68 labelled a_1(1)* 57 to 58 labelled b_1(0)* 57 to 59 labelled a_1(1)* 58 to 49 labelled b_1(0)* 58 to 59 labelled a_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled a_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled a_1(1)* 63 to 64 labelled b_1(1)* 63 to 113 labelled a_1(2)* 64 to 65 labelled b_1(1)* 64 to 104 labelled a_1(2)* 65 to 66 labelled b_1(1)* 65 to 104 labelled a_1(2)* 66 to 67 labelled b_1(1)* 66 to 59 labelled a_1(1)* 67 to 49 labelled b_1(1)* 67 to 59 labelled a_1(1)* 68 to 69 labelled a_1(1)* 69 to 70 labelled a_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled a_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled b_1(1)* 73 to 131 labelled a_1(2)* 74 to 75 labelled b_1(1)* 75 to 76 labelled b_1(1)* 75 to 122 labelled a_1(2)* 76 to 61 labelled b_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)* 101 to 102 labelled b_1(1)* 102 to 103 labelled b_1(1)* 103 to 70 labelled b_1(1)* 104 to 105 labelled a_1(2)* 105 to 106 labelled a_1(2)* 106 to 107 labelled a_1(2)* 107 to 108 labelled a_1(2)* 108 to 109 labelled b_1(2)* 109 to 110 labelled b_1(2)* 109 to 140 labelled a_1(3)* 110 to 111 labelled b_1(2)* 111 to 112 labelled b_1(2)* 111 to 122 labelled a_1(2)* 112 to 61 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 106 labelled b_1(2)* 122 to 123 labelled a_1(2)* 123 to 124 labelled a_1(2)* 124 to 125 labelled a_1(2)* 125 to 126 labelled a_1(2)* 126 to 127 labelled b_1(2)* 127 to 128 labelled b_1(2)* 127 to 158 labelled a_1(3)* 128 to 129 labelled b_1(2)* 129 to 130 labelled b_1(2)* 129 to 149 labelled a_1(3)* 130 to 113 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 124 labelled b_1(2)* 140 to 141 labelled a_1(3)* 141 to 142 labelled a_1(3)* 142 to 143 labelled a_1(3)* 143 to 144 labelled a_1(3)* 144 to 145 labelled b_1(3)* 145 to 146 labelled b_1(3)* 146 to 147 labelled b_1(3)* 147 to 148 labelled b_1(3)* 148 to 124 labelled b_1(3)* 149 to 150 labelled a_1(3)* 150 to 151 labelled a_1(3)* 151 to 152 labelled a_1(3)* 152 to 153 labelled a_1(3)* 153 to 154 labelled b_1(3)* 154 to 155 labelled b_1(3)* 155 to 156 labelled b_1(3)* 156 to 157 labelled b_1(3)* 157 to 116 labelled b_1(3)* 158 to 159 labelled a_1(3)* 159 to 160 labelled a_1(3)* 160 to 161 labelled a_1(3)* 161 to 162 labelled a_1(3)* 162 to 163 labelled b_1(3)* 163 to 164 labelled b_1(3)* 164 to 165 labelled b_1(3)* 165 to 166 labelled b_1(3)* 166 to 151 labelled b_1(3) ---------------------------------------- (4) YES