3.79/1.82 YES 3.79/1.84 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.79/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.79/1.84 3.79/1.84 3.79/1.84 Termination w.r.t. Q of the given QTRS could be proven: 3.79/1.84 3.79/1.84 (0) QTRS 3.79/1.84 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.79/1.84 (2) QTRS 3.79/1.84 (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.79/1.84 (4) YES 3.79/1.84 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (0) 3.79/1.84 Obligation: 3.79/1.84 Q restricted rewrite system: 3.79/1.84 The TRS R consists of the following rules: 3.79/1.84 3.79/1.84 b(c(b(c(a(a(x1)))))) -> a(a(a(b(c(b(c(b(c(x1))))))))) 3.79/1.84 3.79/1.84 Q is empty. 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (1) QTRS Reverse (EQUIVALENT) 3.79/1.84 We applied the QTRS Reverse Processor [REVERSE]. 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (2) 3.79/1.84 Obligation: 3.79/1.84 Q restricted rewrite system: 3.79/1.84 The TRS R consists of the following rules: 3.79/1.84 3.79/1.84 a(a(c(b(c(b(x1)))))) -> c(b(c(b(c(b(a(a(a(x1))))))))) 3.79/1.84 3.79/1.84 Q is empty. 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (3) RFCMatchBoundsTRSProof (EQUIVALENT) 3.79/1.84 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. 3.79/1.84 The following rules were used to construct the certificate: 3.79/1.84 3.79/1.84 a(a(c(b(c(b(x1)))))) -> c(b(c(b(c(b(a(a(a(x1))))))))) 3.79/1.84 3.79/1.84 The certificate found is represented by the following graph. 3.79/1.84 The certificate consists of the following enumerated nodes: 3.79/1.84 2, 4, 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 3.79/1.84 3.79/1.84 Node 2 is start node and node 4 is final node. 3.79/1.84 3.79/1.84 Those nodes are connected through the following edges: 3.79/1.84 3.79/1.84 * 2 to 37 labelled c_1(0)* 4 to 4 labelled #_1(0)* 37 to 38 labelled b_1(0)* 38 to 39 labelled c_1(0)* 39 to 40 labelled b_1(0)* 40 to 41 labelled c_1(0)* 41 to 42 labelled b_1(0)* 42 to 43 labelled a_1(0)* 42 to 53 labelled c_1(1)* 43 to 44 labelled a_1(0)* 43 to 45 labelled c_1(1)* 44 to 4 labelled a_1(0)* 44 to 45 labelled c_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled c_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled c_1(1)* 49 to 50 labelled b_1(1)* 50 to 51 labelled a_1(1)* 50 to 61 labelled c_1(2)* 51 to 52 labelled a_1(1)* 51 to 45 labelled c_1(1)* 52 to 4 labelled a_1(1)* 52 to 45 labelled c_1(1)* 53 to 54 labelled b_1(1)* 54 to 55 labelled c_1(1)* 55 to 56 labelled b_1(1)* 56 to 57 labelled c_1(1)* 57 to 58 labelled b_1(1)* 58 to 59 labelled a_1(1)* 59 to 60 labelled a_1(1)* 59 to 69 labelled c_1(2)* 60 to 48 labelled a_1(1)* 61 to 62 labelled b_1(2)* 62 to 63 labelled c_1(2)* 63 to 64 labelled b_1(2)* 64 to 65 labelled c_1(2)* 65 to 66 labelled b_1(2)* 66 to 67 labelled a_1(2)* 67 to 68 labelled a_1(2)* 67 to 69 labelled c_1(2)* 68 to 48 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 c_1(2)* 73 to 74 labelled b_1(2)* 74 to 75 labelled a_1(2)* 75 to 76 labelled a_1(2)* 75 to 77 labelled c_1(3)* 76 to 62 labelled a_1(2)* 77 to 78 labelled b_1(3)* 78 to 79 labelled c_1(3)* 79 to 80 labelled b_1(3)* 80 to 81 labelled c_1(3)* 81 to 82 labelled b_1(3)* 82 to 83 labelled a_1(3)* 82 to 93 labelled c_1(4)* 83 to 84 labelled a_1(3)* 84 to 66 labelled a_1(3)* 84 to 85 labelled c_1(3)* 85 to 86 labelled b_1(3)* 86 to 87 labelled c_1(3)* 87 to 88 labelled b_1(3)* 88 to 89 labelled c_1(3)* 89 to 90 labelled b_1(3)* 90 to 91 labelled a_1(3)* 91 to 92 labelled a_1(3)* 92 to 72 labelled a_1(3)* 93 to 94 labelled b_1(4)* 94 to 95 labelled c_1(4)* 95 to 96 labelled b_1(4)* 96 to 97 labelled c_1(4)* 97 to 98 labelled b_1(4)* 98 to 99 labelled a_1(4)* 99 to 100 labelled a_1(4)* 100 to 88 labelled a_1(4) 3.79/1.84 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (4) 3.79/1.84 YES 3.79/1.87 EOF