/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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: 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: 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, 45, 46, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 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, 166, 167, 168, 169, 170, 171, 172 Node 10 is start node and node 11 is final node. Those nodes are connected through the following edges: * 10 to 12 labelled b_1(0)* 11 to 11 labelled #_1(0)* 12 to 13 labelled a_1(0)* 13 to 14 labelled b_1(0)* 14 to 15 labelled a_1(0)* 15 to 16 labelled b_1(0)* 16 to 17 labelled a_1(0)* 16 to 26 labelled b_1(1)* 17 to 18 labelled a_1(0)* 17 to 19 labelled b_1(1)* 18 to 11 labelled a_1(0)* 18 to 19 labelled b_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled a_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled a_1(1)* 23 to 33 labelled b_1(2)* 24 to 25 labelled a_1(1)* 24 to 19 labelled b_1(1)* 25 to 11 labelled a_1(1)* 25 to 19 labelled b_1(1)* 26 to 27 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 29 labelled a_1(1)* 29 to 30 labelled b_1(1)* 30 to 31 labelled a_1(1)* 30 to 54 labelled b_1(2)* 31 to 32 labelled a_1(1)* 32 to 21 labelled a_1(1)* 32 to 40 labelled b_1(2)* 33 to 34 labelled a_1(2)* 34 to 35 labelled b_1(2)* 35 to 36 labelled a_1(2)* 36 to 37 labelled b_1(2)* 37 to 38 labelled a_1(2)* 37 to 96 labelled b_1(3)* 38 to 39 labelled a_1(2)* 39 to 21 labelled a_1(2)* 39 to 40 labelled b_1(2)* 40 to 41 labelled a_1(2)* 41 to 42 labelled b_1(2)* 42 to 43 labelled a_1(2)* 43 to 44 labelled b_1(2)* 44 to 45 labelled a_1(2)* 44 to 103 labelled b_1(3)* 45 to 46 labelled a_1(2)* 46 to 19 labelled a_1(2)* 46 to 61 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)* 59 to 60 labelled a_1(2)* 60 to 42 labelled a_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)* 65 to 110 labelled b_1(3)* 66 to 67 labelled a_1(2)* 66 to 110 labelled b_1(3)* 67 to 23 labelled a_1(2)* 67 to 33 labelled b_1(2)* 96 to 97 labelled a_1(3)* 97 to 98 labelled b_1(3)* 98 to 99 labelled a_1(3)* 99 to 100 labelled b_1(3)* 100 to 101 labelled a_1(3)* 101 to 102 labelled a_1(3)* 102 to 42 labelled a_1(3)* 103 to 104 labelled a_1(3)* 104 to 105 labelled b_1(3)* 105 to 106 labelled a_1(3)* 106 to 107 labelled b_1(3)* 107 to 108 labelled a_1(3)* 107 to 124 labelled b_1(4)* 108 to 109 labelled a_1(3)* 109 to 63 labelled a_1(3)* 109 to 117 labelled b_1(3)* 110 to 111 labelled a_1(3)* 111 to 112 labelled b_1(3)* 112 to 113 labelled a_1(3)* 113 to 114 labelled b_1(3)* 114 to 115 labelled a_1(3)* 115 to 116 labelled a_1(3)* 116 to 35 labelled a_1(3)* 117 to 118 labelled a_1(3)* 118 to 119 labelled b_1(3)* 119 to 120 labelled a_1(3)* 120 to 121 labelled b_1(3)* 121 to 122 labelled a_1(3)* 121 to 166 labelled b_1(4)* 122 to 123 labelled a_1(3)* 123 to 110 labelled a_1(3)* 123 to 131 labelled b_1(4)* 124 to 125 labelled a_1(4)* 125 to 126 labelled b_1(4)* 126 to 127 labelled a_1(4)* 127 to 128 labelled b_1(4)* 128 to 129 labelled a_1(4)* 129 to 130 labelled a_1(4)* 130 to 119 labelled a_1(4)* 131 to 132 labelled a_1(4)* 132 to 133 labelled b_1(4)* 133 to 134 labelled a_1(4)* 134 to 135 labelled b_1(4)* 135 to 136 labelled a_1(4)* 136 to 137 labelled a_1(4)* 137 to 114 labelled a_1(4)* 166 to 167 labelled a_1(4)* 167 to 168 labelled b_1(4)* 168 to 169 labelled a_1(4)* 169 to 170 labelled b_1(4)* 170 to 171 labelled a_1(4)* 171 to 172 labelled a_1(4)* 172 to 133 labelled a_1(4) ---------------------------------------- (4) YES