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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 12 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(c(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(c(x1)))) -> c(a(b(c(b(a(a(b(a(a(x1)))))))))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. The following rules were used to construct the certificate: a(a(b(c(x1)))) -> c(a(b(c(b(a(a(b(a(a(x1)))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 4, 14, 15, 16, 17, 18, 19, 20, 21, 22, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121 Node 1 is start node and node 4 is final node. Those nodes are connected through the following edges: * 1 to 14 labelled c_1(0)* 4 to 4 labelled #_1(0)* 14 to 15 labelled a_1(0)* 15 to 16 labelled b_1(0)* 16 to 17 labelled c_1(0)* 17 to 18 labelled b_1(0)* 18 to 19 labelled a_1(0)* 18 to 59 labelled c_1(1)* 19 to 20 labelled a_1(0)* 20 to 21 labelled b_1(0)* 21 to 22 labelled a_1(0)* 21 to 41 labelled c_1(1)* 22 to 4 labelled a_1(0)* 22 to 41 labelled c_1(1)* 41 to 42 labelled a_1(1)* 42 to 43 labelled b_1(1)* 43 to 44 labelled c_1(1)* 44 to 45 labelled b_1(1)* 45 to 46 labelled a_1(1)* 45 to 68 labelled c_1(2)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled a_1(1)* 48 to 41 labelled c_1(1)* 49 to 4 labelled a_1(1)* 49 to 41 labelled c_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled b_1(1)* 61 to 62 labelled c_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled a_1(1)* 64 to 65 labelled a_1(1)* 65 to 66 labelled b_1(1)* 66 to 67 labelled a_1(1)* 67 to 41 labelled a_1(1)* 67 to 77 labelled c_1(2)* 68 to 69 labelled a_1(2)* 69 to 70 labelled b_1(2)* 70 to 71 labelled c_1(2)* 71 to 72 labelled b_1(2)* 72 to 73 labelled a_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled b_1(2)* 75 to 76 labelled a_1(2)* 76 to 41 labelled a_1(2)* 76 to 77 labelled c_1(2)* 77 to 78 labelled a_1(2)* 78 to 79 labelled b_1(2)* 79 to 80 labelled c_1(2)* 80 to 81 labelled b_1(2)* 81 to 82 labelled a_1(2)* 81 to 95 labelled c_1(3)* 82 to 83 labelled a_1(2)* 83 to 84 labelled b_1(2)* 84 to 85 labelled a_1(2)* 84 to 86 labelled c_1(2)* 85 to 44 labelled a_1(2)* 86 to 87 labelled a_1(2)* 87 to 88 labelled b_1(2)* 88 to 89 labelled c_1(2)* 89 to 90 labelled b_1(2)* 90 to 91 labelled a_1(2)* 91 to 92 labelled a_1(2)* 92 to 93 labelled b_1(2)* 93 to 94 labelled a_1(2)* 94 to 68 labelled a_1(2)* 94 to 104 labelled c_1(3)* 95 to 96 labelled a_1(3)* 96 to 97 labelled b_1(3)* 97 to 98 labelled c_1(3)* 98 to 99 labelled b_1(3)* 99 to 100 labelled a_1(3)* 100 to 101 labelled a_1(3)* 101 to 102 labelled b_1(3)* 102 to 103 labelled a_1(3)* 103 to 86 labelled a_1(3)* 103 to 113 labelled c_1(3)* 104 to 105 labelled a_1(3)* 105 to 106 labelled b_1(3)* 106 to 107 labelled c_1(3)* 107 to 108 labelled b_1(3)* 108 to 109 labelled a_1(3)* 109 to 110 labelled a_1(3)* 110 to 111 labelled b_1(3)* 111 to 112 labelled a_1(3)* 112 to 71 labelled a_1(3)* 113 to 114 labelled a_1(3)* 114 to 115 labelled b_1(3)* 115 to 116 labelled c_1(3)* 116 to 117 labelled b_1(3)* 117 to 118 labelled a_1(3)* 118 to 119 labelled a_1(3)* 119 to 120 labelled b_1(3)* 120 to 121 labelled a_1(3)* 121 to 89 labelled a_1(3) ---------------------------------------- (4) YES