/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Strip Symbols Proof [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 14 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(a(a(a(x1)))))) -> a(a(a(b(a(b(a(b(a(x1))))))))) Q is empty. ---------------------------------------- (1) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(b(a(a(a(x1)))))) -> a(a(a(b(a(b(a(b(a(x1))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) Q is empty. ---------------------------------------- (3) 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: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 35, 36, 37, 38, 39, 40, 41, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 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, 190, 191, 192, 193, 194, 195, 196 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 5 labelled a_1(0)* 4 to 4 labelled #_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 7 to 35 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 12 labelled a_1(1)* 10 to 11 labelled a_1(0)* 11 to 4 labelled b_1(0)* 11 to 12 labelled a_1(1)* 12 to 13 labelled a_1(1)* 13 to 14 labelled a_1(1)* 14 to 15 labelled b_1(1)* 14 to 66 labelled a_1(2)* 15 to 16 labelled a_1(1)* 16 to 17 labelled b_1(1)* 16 to 12 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 4 labelled b_1(1)* 18 to 12 labelled a_1(1)* 35 to 36 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 38 labelled b_1(1)* 38 to 39 labelled a_1(1)* 39 to 40 labelled b_1(1)* 39 to 73 labelled a_1(2)* 40 to 41 labelled a_1(1)* 41 to 12 labelled b_1(1)* 66 to 67 labelled a_1(2)* 67 to 68 labelled a_1(2)* 68 to 69 labelled b_1(2)* 69 to 70 labelled a_1(2)* 70 to 71 labelled b_1(2)* 70 to 73 labelled a_1(2)* 71 to 72 labelled a_1(2)* 72 to 12 labelled b_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled a_1(2)* 75 to 76 labelled b_1(2)* 76 to 77 labelled a_1(2)* 77 to 78 labelled b_1(2)* 77 to 88 labelled a_1(3)* 78 to 79 labelled a_1(2)* 79 to 14 labelled b_1(2)* 88 to 89 labelled a_1(3)* 89 to 90 labelled a_1(3)* 90 to 91 labelled b_1(3)* 90 to 102 labelled a_1(4)* 91 to 92 labelled a_1(3)* 92 to 93 labelled b_1(3)* 93 to 94 labelled a_1(3)* 94 to 67 labelled b_1(3)* 94 to 95 labelled a_1(3)* 95 to 96 labelled a_1(3)* 96 to 97 labelled a_1(3)* 97 to 98 labelled b_1(3)* 98 to 99 labelled a_1(3)* 99 to 100 labelled b_1(3)* 99 to 109 labelled a_1(3)* 100 to 101 labelled a_1(3)* 101 to 73 labelled b_1(3)* 102 to 103 labelled a_1(4)* 103 to 104 labelled a_1(4)* 104 to 105 labelled b_1(4)* 105 to 106 labelled a_1(4)* 106 to 107 labelled b_1(4)* 106 to 190 labelled a_1(4)* 107 to 108 labelled a_1(4)* 108 to 95 labelled b_1(4)* 109 to 110 labelled a_1(3)* 110 to 111 labelled a_1(3)* 111 to 112 labelled b_1(3)* 112 to 113 labelled a_1(3)* 113 to 114 labelled b_1(3)* 114 to 115 labelled a_1(3)* 115 to 75 labelled b_1(3)* 190 to 191 labelled a_1(4)* 191 to 192 labelled a_1(4)* 192 to 193 labelled b_1(4)* 193 to 194 labelled a_1(4)* 194 to 195 labelled b_1(4)* 195 to 196 labelled a_1(4)* 196 to 97 labelled b_1(4) ---------------------------------------- (4) YES