/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 8 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(a(a(a(b(a(a(x1)))))))))) -> a(b(a(a(a(a(b(b(a(a(a(a(b(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: a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) Q is empty. ---------------------------------------- (5) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158 Node 30 is start node and node 31 is final node. Those nodes are connected through the following edges: * 30 to 32 labelled b_1(0)* 31 to 31 labelled #_1(0)* 32 to 33 labelled a_1(0)* 33 to 34 labelled a_1(0)* 34 to 35 labelled a_1(0)* 35 to 36 labelled a_1(0)* 36 to 37 labelled b_1(0)* 37 to 38 labelled b_1(0)* 38 to 39 labelled a_1(0)* 38 to 125 labelled b_1(1)* 39 to 40 labelled a_1(0)* 40 to 41 labelled a_1(0)* 40 to 102 labelled b_1(1)* 41 to 42 labelled a_1(0)* 42 to 31 labelled b_1(0)* 102 to 103 labelled a_1(1)* 103 to 104 labelled a_1(1)* 104 to 105 labelled a_1(1)* 105 to 106 labelled a_1(1)* 106 to 107 labelled b_1(1)* 107 to 108 labelled b_1(1)* 108 to 109 labelled a_1(1)* 108 to 148 labelled b_1(2)* 109 to 110 labelled a_1(1)* 110 to 111 labelled a_1(1)* 110 to 102 labelled b_1(1)* 111 to 112 labelled a_1(1)* 112 to 31 labelled b_1(1)* 125 to 126 labelled a_1(1)* 126 to 127 labelled a_1(1)* 127 to 128 labelled a_1(1)* 128 to 129 labelled a_1(1)* 129 to 130 labelled b_1(1)* 130 to 131 labelled b_1(1)* 131 to 132 labelled a_1(1)* 131 to 148 labelled b_1(2)* 132 to 133 labelled a_1(1)* 133 to 134 labelled a_1(1)* 133 to 102 labelled b_1(1)* 134 to 135 labelled a_1(1)* 135 to 108 labelled b_1(1)* 148 to 149 labelled a_1(2)* 149 to 150 labelled a_1(2)* 150 to 151 labelled a_1(2)* 151 to 152 labelled a_1(2)* 152 to 153 labelled b_1(2)* 153 to 154 labelled b_1(2)* 154 to 155 labelled a_1(2)* 154 to 148 labelled b_1(2)* 155 to 156 labelled a_1(2)* 156 to 157 labelled a_1(2)* 156 to 102 labelled b_1(1)* 157 to 158 labelled a_1(2)* 158 to 108 labelled b_1(2) ---------------------------------------- (6) YES