3.45/1.53 YES 3.45/1.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.45/1.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.45/1.54 3.45/1.54 3.45/1.54 Termination w.r.t. Q of the given QTRS could be proven: 3.45/1.54 3.45/1.54 (0) QTRS 3.45/1.54 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.45/1.54 (2) YES 3.45/1.54 3.45/1.54 3.45/1.54 ---------------------------------------- 3.45/1.54 3.45/1.54 (0) 3.45/1.54 Obligation: 3.45/1.54 Q restricted rewrite system: 3.45/1.54 The TRS R consists of the following rules: 3.45/1.54 3.45/1.54 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 3.45/1.54 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 3.45/1.54 3.45/1.54 Q is empty. 3.45/1.54 3.45/1.54 ---------------------------------------- 3.45/1.54 3.45/1.54 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.45/1.54 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. 3.45/1.54 The following rules were used to construct the certificate: 3.45/1.54 3.45/1.54 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 3.45/1.54 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 3.45/1.54 3.45/1.54 The certificate found is represented by the following graph. 3.45/1.54 The certificate consists of the following enumerated nodes: 3.45/1.54 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, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128 3.45/1.54 3.45/1.54 Node 1 is start node and node 2 is final node. 3.45/1.54 3.45/1.54 Those nodes are connected through the following edges: 3.45/1.54 3.45/1.54 * 1 to 3 labelled 1_1(0)* 1 to 12 labelled 1_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled 2_1(0)* 4 to 5 labelled 1_1(0)* 5 to 6 labelled 1_1(0)* 6 to 7 labelled 0_1(0)* 6 to 45 labelled 1_1(1)* 6 to 54 labelled 1_1(1)* 7 to 8 labelled 1_1(0)* 8 to 9 labelled 2_1(0)* 9 to 10 labelled 0_1(0)* 9 to 24 labelled 1_1(1)* 9 to 33 labelled 1_1(1)* 10 to 11 labelled 1_1(0)* 11 to 2 labelled 2_1(0)* 12 to 13 labelled 2_1(0)* 13 to 14 labelled 1_1(0)* 14 to 15 labelled 1_1(0)* 15 to 16 labelled 0_1(0)* 15 to 66 labelled 1_1(1)* 15 to 75 labelled 1_1(1)* 16 to 17 labelled 1_1(0)* 17 to 18 labelled 2_1(0)* 18 to 19 labelled 0_1(0)* 18 to 45 labelled 1_1(1)* 18 to 54 labelled 1_1(1)* 19 to 20 labelled 1_1(0)* 20 to 21 labelled 2_1(0)* 21 to 22 labelled 0_1(0)* 21 to 24 labelled 1_1(1)* 21 to 33 labelled 1_1(1)* 22 to 23 labelled 1_1(0)* 23 to 2 labelled 2_1(0)* 24 to 25 labelled 2_1(1)* 25 to 26 labelled 1_1(1)* 26 to 27 labelled 1_1(1)* 27 to 28 labelled 0_1(1)* 27 to 87 labelled 1_1(2)* 27 to 96 labelled 1_1(2)* 28 to 29 labelled 1_1(1)* 29 to 30 labelled 2_1(1)* 30 to 31 labelled 0_1(1)* 30 to 24 labelled 1_1(1)* 30 to 33 labelled 1_1(1)* 31 to 32 labelled 1_1(1)* 32 to 2 labelled 2_1(1)* 33 to 34 labelled 2_1(1)* 34 to 35 labelled 1_1(1)* 35 to 36 labelled 1_1(1)* 36 to 37 labelled 0_1(1)* 36 to 108 labelled 1_1(2)* 36 to 117 labelled 1_1(2)* 37 to 38 labelled 1_1(1)* 38 to 39 labelled 2_1(1)* 39 to 40 labelled 0_1(1)* 39 to 87 labelled 1_1(2)* 39 to 96 labelled 1_1(2)* 40 to 41 labelled 1_1(1)* 41 to 42 labelled 2_1(1)* 42 to 43 labelled 0_1(1)* 42 to 24 labelled 1_1(1)* 42 to 33 labelled 1_1(1)* 43 to 44 labelled 1_1(1)* 44 to 2 labelled 2_1(1)* 45 to 46 labelled 2_1(1)* 46 to 47 labelled 1_1(1)* 47 to 48 labelled 1_1(1)* 48 to 49 labelled 0_1(1)* 49 to 50 labelled 1_1(1)* 50 to 51 labelled 2_1(1)* 51 to 52 labelled 0_1(1)* 52 to 53 labelled 1_1(1)* 53 to 24 labelled 2_1(1)* 53 to 33 labelled 2_1(1)* 54 to 55 labelled 2_1(1)* 55 to 56 labelled 1_1(1)* 56 to 57 labelled 1_1(1)* 57 to 58 labelled 0_1(1)* 58 to 59 labelled 1_1(1)* 59 to 60 labelled 2_1(1)* 60 to 61 labelled 0_1(1)* 61 to 62 labelled 1_1(1)* 62 to 63 labelled 2_1(1)* 63 to 64 labelled 0_1(1)* 64 to 65 labelled 1_1(1)* 65 to 24 labelled 2_1(1)* 65 to 33 labelled 2_1(1)* 66 to 67 labelled 2_1(1)* 67 to 68 labelled 1_1(1)* 68 to 69 labelled 1_1(1)* 69 to 70 labelled 0_1(1)* 70 to 71 labelled 1_1(1)* 71 to 72 labelled 2_1(1)* 72 to 73 labelled 0_1(1)* 73 to 74 labelled 1_1(1)* 74 to 45 labelled 2_1(1)* 74 to 54 labelled 2_1(1)* 75 to 76 labelled 2_1(1)* 76 to 77 labelled 1_1(1)* 77 to 78 labelled 1_1(1)* 78 to 79 labelled 0_1(1)* 79 to 80 labelled 1_1(1)* 80 to 81 labelled 2_1(1)* 81 to 82 labelled 0_1(1)* 82 to 83 labelled 1_1(1)* 83 to 84 labelled 2_1(1)* 84 to 85 labelled 0_1(1)* 85 to 86 labelled 1_1(1)* 86 to 45 labelled 2_1(1)* 86 to 54 labelled 2_1(1)* 87 to 88 labelled 2_1(2)* 88 to 89 labelled 1_1(2)* 89 to 90 labelled 1_1(2)* 90 to 91 labelled 0_1(2)* 91 to 92 labelled 1_1(2)* 92 to 93 labelled 2_1(2)* 93 to 94 labelled 0_1(2)* 94 to 95 labelled 1_1(2)* 95 to 24 labelled 2_1(2)* 95 to 33 labelled 2_1(2)* 96 to 97 labelled 2_1(2)* 97 to 98 labelled 1_1(2)* 98 to 99 labelled 1_1(2)* 99 to 100 labelled 0_1(2)* 100 to 101 labelled 1_1(2)* 101 to 102 labelled 2_1(2)* 102 to 103 labelled 0_1(2)* 103 to 104 labelled 1_1(2)* 104 to 105 labelled 2_1(2)* 105 to 106 labelled 0_1(2)* 106 to 107 labelled 1_1(2)* 107 to 24 labelled 2_1(2)* 107 to 33 labelled 2_1(2)* 108 to 109 labelled 2_1(2)* 109 to 110 labelled 1_1(2)* 110 to 111 labelled 1_1(2)* 111 to 112 labelled 0_1(2)* 112 to 113 labelled 1_1(2)* 113 to 114 labelled 2_1(2)* 114 to 115 labelled 0_1(2)* 115 to 116 labelled 1_1(2)* 116 to 87 labelled 2_1(2)* 116 to 96 labelled 2_1(2)* 117 to 118 labelled 2_1(2)* 118 to 119 labelled 1_1(2)* 119 to 120 labelled 1_1(2)* 120 to 121 labelled 0_1(2)* 121 to 122 labelled 1_1(2)* 122 to 123 labelled 2_1(2)* 123 to 124 labelled 0_1(2)* 124 to 125 labelled 1_1(2)* 125 to 126 labelled 2_1(2)* 126 to 127 labelled 0_1(2)* 127 to 128 labelled 1_1(2)* 128 to 87 labelled 2_1(2)* 128 to 96 labelled 2_1(2) 3.45/1.54 3.45/1.54 3.45/1.54 ---------------------------------------- 3.45/1.54 3.45/1.54 (2) 3.45/1.54 YES 3.45/1.58 EOF