/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4)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: t(o(x1)) -> m(a(x1)) t(e(x1)) -> n(s(x1)) a(l(x1)) -> a(t(x1)) o(m(a(x1))) -> t(e(n(x1))) s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) n(s(x1)) -> a(l(a(t(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: o(t(x1)) -> a(m(x1)) e(t(x1)) -> s(n(x1)) l(a(x1)) -> t(a(x1)) a(m(o(x1))) -> n(e(t(x1))) a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) s(n(x1)) -> t(a(l(a(x1)))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 5. This implies Q-termination of R. The following rules were used to construct the certificate: o(t(x1)) -> a(m(x1)) e(t(x1)) -> s(n(x1)) l(a(x1)) -> t(a(x1)) a(m(o(x1))) -> n(e(t(x1))) a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) s(n(x1)) -> t(a(l(a(x1)))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 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, 84, 85, 86, 87, 88, 89, 93, 94, 95, 96, 98, 110, 111, 112, 113, 115, 116, 129 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 23 labelled a_1(0)* 3 to 24 labelled s_1(0)* 3 to 25 labelled t_1(0)* 3 to 26 labelled n_1(0)* 3 to 28 labelled e_1(0)* 3 to 35 labelled t_1(0)* 3 to 38 labelled t_1(1)* 3 to 41 labelled s_1(1)* 3 to 42 labelled n_1(1)* 3 to 55 labelled t_1(2)* 4 to 4 labelled #_1(0)* 23 to 4 labelled m_1(0)* 24 to 4 labelled n_1(0)* 25 to 4 labelled a_1(0)* 25 to 42 labelled n_1(1)* 25 to 44 labelled e_1(1)* 25 to 58 labelled s_1(2)* 25 to 84 labelled t_1(3)* 26 to 27 labelled e_1(0)* 26 to 51 labelled s_1(1)* 26 to 59 labelled t_1(2)* 27 to 4 labelled t_1(0)* 28 to 29 labelled t_1(0)* 29 to 30 labelled a_1(0)* 29 to 53 labelled n_1(1)* 30 to 31 labelled m_1(0)* 31 to 32 labelled o_1(0)* 31 to 52 labelled a_1(1)* 32 to 33 labelled t_1(0)* 33 to 34 labelled a_1(0)* 34 to 4 labelled l_1(0)* 34 to 40 labelled t_1(1)* 35 to 36 labelled a_1(0)* 36 to 37 labelled l_1(0)* 36 to 40 labelled t_1(1)* 37 to 4 labelled a_1(0)* 37 to 42 labelled n_1(1)* 37 to 44 labelled e_1(1)* 37 to 58 labelled s_1(2)* 37 to 84 labelled t_1(3)* 38 to 39 labelled a_1(1)* 39 to 40 labelled l_1(1)* 39 to 61 labelled t_1(2)* 40 to 4 labelled a_1(1)* 40 to 42 labelled n_1(1)* 40 to 44 labelled e_1(1)* 40 to 58 labelled s_1(2)* 40 to 84 labelled t_1(3)* 41 to 29 labelled n_1(1)* 42 to 43 labelled e_1(1)* 42 to 62 labelled s_1(2)* 42 to 87 labelled t_1(3)* 43 to 4 labelled t_1(1)* 44 to 45 labelled t_1(1)* 45 to 46 labelled a_1(1)* 45 to 65 labelled n_1(2)* 46 to 47 labelled m_1(1)* 47 to 48 labelled o_1(1)* 47 to 63 labelled a_1(2)* 48 to 49 labelled t_1(1)* 49 to 50 labelled a_1(1)* 50 to 4 labelled l_1(1)* 50 to 40 labelled t_1(1)* 51 to 4 labelled n_1(1)* 52 to 33 labelled m_1(1)* 53 to 54 labelled e_1(1)* 53 to 64 labelled s_1(2)* 53 to 93 labelled t_1(3)* 54 to 32 labelled t_1(1)* 55 to 56 labelled a_1(2)* 56 to 57 labelled l_1(2)* 56 to 96 labelled t_1(3)* 57 to 29 labelled a_1(2)* 58 to 45 labelled n_1(2)* 59 to 60 labelled a_1(2)* 60 to 61 labelled l_1(2)* 60 to 89 labelled t_1(3)* 61 to 4 labelled a_1(2)* 61 to 42 labelled n_1(1)* 61 to 44 labelled e_1(1)* 61 to 58 labelled s_1(2)* 61 to 84 labelled t_1(3)* 62 to 4 labelled n_1(2)* 63 to 49 labelled m_1(2)* 64 to 32 labelled n_1(2)* 65 to 66 labelled e_1(2)* 65 to 98 labelled s_1(3)* 65 to 110 labelled t_1(4)* 66 to 48 labelled t_1(2)* 84 to 85 labelled a_1(3)* 85 to 86 labelled l_1(3)* 85 to 113 labelled t_1(4)* 86 to 45 labelled a_1(3)* 87 to 88 labelled a_1(3)* 88 to 89 labelled l_1(3)* 88 to 115 labelled t_1(4)* 89 to 4 labelled a_1(3)* 89 to 42 labelled n_1(1)* 89 to 44 labelled e_1(1)* 89 to 58 labelled s_1(2)* 89 to 84 labelled t_1(3)* 93 to 94 labelled a_1(3)* 94 to 95 labelled l_1(3)* 94 to 116 labelled t_1(4)* 95 to 32 labelled a_1(3)* 96 to 29 labelled a_1(3)* 98 to 48 labelled n_1(3)* 110 to 111 labelled a_1(4)* 111 to 112 labelled l_1(4)* 111 to 129 labelled t_1(5)* 112 to 48 labelled a_1(4)* 113 to 45 labelled a_1(4)* 115 to 4 labelled a_1(4)* 115 to 42 labelled n_1(1)* 115 to 44 labelled e_1(1)* 115 to 58 labelled s_1(2)* 115 to 84 labelled t_1(3)* 116 to 32 labelled a_1(4)* 129 to 48 labelled a_1(5) ---------------------------------------- (4) YES