/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 9 ms] (2) YES ----------------------------------------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) 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(a(b(b(x1))))) -> b(b(b(b(b(a(a(a(a(a(x1)))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 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, 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, 82, 83, 84, 85, 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 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled b_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled b_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 7 to 21 labelled b_1(1)* 8 to 9 labelled a_1(0)* 8 to 21 labelled b_1(1)* 9 to 10 labelled a_1(0)* 9 to 12 labelled b_1(1)* 10 to 11 labelled a_1(0)* 10 to 12 labelled b_1(1)* 11 to 2 labelled a_1(0)* 11 to 12 labelled b_1(1)* 12 to 13 labelled b_1(1)* 13 to 14 labelled b_1(1)* 14 to 15 labelled b_1(1)* 15 to 16 labelled b_1(1)* 16 to 17 labelled a_1(1)* 16 to 30 labelled b_1(2)* 17 to 18 labelled a_1(1)* 17 to 30 labelled b_1(2)* 18 to 19 labelled a_1(1)* 18 to 12 labelled b_1(1)* 19 to 20 labelled a_1(1)* 19 to 12 labelled b_1(1)* 20 to 2 labelled a_1(1)* 20 to 12 labelled b_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled b_1(1)* 24 to 25 labelled b_1(1)* 25 to 26 labelled a_1(1)* 26 to 27 labelled a_1(1)* 27 to 28 labelled a_1(1)* 27 to 39 labelled b_1(2)* 28 to 29 labelled a_1(1)* 29 to 13 labelled a_1(1)* 30 to 31 labelled b_1(2)* 31 to 32 labelled b_1(2)* 32 to 33 labelled b_1(2)* 33 to 34 labelled b_1(2)* 34 to 35 labelled a_1(2)* 35 to 36 labelled a_1(2)* 36 to 37 labelled a_1(2)* 36 to 39 labelled b_1(2)* 37 to 38 labelled a_1(2)* 38 to 13 labelled a_1(2)* 39 to 40 labelled b_1(2)* 40 to 41 labelled b_1(2)* 41 to 42 labelled b_1(2)* 42 to 43 labelled b_1(2)* 43 to 44 labelled a_1(2)* 44 to 45 labelled a_1(2)* 45 to 46 labelled a_1(2)* 45 to 48 labelled b_1(2)* 46 to 47 labelled a_1(2)* 47 to 15 labelled a_1(2)* 48 to 49 labelled b_1(2)* 49 to 50 labelled b_1(2)* 50 to 51 labelled b_1(2)* 51 to 52 labelled b_1(2)* 52 to 53 labelled a_1(2)* 53 to 54 labelled a_1(2)* 54 to 55 labelled a_1(2)* 54 to 57 labelled b_1(3)* 55 to 56 labelled a_1(2)* 56 to 30 labelled a_1(2)* 57 to 58 labelled b_1(3)* 58 to 59 labelled b_1(3)* 59 to 60 labelled b_1(3)* 60 to 61 labelled b_1(3)* 61 to 62 labelled a_1(3)* 62 to 63 labelled a_1(3)* 63 to 64 labelled a_1(3)* 63 to 66 labelled b_1(3)* 64 to 65 labelled a_1(3)* 65 to 32 labelled a_1(3)* 66 to 67 labelled b_1(3)* 67 to 68 labelled b_1(3)* 68 to 69 labelled b_1(3)* 69 to 70 labelled b_1(3)* 70 to 71 labelled a_1(3)* 71 to 72 labelled a_1(3)* 71 to 84 labelled b_1(4)* 72 to 73 labelled a_1(3)* 73 to 74 labelled a_1(3)* 74 to 34 labelled a_1(3)* 74 to 75 labelled b_1(3)* 75 to 76 labelled b_1(3)* 76 to 77 labelled b_1(3)* 77 to 78 labelled b_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 82 labelled a_1(3)* 81 to 93 labelled b_1(3)* 82 to 83 labelled a_1(3)* 83 to 40 labelled a_1(3)* 84 to 85 labelled b_1(4)* 85 to 86 labelled b_1(4)* 86 to 87 labelled b_1(4)* 87 to 88 labelled b_1(4)* 88 to 89 labelled a_1(4)* 89 to 90 labelled a_1(4)* 90 to 91 labelled a_1(4)* 90 to 102 labelled b_1(4)* 91 to 92 labelled a_1(4)* 92 to 76 labelled a_1(4)* 93 to 94 labelled b_1(3)* 94 to 95 labelled b_1(3)* 95 to 96 labelled b_1(3)* 96 to 97 labelled b_1(3)* 97 to 98 labelled a_1(3)* 98 to 99 labelled a_1(3)* 99 to 100 labelled a_1(3)* 100 to 101 labelled a_1(3)* 101 to 42 labelled a_1(3)* 102 to 103 labelled b_1(4)* 103 to 104 labelled b_1(4)* 104 to 105 labelled b_1(4)* 105 to 106 labelled b_1(4)* 106 to 107 labelled a_1(4)* 107 to 108 labelled a_1(4)* 108 to 109 labelled a_1(4)* 109 to 110 labelled a_1(4)* 110 to 78 labelled a_1(4) ---------------------------------------- (2) YES