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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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(b(b(x1)))) -> 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(x1)))) -> a(a(a(a(a(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 4. This implies Q-termination of R. The following rules were used to construct the certificate: b(b(a(a(x1)))) -> a(a(a(a(a(b(b(b(x1)))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 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 Node 24 is start node and node 25 is final node. Those nodes are connected through the following edges: * 24 to 26 labelled a_1(0)* 25 to 25 labelled #_1(0)* 26 to 27 labelled a_1(0)* 27 to 28 labelled a_1(0)* 28 to 29 labelled a_1(0)* 29 to 30 labelled a_1(0)* 30 to 31 labelled b_1(0)* 30 to 96 labelled a_1(1)* 31 to 32 labelled b_1(0)* 31 to 33 labelled a_1(1)* 32 to 25 labelled b_1(0)* 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 a_1(1)* 37 to 38 labelled b_1(1)* 37 to 103 labelled a_1(2)* 38 to 39 labelled b_1(1)* 38 to 33 labelled a_1(1)* 39 to 25 labelled b_1(1)* 39 to 33 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 a_1(1)* 100 to 101 labelled b_1(1)* 101 to 102 labelled b_1(1)* 101 to 110 labelled a_1(2)* 102 to 34 labelled b_1(1)* 103 to 104 labelled a_1(2)* 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 b_1(2)* 108 to 109 labelled b_1(2)* 108 to 110 labelled a_1(2)* 109 to 34 labelled b_1(2)* 110 to 111 labelled a_1(2)* 111 to 112 labelled a_1(2)* 112 to 113 labelled a_1(2)* 113 to 114 labelled a_1(2)* 114 to 115 labelled b_1(2)* 115 to 116 labelled b_1(2)* 115 to 117 labelled a_1(2)* 116 to 36 labelled b_1(2)* 117 to 118 labelled a_1(2)* 118 to 119 labelled a_1(2)* 119 to 120 labelled a_1(2)* 120 to 121 labelled a_1(2)* 121 to 122 labelled b_1(2)* 122 to 123 labelled b_1(2)* 122 to 124 labelled a_1(3)* 123 to 103 labelled b_1(2)* 124 to 125 labelled a_1(3)* 125 to 126 labelled a_1(3)* 126 to 127 labelled a_1(3)* 127 to 128 labelled a_1(3)* 128 to 129 labelled b_1(3)* 129 to 130 labelled b_1(3)* 129 to 131 labelled a_1(3)* 130 to 105 labelled b_1(3)* 131 to 132 labelled a_1(3)* 132 to 133 labelled a_1(3)* 133 to 134 labelled a_1(3)* 134 to 135 labelled a_1(3)* 135 to 136 labelled b_1(3)* 135 to 145 labelled a_1(4)* 136 to 137 labelled b_1(3)* 137 to 107 labelled b_1(3)* 137 to 138 labelled a_1(3)* 138 to 139 labelled a_1(3)* 139 to 140 labelled a_1(3)* 140 to 141 labelled a_1(3)* 141 to 142 labelled a_1(3)* 142 to 143 labelled b_1(3)* 143 to 144 labelled b_1(3)* 143 to 152 labelled a_1(3)* 144 to 111 labelled b_1(3)* 145 to 146 labelled a_1(4)* 146 to 147 labelled a_1(4)* 147 to 148 labelled a_1(4)* 148 to 149 labelled a_1(4)* 149 to 150 labelled b_1(4)* 150 to 151 labelled b_1(4)* 150 to 159 labelled a_1(4)* 151 to 139 labelled b_1(4)* 152 to 153 labelled a_1(3)* 153 to 154 labelled a_1(3)* 154 to 155 labelled a_1(3)* 155 to 156 labelled a_1(3)* 156 to 157 labelled b_1(3)* 157 to 158 labelled b_1(3)* 158 to 113 labelled b_1(3)* 159 to 160 labelled a_1(4)* 160 to 161 labelled a_1(4)* 161 to 162 labelled a_1(4)* 162 to 163 labelled a_1(4)* 163 to 164 labelled b_1(4)* 164 to 165 labelled b_1(4)* 165 to 141 labelled b_1(4) ---------------------------------------- (4) YES