3.30/1.67 YES 3.30/1.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.30/1.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.30/1.68 3.30/1.68 3.30/1.68 Termination w.r.t. Q of the given QTRS could be proven: 3.30/1.68 3.30/1.68 (0) QTRS 3.30/1.68 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.30/1.68 (2) YES 3.30/1.68 3.30/1.68 3.30/1.68 ---------------------------------------- 3.30/1.68 3.30/1.68 (0) 3.30/1.68 Obligation: 3.30/1.68 Q restricted rewrite system: 3.30/1.68 The TRS R consists of the following rules: 3.30/1.68 3.30/1.68 b(a(b(a(a(x1))))) -> a(a(a(b(a(b(a(b(x1)))))))) 3.30/1.68 3.30/1.68 Q is empty. 3.30/1.68 3.30/1.68 ---------------------------------------- 3.30/1.68 3.30/1.68 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.30/1.68 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. 3.30/1.68 The following rules were used to construct the certificate: 3.30/1.68 3.30/1.68 b(a(b(a(a(x1))))) -> a(a(a(b(a(b(a(b(x1)))))))) 3.30/1.68 3.30/1.68 The certificate found is represented by the following graph. 3.30/1.68 The certificate consists of the following enumerated nodes: 3.30/1.68 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 3.30/1.68 3.30/1.68 Node 1 is start node and node 2 is final node. 3.30/1.68 3.30/1.68 Those nodes are connected through the following edges: 3.30/1.68 3.30/1.68 * 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled b_1(0)* 5 to 17 labelled a_1(1)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 7 to 10 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 2 labelled b_1(0)* 9 to 10 labelled a_1(1)* 10 to 11 labelled a_1(1)* 11 to 12 labelled a_1(1)* 12 to 13 labelled b_1(1)* 12 to 24 labelled a_1(2)* 13 to 14 labelled a_1(1)* 14 to 15 labelled b_1(1)* 14 to 10 labelled a_1(1)* 15 to 16 labelled a_1(1)* 16 to 2 labelled b_1(1)* 16 to 10 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 19 labelled a_1(1)* 19 to 20 labelled b_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 31 labelled a_1(2)* 22 to 23 labelled a_1(1)* 23 to 10 labelled b_1(1)* 24 to 25 labelled a_1(2)* 25 to 26 labelled a_1(2)* 26 to 27 labelled b_1(2)* 27 to 28 labelled a_1(2)* 28 to 29 labelled b_1(2)* 28 to 31 labelled a_1(2)* 29 to 30 labelled a_1(2)* 30 to 10 labelled b_1(2)* 31 to 32 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled b_1(2)* 34 to 35 labelled a_1(2)* 35 to 36 labelled b_1(2)* 35 to 38 labelled a_1(3)* 36 to 37 labelled a_1(2)* 37 to 12 labelled b_1(2)* 38 to 39 labelled a_1(3)* 39 to 40 labelled a_1(3)* 40 to 41 labelled b_1(3)* 40 to 52 labelled a_1(4)* 41 to 42 labelled a_1(3)* 42 to 43 labelled b_1(3)* 43 to 44 labelled a_1(3)* 44 to 25 labelled b_1(3)* 44 to 45 labelled a_1(3)* 45 to 46 labelled a_1(3)* 46 to 47 labelled a_1(3)* 47 to 48 labelled b_1(3)* 48 to 49 labelled a_1(3)* 49 to 50 labelled b_1(3)* 49 to 59 labelled a_1(3)* 50 to 51 labelled a_1(3)* 51 to 31 labelled b_1(3)* 52 to 53 labelled a_1(4)* 53 to 54 labelled a_1(4)* 54 to 55 labelled b_1(4)* 55 to 56 labelled a_1(4)* 56 to 57 labelled b_1(4)* 56 to 66 labelled a_1(4)* 57 to 58 labelled a_1(4)* 58 to 45 labelled b_1(4)* 59 to 60 labelled a_1(3)* 60 to 61 labelled a_1(3)* 61 to 62 labelled b_1(3)* 62 to 63 labelled a_1(3)* 63 to 64 labelled b_1(3)* 64 to 65 labelled a_1(3)* 65 to 33 labelled b_1(3)* 66 to 67 labelled a_1(4)* 67 to 68 labelled a_1(4)* 68 to 69 labelled b_1(4)* 69 to 70 labelled a_1(4)* 70 to 71 labelled b_1(4)* 71 to 72 labelled a_1(4)* 72 to 47 labelled b_1(4) 3.30/1.68 3.30/1.68 3.30/1.68 ---------------------------------------- 3.30/1.68 3.30/1.68 (2) 3.30/1.68 YES 3.61/1.71 EOF