/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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: b(a(b(a(c(x1))))) -> a(c(b(a(c(b(b(a(b(b(a(b(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: b(a(b(a(c(x1))))) -> a(c(b(a(c(b(b(a(b(b(a(b(a(x1))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 15, 16, 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 Node 15 is start node and node 16 is final node. Those nodes are connected through the following edges: * 15 to 29 labelled a_1(0)* 16 to 16 labelled #_1(0)* 29 to 30 labelled c_1(0)* 30 to 31 labelled b_1(0)* 31 to 32 labelled a_1(0)* 32 to 33 labelled c_1(0)* 33 to 34 labelled b_1(0)* 34 to 35 labelled b_1(0)* 34 to 53 labelled a_1(1)* 35 to 36 labelled a_1(0)* 36 to 37 labelled b_1(0)* 37 to 38 labelled b_1(0)* 37 to 41 labelled a_1(1)* 38 to 39 labelled a_1(0)* 39 to 40 labelled b_1(0)* 39 to 41 labelled a_1(1)* 40 to 16 labelled a_1(0)* 41 to 42 labelled c_1(1)* 42 to 43 labelled b_1(1)* 43 to 44 labelled a_1(1)* 44 to 45 labelled c_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled b_1(1)* 46 to 65 labelled a_1(2)* 47 to 48 labelled a_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled b_1(1)* 49 to 41 labelled a_1(1)* 50 to 51 labelled a_1(1)* 51 to 52 labelled b_1(1)* 51 to 41 labelled a_1(1)* 52 to 16 labelled a_1(1)* 53 to 54 labelled c_1(1)* 54 to 55 labelled b_1(1)* 55 to 56 labelled a_1(1)* 56 to 57 labelled c_1(1)* 57 to 58 labelled b_1(1)* 58 to 59 labelled b_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled b_1(1)* 61 to 62 labelled b_1(1)* 62 to 63 labelled a_1(1)* 63 to 64 labelled b_1(1)* 63 to 77 labelled a_1(2)* 64 to 42 labelled a_1(1)* 65 to 66 labelled c_1(2)* 66 to 67 labelled b_1(2)* 67 to 68 labelled a_1(2)* 68 to 69 labelled c_1(2)* 69 to 70 labelled b_1(2)* 70 to 71 labelled b_1(2)* 71 to 72 labelled a_1(2)* 72 to 73 labelled b_1(2)* 73 to 74 labelled b_1(2)* 74 to 75 labelled a_1(2)* 75 to 76 labelled b_1(2)* 75 to 77 labelled a_1(2)* 76 to 42 labelled a_1(2)* 77 to 78 labelled c_1(2)* 78 to 79 labelled b_1(2)* 79 to 80 labelled a_1(2)* 80 to 81 labelled c_1(2)* 81 to 82 labelled b_1(2)* 82 to 83 labelled b_1(2)* 83 to 84 labelled a_1(2)* 84 to 85 labelled b_1(2)* 85 to 86 labelled b_1(2)* 86 to 87 labelled a_1(2)* 87 to 88 labelled b_1(2)* 87 to 89 labelled a_1(2)* 88 to 45 labelled a_1(2)* 89 to 90 labelled c_1(2)* 90 to 91 labelled b_1(2)* 91 to 92 labelled a_1(2)* 92 to 93 labelled c_1(2)* 93 to 94 labelled b_1(2)* 94 to 95 labelled b_1(2)* 95 to 96 labelled a_1(2)* 96 to 97 labelled b_1(2)* 97 to 98 labelled b_1(2)* 98 to 99 labelled a_1(2)* 99 to 100 labelled b_1(2)* 99 to 101 labelled a_1(3)* 100 to 66 labelled a_1(2)* 101 to 102 labelled c_1(3)* 102 to 103 labelled b_1(3)* 103 to 104 labelled a_1(3)* 104 to 105 labelled c_1(3)* 105 to 106 labelled b_1(3)* 106 to 107 labelled b_1(3)* 107 to 108 labelled a_1(3)* 108 to 109 labelled b_1(3)* 109 to 110 labelled b_1(3)* 110 to 111 labelled a_1(3)* 111 to 112 labelled b_1(3)* 112 to 69 labelled a_1(3) ---------------------------------------- (4) YES