/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 27 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> a(b(b(b(x1)))) b(a(x1)) -> b(b(c(x1))) a(b(b(c(x1)))) -> a(a(a(b(x1)))) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. The following rules were used to construct the certificate: a(a(x1)) -> a(b(b(b(x1)))) b(a(x1)) -> b(b(c(x1))) a(b(b(c(x1)))) -> a(a(a(b(x1)))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 87, 88, 89, 90 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 5 labelled a_1(0)* 1 to 8 labelled b_1(0)* 1 to 10 labelled a_1(0)* 1 to 40 labelled a_1(1)* 2 to 2 labelled #_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled b_1(0)* 7 to 2 labelled b_1(0)* 7 to 43 labelled b_1(1)* 8 to 9 labelled b_1(0)* 9 to 2 labelled c_1(0)* 10 to 11 labelled a_1(0)* 10 to 45 labelled a_1(1)* 11 to 12 labelled a_1(0)* 11 to 48 labelled a_1(1)* 11 to 55 labelled a_1(2)* 12 to 2 labelled b_1(0)* 12 to 43 labelled b_1(1)* 40 to 41 labelled b_1(1)* 41 to 42 labelled b_1(1)* 42 to 11 labelled b_1(1)* 42 to 45 labelled b_1(1)* 42 to 53 labelled b_1(2)* 43 to 44 labelled b_1(1)* 44 to 2 labelled c_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled b_1(1)* 46 to 12 labelled c_1(1)* 47 to 12 labelled b_1(1)* 47 to 48 labelled b_1(1)* 47 to 55 labelled b_1(1)* 47 to 61 labelled b_1(2)* 48 to 49 labelled a_1(1)* 48 to 58 labelled a_1(2)* 49 to 50 labelled a_1(1)* 49 to 48 labelled a_1(1)* 49 to 55 labelled a_1(2)* 49 to 63 labelled a_1(2)* 49 to 70 labelled a_1(3)* 50 to 2 labelled b_1(1)* 50 to 43 labelled b_1(1)* 53 to 54 labelled b_1(2)* 54 to 48 labelled c_1(2)* 54 to 55 labelled c_1(2)* 55 to 56 labelled b_1(2)* 56 to 57 labelled b_1(2)* 57 to 49 labelled b_1(2)* 57 to 58 labelled b_1(2)* 57 to 53 labelled b_1(2)* 57 to 68 labelled b_1(3)* 58 to 59 labelled b_1(2)* 59 to 60 labelled b_1(2)* 59 to 50 labelled c_1(2)* 60 to 50 labelled b_1(2)* 60 to 48 labelled b_1(2)* 60 to 61 labelled b_1(2)* 60 to 66 labelled b_1(3)* 60 to 55 labelled b_1(2)* 60 to 63 labelled b_1(2)* 60 to 70 labelled b_1(2)* 61 to 62 labelled b_1(2)* 62 to 49 labelled c_1(2)* 62 to 58 labelled c_1(2)* 63 to 64 labelled a_1(2)* 63 to 73 labelled a_1(3)* 63 to 58 labelled a_1(2)* 64 to 65 labelled a_1(2)* 64 to 48 labelled a_1(1)* 64 to 55 labelled a_1(2)* 64 to 63 labelled a_1(2)* 64 to 70 labelled a_1(3)* 65 to 2 labelled b_1(2)* 65 to 43 labelled b_1(1)* 66 to 67 labelled b_1(3)* 67 to 58 labelled c_1(3)* 67 to 64 labelled c_1(3)* 67 to 73 labelled c_1(3)* 68 to 69 labelled b_1(3)* 69 to 55 labelled c_1(3)* 69 to 63 labelled c_1(3)* 69 to 70 labelled c_1(3)* 70 to 71 labelled b_1(3)* 71 to 72 labelled b_1(3)* 72 to 64 labelled b_1(3)* 72 to 73 labelled b_1(3)* 72 to 53 labelled b_1(2)* 72 to 58 labelled b_1(3)* 72 to 68 labelled b_1(3)* 72 to 89 labelled b_1(4)* 73 to 74 labelled b_1(3)* 74 to 75 labelled b_1(3)* 74 to 65 labelled c_1(3)* 75 to 65 labelled b_1(3)* 75 to 55 labelled b_1(3)* 75 to 63 labelled b_1(3)* 75 to 66 labelled b_1(3)* 75 to 87 labelled b_1(4)* 75 to 70 labelled b_1(3)* 87 to 88 labelled b_1(4)* 88 to 73 labelled c_1(4)* 89 to 90 labelled b_1(4)* 90 to 70 labelled c_1(4) ---------------------------------------- (2) YES