/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 11 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(a(a(x1))))) -> a(a(a(b(a(b(a(b(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: a(a(b(a(b(x1))))) -> b(a(b(a(b(a(a(a(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: a(a(b(a(b(x1))))) -> b(a(b(a(b(a(a(a(x1)))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 2, 4, 19, 20, 21, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 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, 77, 78, 79, 80, 81, 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 2 is start node and node 4 is final node. Those nodes are connected through the following edges: * 2 to 19 labelled b_1(0)* 4 to 4 labelled #_1(0)* 19 to 20 labelled a_1(0)* 20 to 21 labelled b_1(0)* 21 to 22 labelled a_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled a_1(0)* 23 to 40 labelled b_1(1)* 24 to 25 labelled a_1(0)* 24 to 33 labelled b_1(1)* 25 to 4 labelled a_1(0)* 25 to 33 labelled b_1(1)* 33 to 34 labelled a_1(1)* 34 to 35 labelled b_1(1)* 35 to 36 labelled a_1(1)* 36 to 37 labelled b_1(1)* 37 to 38 labelled a_1(1)* 37 to 47 labelled b_1(2)* 38 to 39 labelled a_1(1)* 38 to 33 labelled b_1(1)* 39 to 4 labelled a_1(1)* 39 to 33 labelled b_1(1)* 40 to 41 labelled a_1(1)* 41 to 42 labelled b_1(1)* 42 to 43 labelled a_1(1)* 43 to 44 labelled b_1(1)* 44 to 45 labelled a_1(1)* 44 to 61 labelled b_1(2)* 45 to 46 labelled a_1(1)* 46 to 35 labelled a_1(1)* 46 to 54 labelled b_1(2)* 47 to 48 labelled a_1(2)* 48 to 49 labelled b_1(2)* 49 to 50 labelled a_1(2)* 50 to 51 labelled b_1(2)* 51 to 52 labelled a_1(2)* 51 to 75 labelled b_1(3)* 52 to 53 labelled a_1(2)* 53 to 35 labelled a_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled a_1(2)* 55 to 56 labelled b_1(2)* 56 to 57 labelled a_1(2)* 57 to 58 labelled b_1(2)* 58 to 59 labelled a_1(2)* 58 to 124 labelled b_1(3)* 59 to 60 labelled a_1(2)* 60 to 33 labelled a_1(2)* 60 to 68 labelled b_1(2)* 61 to 62 labelled a_1(2)* 62 to 63 labelled b_1(2)* 63 to 64 labelled a_1(2)* 64 to 65 labelled b_1(2)* 65 to 66 labelled a_1(2)* 66 to 67 labelled a_1(2)* 67 to 56 labelled a_1(2)* 68 to 69 labelled a_1(2)* 69 to 70 labelled b_1(2)* 70 to 71 labelled a_1(2)* 71 to 72 labelled b_1(2)* 72 to 73 labelled a_1(2)* 72 to 131 labelled b_1(3)* 73 to 74 labelled a_1(2)* 73 to 131 labelled b_1(3)* 74 to 37 labelled a_1(2)* 74 to 47 labelled b_1(2)* 75 to 76 labelled a_1(3)* 76 to 77 labelled b_1(3)* 77 to 78 labelled a_1(3)* 78 to 79 labelled b_1(3)* 79 to 80 labelled a_1(3)* 80 to 81 labelled a_1(3)* 81 to 56 labelled a_1(3)* 124 to 125 labelled a_1(3)* 125 to 126 labelled b_1(3)* 126 to 127 labelled a_1(3)* 127 to 128 labelled b_1(3)* 128 to 129 labelled a_1(3)* 128 to 145 labelled b_1(4)* 129 to 130 labelled a_1(3)* 130 to 70 labelled a_1(3)* 130 to 138 labelled b_1(3)* 131 to 132 labelled a_1(3)* 132 to 133 labelled b_1(3)* 133 to 134 labelled a_1(3)* 134 to 135 labelled b_1(3)* 135 to 136 labelled a_1(3)* 136 to 137 labelled a_1(3)* 137 to 49 labelled a_1(3)* 138 to 139 labelled a_1(3)* 139 to 140 labelled b_1(3)* 140 to 141 labelled a_1(3)* 141 to 142 labelled b_1(3)* 142 to 143 labelled a_1(3)* 142 to 159 labelled b_1(4)* 143 to 144 labelled a_1(3)* 144 to 131 labelled a_1(3)* 144 to 152 labelled b_1(4)* 145 to 146 labelled a_1(4)* 146 to 147 labelled b_1(4)* 147 to 148 labelled a_1(4)* 148 to 149 labelled b_1(4)* 149 to 150 labelled a_1(4)* 150 to 151 labelled a_1(4)* 151 to 140 labelled a_1(4)* 152 to 153 labelled a_1(4)* 153 to 154 labelled b_1(4)* 154 to 155 labelled a_1(4)* 155 to 156 labelled b_1(4)* 156 to 157 labelled a_1(4)* 157 to 158 labelled a_1(4)* 158 to 135 labelled a_1(4)* 159 to 160 labelled a_1(4)* 160 to 161 labelled b_1(4)* 161 to 162 labelled a_1(4)* 162 to 163 labelled b_1(4)* 163 to 164 labelled a_1(4)* 164 to 165 labelled a_1(4)* 165 to 154 labelled a_1(4) ---------------------------------------- (4) YES