/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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(c(x1)) -> a(b(x1)) b(x1) -> a(a(x1)) b(b(b(x1))) -> a(c(b(x1))) a(c(a(x1))) -> a(c(c(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: c(c(x1)) -> b(a(x1)) b(x1) -> a(a(x1)) b(b(b(x1))) -> b(c(a(x1))) a(c(a(x1))) -> c(c(a(x1))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 6. This implies Q-termination of R. The following rules were used to construct the certificate: c(c(x1)) -> b(a(x1)) b(x1) -> a(a(x1)) b(b(b(x1))) -> b(c(a(x1))) a(c(a(x1))) -> c(c(a(x1))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 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, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85 Node 31 is start node and node 32 is final node. Those nodes are connected through the following edges: * 31 to 33 labelled b_1(0), a_1(0)* 31 to 34 labelled b_1(0), c_1(0)* 31 to 36 labelled a_1(1)* 31 to 37 labelled b_1(1)* 31 to 40 labelled a_1(2)* 31 to 51 labelled c_1(1)* 31 to 53 labelled c_1(2)* 31 to 55 labelled b_1(1)* 31 to 58 labelled b_1(2)* 31 to 59 labelled b_1(3)* 31 to 62 labelled a_1(3)* 31 to 63 labelled a_1(4)* 32 to 32 labelled #_1(0)* 33 to 32 labelled a_1(0)* 33 to 38 labelled c_1(1)* 33 to 41 labelled b_1(2)* 33 to 43 labelled a_1(3)* 34 to 35 labelled c_1(0)* 34 to 42 labelled b_1(1)* 34 to 44 labelled a_1(2)* 34 to 64 labelled b_1(2)* 34 to 72 labelled a_1(3)* 35 to 32 labelled a_1(0)* 35 to 38 labelled c_1(1)* 35 to 41 labelled b_1(2)* 35 to 43 labelled a_1(3)* 36 to 33 labelled a_1(1)* 36 to 34 labelled a_1(1)* 36 to 38 labelled c_1(1)* 36 to 41 labelled b_1(2)* 36 to 43 labelled a_1(3)* 36 to 53 labelled c_1(2)* 36 to 59 labelled b_1(3)* 36 to 63 labelled a_1(4)* 37 to 35 labelled a_1(1)* 37 to 53 labelled c_1(2)* 37 to 59 labelled b_1(3)* 37 to 63 labelled a_1(4)* 38 to 39 labelled c_1(1)* 38 to 45 labelled b_1(2)* 38 to 48 labelled a_1(3)* 38 to 66 labelled b_1(3)* 38 to 73 labelled a_1(4)* 39 to 32 labelled a_1(1)* 39 to 38 labelled c_1(1)* 39 to 41 labelled b_1(2)* 39 to 43 labelled a_1(3), a_1(1)* 40 to 37 labelled a_1(2)* 40 to 55 labelled a_1(2)* 40 to 68 labelled c_1(2)* 40 to 74 labelled b_1(3)* 40 to 64 labelled c_1(2)* 40 to 76 labelled a_1(4)* 41 to 39 labelled a_1(2)* 41 to 53 labelled c_1(2)* 41 to 59 labelled b_1(3)* 41 to 63 labelled a_1(4)* 42 to 38 labelled a_1(1)* 42 to 46 labelled c_1(2)* 42 to 49 labelled b_1(3)* 42 to 50 labelled a_1(4)* 43 to 41 labelled a_1(3)* 44 to 42 labelled a_1(2)* 44 to 70 labelled c_1(3)* 44 to 75 labelled b_1(4)* 44 to 77 labelled a_1(5)* 45 to 38 labelled a_1(2)* 45 to 46 labelled c_1(2)* 45 to 49 labelled b_1(3)* 45 to 50 labelled a_1(4)* 46 to 47 labelled c_1(2)* 46 to 45 labelled b_1(2)* 46 to 48 labelled a_1(3)* 46 to 66 labelled b_1(3)* 46 to 73 labelled a_1(4)* 47 to 32 labelled a_1(2)* 47 to 38 labelled c_1(1)* 47 to 41 labelled b_1(2)* 47 to 43 labelled a_1(2), a_1(3)* 48 to 45 labelled a_1(3)* 48 to 70 labelled c_1(3)* 48 to 75 labelled b_1(4)* 48 to 77 labelled a_1(5)* 49 to 47 labelled a_1(3)* 49 to 53 labelled c_1(2)* 49 to 59 labelled b_1(3)* 49 to 63 labelled a_1(4)* 50 to 49 labelled a_1(4)* 51 to 52 labelled c_1(1)* 52 to 48 labelled a_1(1)* 52 to 73 labelled a_1(1)* 53 to 54 labelled c_1(2)* 54 to 48 labelled a_1(2)* 54 to 73 labelled a_1(2)* 55 to 56 labelled c_1(1)* 56 to 49 labelled a_1(1)* 56 to 59 labelled a_1(1)* 58 to 52 labelled a_1(2)* 59 to 54 labelled a_1(3)* 62 to 58 labelled a_1(3)* 63 to 59 labelled a_1(4)* 64 to 65 labelled c_1(2)* 65 to 59 labelled a_1(2)* 66 to 67 labelled c_1(3)* 67 to 59 labelled a_1(3)* 68 to 69 labelled c_1(2)* 69 to 49 labelled a_1(2)* 70 to 71 labelled c_1(3)* 71 to 48 labelled a_1(3)* 71 to 73 labelled a_1(3)* 72 to 64 labelled a_1(3)* 72 to 66 labelled c_1(3)* 72 to 80 labelled b_1(4)* 72 to 84 labelled a_1(5)* 73 to 66 labelled a_1(4)* 73 to 78 labelled c_1(4)* 73 to 81 labelled b_1(5)* 73 to 85 labelled a_1(6)* 74 to 69 labelled a_1(3)* 74 to 65 labelled a_1(3)* 75 to 71 labelled a_1(4)* 76 to 74 labelled a_1(4)* 77 to 75 labelled a_1(5)* 78 to 79 labelled c_1(4)* 79 to 59 labelled a_1(4)* 80 to 67 labelled a_1(4)* 81 to 79 labelled a_1(5)* 84 to 80 labelled a_1(5)* 85 to 81 labelled a_1(6) ---------------------------------------- (4) YES