3.40/2.13 YES 3.73/2.15 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.73/2.15 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.73/2.15 3.73/2.15 3.73/2.15 Termination w.r.t. Q of the given QTRS could be proven: 3.73/2.15 3.73/2.15 (0) QTRS 3.73/2.15 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.73/2.15 (2) QTRS 3.73/2.15 (3) RFCMatchBoundsTRSProof [EQUIVALENT, 21 ms] 3.73/2.15 (4) YES 3.73/2.15 3.73/2.15 3.73/2.15 ---------------------------------------- 3.73/2.15 3.73/2.15 (0) 3.73/2.15 Obligation: 3.73/2.15 Q restricted rewrite system: 3.73/2.15 The TRS R consists of the following rules: 3.73/2.15 3.73/2.15 t(o(x1)) -> m(a(x1)) 3.73/2.15 t(e(x1)) -> n(s(x1)) 3.73/2.15 a(l(x1)) -> a(t(x1)) 3.73/2.15 o(m(a(x1))) -> t(e(n(x1))) 3.73/2.15 s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) 3.73/2.15 n(s(x1)) -> a(l(a(t(x1)))) 3.73/2.15 3.73/2.15 Q is empty. 3.73/2.15 3.73/2.15 ---------------------------------------- 3.73/2.15 3.73/2.15 (1) QTRS Reverse (EQUIVALENT) 3.73/2.15 We applied the QTRS Reverse Processor [REVERSE]. 3.73/2.15 ---------------------------------------- 3.73/2.15 3.73/2.15 (2) 3.73/2.15 Obligation: 3.73/2.15 Q restricted rewrite system: 3.73/2.15 The TRS R consists of the following rules: 3.73/2.15 3.73/2.15 o(t(x1)) -> a(m(x1)) 3.73/2.15 e(t(x1)) -> s(n(x1)) 3.73/2.15 l(a(x1)) -> t(a(x1)) 3.73/2.15 a(m(o(x1))) -> n(e(t(x1))) 3.73/2.15 a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) 3.73/2.15 s(n(x1)) -> t(a(l(a(x1)))) 3.73/2.15 3.73/2.15 Q is empty. 3.73/2.15 3.73/2.15 ---------------------------------------- 3.73/2.15 3.73/2.15 (3) RFCMatchBoundsTRSProof (EQUIVALENT) 3.73/2.15 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 5. This implies Q-termination of R. 3.73/2.15 The following rules were used to construct the certificate: 3.73/2.15 3.73/2.15 o(t(x1)) -> a(m(x1)) 3.73/2.15 e(t(x1)) -> s(n(x1)) 3.73/2.15 l(a(x1)) -> t(a(x1)) 3.73/2.15 a(m(o(x1))) -> n(e(t(x1))) 3.73/2.15 a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) 3.73/2.15 s(n(x1)) -> t(a(l(a(x1)))) 3.73/2.15 3.73/2.15 The certificate found is represented by the following graph. 3.73/2.15 The certificate consists of the following enumerated nodes: 3.73/2.15 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 45, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 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 3.73/2.15 3.73/2.15 Node 18 is start node and node 19 is final node. 3.73/2.15 3.73/2.15 Those nodes are connected through the following edges: 3.73/2.15 3.73/2.15 * 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 45 labelled t_1(1)* 18 to 49 labelled s_1(1)* 18 to 51 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 51 labelled n_1(1)* 22 to 54 labelled e_1(1)* 22 to 71 labelled s_1(2)* 22 to 80 labelled t_1(3)* 23 to 24 labelled e_1(0)* 23 to 64 labelled s_1(1)* 23 to 72 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 65 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 48 labelled t_1(1)* 32 to 33 labelled a_1(0)* 33 to 34 labelled l_1(0)* 33 to 48 labelled t_1(1)* 34 to 19 labelled a_1(0)* 34 to 51 labelled n_1(1)* 34 to 54 labelled e_1(1)* 34 to 71 labelled s_1(2)* 34 to 80 labelled t_1(3)* 45 to 47 labelled a_1(1)* 47 to 48 labelled l_1(1)* 47 to 74 labelled t_1(2)* 48 to 19 labelled a_1(1)* 48 to 51 labelled n_1(1)* 48 to 54 labelled e_1(1)* 48 to 71 labelled s_1(2)* 48 to 80 labelled t_1(3)* 49 to 26 labelled n_1(1)* 51 to 52 labelled e_1(1)* 51 to 75 labelled s_1(2)* 51 to 83 labelled t_1(3)* 52 to 19 labelled t_1(1)* 54 to 55 labelled t_1(1)* 55 to 56 labelled a_1(1)* 55 to 78 labelled n_1(2)* 56 to 57 labelled m_1(1)* 57 to 58 labelled o_1(1)* 57 to 76 labelled a_1(2)* 58 to 59 labelled t_1(1)* 59 to 60 labelled a_1(1)* 60 to 19 labelled l_1(1)* 60 to 48 labelled t_1(1)* 64 to 19 labelled n_1(1)* 65 to 30 labelled m_1(1)* 66 to 67 labelled e_1(1)* 66 to 77 labelled s_1(2)* 66 to 86 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 89 labelled t_1(3)* 70 to 26 labelled a_1(2)* 71 to 55 labelled n_1(2)* 72 to 73 labelled a_1(2)* 73 to 74 labelled l_1(2)* 73 to 85 labelled t_1(3)* 74 to 19 labelled a_1(2)* 74 to 51 labelled n_1(1)* 74 to 54 labelled e_1(1)* 74 to 71 labelled s_1(2)* 74 to 80 labelled t_1(3)* 75 to 19 labelled n_1(2)* 76 to 59 labelled m_1(2)* 77 to 29 labelled n_1(2)* 78 to 79 labelled e_1(2)* 78 to 90 labelled s_1(3)* 78 to 91 labelled t_1(4)* 79 to 58 labelled t_1(2)* 80 to 81 labelled a_1(3)* 81 to 82 labelled l_1(3)* 81 to 94 labelled t_1(4)* 82 to 55 labelled a_1(3)* 83 to 84 labelled a_1(3)* 84 to 85 labelled l_1(3)* 84 to 95 labelled t_1(4)* 85 to 19 labelled a_1(3)* 85 to 51 labelled n_1(1)* 85 to 54 labelled e_1(1)* 85 to 71 labelled s_1(2)* 85 to 80 labelled t_1(3)* 86 to 87 labelled a_1(3)* 87 to 88 labelled l_1(3)* 87 to 96 labelled t_1(4)* 88 to 29 labelled a_1(3)* 89 to 26 labelled a_1(3)* 90 to 58 labelled n_1(3)* 91 to 92 labelled a_1(4)* 92 to 93 labelled l_1(4)* 92 to 97 labelled t_1(5)* 93 to 58 labelled a_1(4)* 94 to 55 labelled a_1(4)* 95 to 19 labelled a_1(4)* 95 to 51 labelled n_1(1)* 95 to 54 labelled e_1(1)* 95 to 71 labelled s_1(2)* 95 to 80 labelled t_1(3)* 96 to 29 labelled a_1(4)* 97 to 58 labelled a_1(5) 3.73/2.15 3.73/2.15 3.73/2.15 ---------------------------------------- 3.73/2.15 3.73/2.15 (4) 3.73/2.15 YES 3.79/2.33 EOF