/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 9 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> a(b(a(x1))) b(a(b(x1))) -> a(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: a(a(x1)) -> a(b(a(x1))) b(a(b(x1))) -> a(c(a(x1))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 5. This implies Q-termination of R. The following rules were used to construct the certificate: a(a(x1)) -> a(b(a(x1))) b(a(b(x1))) -> a(c(a(x1))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 7, 8, 9, 10, 11, 12, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 47, 48, 51, 52, 53, 54, 55, 56, 59, 60 Node 7 is start node and node 8 is final node. Those nodes are connected through the following edges: * 7 to 9 labelled a_1(0)* 7 to 11 labelled a_1(0)* 7 to 31 labelled a_1(1)* 8 to 8 labelled #_1(0)* 9 to 10 labelled b_1(0)* 9 to 29 labelled a_1(1)* 10 to 8 labelled a_1(0)* 10 to 27 labelled a_1(1)* 10 to 33 labelled a_1(2)* 10 to 37 labelled a_1(3)* 11 to 12 labelled c_1(0)* 12 to 8 labelled a_1(0)* 12 to 27 labelled a_1(1)* 12 to 33 labelled a_1(2)* 12 to 37 labelled a_1(3)* 27 to 28 labelled b_1(1)* 27 to 29 labelled a_1(1)* 27 to 35 labelled a_1(2)* 28 to 8 labelled a_1(1)* 28 to 27 labelled a_1(1)* 28 to 33 labelled a_1(2)* 28 to 37 labelled a_1(3)* 29 to 30 labelled c_1(1)* 30 to 8 labelled a_1(1)* 30 to 27 labelled a_1(1)* 30 to 28 labelled a_1(1)* 30 to 33 labelled a_1(2)* 30 to 34 labelled a_1(1)* 30 to 37 labelled a_1(3)* 30 to 38 labelled a_1(1)* 31 to 32 labelled b_1(1)* 32 to 29 labelled a_1(1)* 33 to 34 labelled b_1(2)* 33 to 29 labelled a_1(1)* 33 to 35 labelled a_1(2)* 33 to 47 labelled a_1(3)* 34 to 29 labelled a_1(2)* 34 to 8 labelled a_1(2)* 34 to 27 labelled a_1(2), a_1(1)* 34 to 33 labelled a_1(2)* 34 to 35 labelled a_1(2)* 34 to 37 labelled a_1(3), a_1(2)* 34 to 47 labelled a_1(2)* 35 to 36 labelled c_1(2)* 36 to 28 labelled a_1(2)* 36 to 33 labelled a_1(2)* 36 to 41 labelled a_1(3)* 36 to 34 labelled a_1(2)* 36 to 37 labelled a_1(3)* 36 to 51 labelled a_1(4)* 36 to 38 labelled a_1(2)* 37 to 38 labelled b_1(3)* 38 to 35 labelled a_1(3)* 38 to 47 labelled a_1(3)* 41 to 42 labelled b_1(3)* 41 to 47 labelled a_1(3)* 41 to 29 labelled a_1(1)* 41 to 35 labelled a_1(2)* 41 to 55 labelled a_1(4)* 42 to 33 labelled a_1(3), a_1(2)* 42 to 37 labelled a_1(3)* 42 to 29 labelled a_1(3)* 42 to 8 labelled a_1(3)* 42 to 27 labelled a_1(3), a_1(1)* 42 to 51 labelled a_1(4)* 47 to 48 labelled c_1(3)* 48 to 34 labelled a_1(3)* 48 to 38 labelled a_1(3)* 48 to 41 labelled a_1(3)* 48 to 33 labelled a_1(2)* 48 to 37 labelled a_1(3)* 48 to 53 labelled a_1(4)* 48 to 51 labelled a_1(4)* 48 to 59 labelled a_1(5)* 51 to 52 labelled b_1(4)* 52 to 47 labelled a_1(4)* 52 to 55 labelled a_1(4)* 53 to 54 labelled b_1(4)* 53 to 55 labelled a_1(4)* 54 to 37 labelled a_1(4)* 54 to 35 labelled a_1(4)* 55 to 56 labelled c_1(4)* 56 to 38 labelled a_1(4)* 56 to 53 labelled a_1(4)* 56 to 51 labelled a_1(4)* 56 to 52 labelled a_1(4)* 56 to 59 labelled a_1(5)* 59 to 60 labelled b_1(5)* 60 to 55 labelled a_1(5)* 60 to 47 labelled a_1(5) ---------------------------------------- (4) YES