/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 16 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: 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 43, 44, 49, 51, 53, 55, 56, 57, 58, 61, 62, 66, 67, 68, 69, 70, 75, 76, 77, 78, 82, 83, 84, 85, 86, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 123, 124, 125, 126, 127, 128, 138 Node 18 is start node and node 19 is final node. Those nodes are connected through the following edges: * 18 to 20 labelled a_1(0)* 18 to 21 labelled s_1(0)* 18 to 22 labelled t_1(0)* 18 to 23 labelled n_1(0)* 18 to 25 labelled e_1(0)* 18 to 32 labelled t_1(0)* 18 to 35 labelled t_1(1)* 18 to 42 labelled s_1(1)* 18 to 43 labelled n_1(1)* 18 to 68 labelled t_1(2)* 19 to 19 labelled #_1(0)* 20 to 19 labelled m_1(0)* 21 to 19 labelled n_1(0)* 22 to 19 labelled a_1(0)* 22 to 43 labelled n_1(1)* 22 to 49 labelled e_1(1)* 22 to 75 labelled s_1(2)* 22 to 99 labelled t_1(3)* 23 to 24 labelled e_1(0)* 23 to 61 labelled s_1(1)* 23 to 76 labelled t_1(2)* 24 to 19 labelled t_1(0)* 25 to 26 labelled t_1(0)* 26 to 27 labelled a_1(0)* 26 to 66 labelled n_1(1)* 27 to 28 labelled m_1(0)* 28 to 29 labelled o_1(0)* 28 to 62 labelled a_1(1)* 29 to 30 labelled t_1(0)* 30 to 31 labelled a_1(0)* 31 to 19 labelled l_1(0)* 31 to 40 labelled t_1(1)* 32 to 33 labelled a_1(0)* 33 to 34 labelled l_1(0)* 33 to 40 labelled t_1(1)* 34 to 19 labelled a_1(0)* 34 to 43 labelled n_1(1)* 34 to 49 labelled e_1(1)* 34 to 75 labelled s_1(2)* 34 to 99 labelled t_1(3)* 35 to 39 labelled a_1(1)* 39 to 40 labelled l_1(1)* 39 to 78 labelled t_1(2)* 40 to 19 labelled a_1(1)* 40 to 43 labelled n_1(1)* 40 to 49 labelled e_1(1)* 40 to 75 labelled s_1(2)* 40 to 99 labelled t_1(3)* 42 to 26 labelled n_1(1)* 43 to 44 labelled e_1(1)* 43 to 82 labelled s_1(2)* 43 to 102 labelled t_1(3)* 44 to 19 labelled t_1(1)* 49 to 51 labelled t_1(1)* 51 to 53 labelled a_1(1)* 51 to 85 labelled n_1(2)* 53 to 55 labelled m_1(1)* 55 to 56 labelled o_1(1)* 55 to 83 labelled a_1(2)* 56 to 57 labelled t_1(1)* 57 to 58 labelled a_1(1)* 58 to 19 labelled l_1(1)* 58 to 40 labelled t_1(1)* 61 to 19 labelled n_1(1)* 62 to 30 labelled m_1(1)* 66 to 67 labelled e_1(1)* 66 to 84 labelled s_1(2)* 66 to 105 labelled t_1(3)* 67 to 29 labelled t_1(1)* 68 to 69 labelled a_1(2)* 69 to 70 labelled l_1(2)* 69 to 108 labelled t_1(3)* 70 to 26 labelled a_1(2)* 75 to 51 labelled n_1(2)* 76 to 77 labelled a_1(2)* 77 to 78 labelled l_1(2)* 77 to 104 labelled t_1(3)* 78 to 19 labelled a_1(2)* 78 to 43 labelled n_1(1)* 78 to 49 labelled e_1(1)* 78 to 75 labelled s_1(2)* 78 to 99 labelled t_1(3)* 82 to 19 labelled n_1(2)* 83 to 57 labelled m_1(2)* 84 to 29 labelled n_1(2)* 85 to 86 labelled e_1(2)* 85 to 109 labelled s_1(3)* 85 to 123 labelled t_1(4)* 86 to 56 labelled t_1(2)* 99 to 100 labelled a_1(3)* 100 to 101 labelled l_1(3)* 100 to 126 labelled t_1(4)* 101 to 51 labelled a_1(3)* 102 to 103 labelled a_1(3)* 103 to 104 labelled l_1(3)* 103 to 127 labelled t_1(4)* 104 to 19 labelled a_1(3)* 104 to 43 labelled n_1(1)* 104 to 49 labelled e_1(1)* 104 to 75 labelled s_1(2)* 104 to 99 labelled t_1(3)* 105 to 106 labelled a_1(3)* 106 to 107 labelled l_1(3)* 106 to 128 labelled t_1(4)* 107 to 29 labelled a_1(3)* 108 to 26 labelled a_1(3)* 109 to 56 labelled n_1(3)* 123 to 124 labelled a_1(4)* 124 to 125 labelled l_1(4)* 124 to 138 labelled t_1(5)* 125 to 56 labelled a_1(4)* 126 to 51 labelled a_1(4)* 127 to 19 labelled a_1(4)* 127 to 43 labelled n_1(1)* 127 to 49 labelled e_1(1)* 127 to 75 labelled s_1(2)* 127 to 99 labelled t_1(3)* 128 to 29 labelled a_1(4)* 138 to 56 labelled a_1(5) ---------------------------------------- (4) YES