/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 45 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(c(a(x1))) -> c(a(c(x1))) a(a(b(x1))) -> a(d(b(x1))) a(b(x1)) -> b(a(a(x1))) d(d(x1)) -> a(d(b(x1))) b(b(x1)) -> b(c(x1)) a(d(c(x1))) -> c(a(x1)) b(c(x1)) -> a(a(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(c(a(x1))) -> c(a(c(x1))) b(a(a(x1))) -> b(d(a(x1))) b(a(x1)) -> a(a(b(x1))) d(d(x1)) -> b(d(a(x1))) b(b(x1)) -> c(b(x1)) c(d(a(x1))) -> a(c(x1)) c(b(x1)) -> a(a(a(x1))) 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: a(c(a(x1))) -> c(a(c(x1))) b(a(a(x1))) -> b(d(a(x1))) b(a(x1)) -> a(a(b(x1))) d(d(x1)) -> b(d(a(x1))) b(b(x1)) -> c(b(x1)) c(d(a(x1))) -> a(c(x1)) c(b(x1)) -> a(a(a(x1))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 11, 12, 13, 14, 15, 16, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 140, 141 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 11 labelled c_1(0)* 3 to 13 labelled b_1(0)* 3 to 15 labelled a_1(0)* 3 to 16 labelled c_1(0)* 3 to 12 labelled a_1(0), c_1(1)* 3 to 24 labelled a_1(1)* 3 to 33 labelled c_1(1)* 3 to 58 labelled c_1(2)* 4 to 4 labelled #_1(0)* 11 to 12 labelled a_1(0), c_1(1)* 11 to 33 labelled c_1(1)* 12 to 4 labelled c_1(0)* 12 to 26 labelled a_1(1)* 12 to 24 labelled a_1(1)* 12 to 12 labelled c_1(1)* 12 to 35 labelled c_1(2)* 12 to 58 labelled c_1(2)* 12 to 37 labelled c_1(2)* 12 to 60 labelled c_1(2)* 13 to 14 labelled d_1(0)* 14 to 4 labelled a_1(0)* 14 to 12 labelled c_1(1)* 15 to 16 labelled a_1(0)* 15 to 33 labelled c_1(1)* 16 to 4 labelled b_1(0), a_1(0)* 16 to 27 labelled b_1(1)* 16 to 29 labelled a_1(1)* 16 to 30 labelled c_1(1)* 16 to 12 labelled c_1(1)* 16 to 31 labelled a_1(2)* 16 to 60 labelled c_1(2)* 16 to 62 labelled c_1(3)* 24 to 25 labelled a_1(1)* 24 to 35 labelled c_1(2)* 25 to 4 labelled a_1(1)* 25 to 27 labelled a_1(1)* 25 to 12 labelled c_1(1)* 26 to 4 labelled c_1(1)* 26 to 26 labelled a_1(1)* 26 to 24 labelled a_1(1)* 26 to 34 labelled c_1(1)* 26 to 12 labelled c_1(1)* 26 to 35 labelled c_1(2)* 26 to 58 labelled c_1(2)* 26 to 36 labelled c_1(1)* 26 to 59 labelled c_1(1)* 26 to 37 labelled c_1(2)* 26 to 38 labelled c_1(1)* 26 to 60 labelled c_1(2)* 27 to 28 labelled d_1(1)* 28 to 4 labelled a_1(1)* 28 to 12 labelled c_1(1)* 29 to 30 labelled a_1(1)* 29 to 37 labelled c_1(2)* 30 to 4 labelled b_1(1)* 30 to 27 labelled b_1(1)* 30 to 29 labelled a_1(1)* 30 to 30 labelled c_1(1)* 30 to 31 labelled a_1(2)* 30 to 60 labelled c_1(2)* 30 to 62 labelled c_1(3)* 31 to 32 labelled a_1(2)* 31 to 35 labelled c_1(2)* 32 to 4 labelled a_1(2)* 32 to 12 labelled c_1(1)* 32 to 27 labelled a_1(2)* 33 to 34 labelled a_1(1)* 33 to 35 labelled c_1(2)* 34 to 26 labelled c_1(1)* 34 to 24 labelled c_1(1)* 34 to 29 labelled c_1(1)* 34 to 31 labelled c_1(1)* 34 to 61 labelled c_1(1)* 34 to 63 labelled c_1(1)* 35 to 36 labelled a_1(2)* 35 to 35 labelled c_1(2)* 35 to 12 labelled c_1(1)* 35 to 37 labelled c_1(2)* 35 to 64 labelled c_1(3)* 35 to 62 labelled c_1(3)* 36 to 26 labelled c_1(2), a_1(1)* 36 to 24 labelled c_1(2), a_1(1)* 36 to 25 labelled c_1(2)* 36 to 30 labelled c_1(2)* 36 to 4 labelled c_1(2)* 36 to 27 labelled c_1(2)* 36 to 31 labelled a_1(2)* 36 to 59 labelled c_1(2)* 36 to 32 labelled c_1(2)* 36 to 36 labelled a_1(2)* 36 to 12 labelled c_1(1)* 36 to 35 labelled c_1(2)* 36 to 58 labelled c_1(2)* 36 to 62 labelled c_1(3)* 36 to 37 labelled c_1(2)* 36 to 64 labelled c_1(3)* 36 to 60 labelled c_1(2)* 37 to 38 labelled a_1(2)* 37 to 35 labelled c_1(2)* 37 to 66 labelled c_1(3)* 38 to 29 labelled c_1(2)* 38 to 31 labelled c_1(2)* 38 to 61 labelled c_1(2)* 38 to 63 labelled c_1(2)* 58 to 59 labelled a_1(2)* 58 to 35 labelled c_1(2)* 58 to 64 labelled c_1(3)* 58 to 62 labelled c_1(3)* 59 to 36 labelled c_1(2)* 60 to 61 labelled a_1(2)* 61 to 38 labelled c_1(2)* 62 to 63 labelled a_1(3)* 62 to 35 labelled c_1(2)* 62 to 64 labelled c_1(3)* 62 to 62 labelled c_1(3)* 63 to 36 labelled c_1(3)* 64 to 65 labelled a_1(3)* 64 to 66 labelled c_1(3)* 64 to 12 labelled c_1(1)* 64 to 35 labelled c_1(2)* 64 to 62 labelled c_1(3)* 64 to 64 labelled c_1(3)* 64 to 140 labelled c_1(4)* 65 to 31 labelled c_1(3)* 65 to 4 labelled c_1(3)* 65 to 27 labelled c_1(3)* 65 to 26 labelled a_1(1)* 65 to 24 labelled a_1(1)* 65 to 59 labelled c_1(3)* 65 to 38 labelled c_1(3)* 65 to 63 labelled c_1(3)* 65 to 65 labelled c_1(3)* 65 to 36 labelled a_1(2)* 65 to 12 labelled c_1(1)* 65 to 35 labelled c_1(2)* 65 to 58 labelled c_1(2)* 65 to 62 labelled c_1(3)* 65 to 64 labelled c_1(3)* 65 to 60 labelled c_1(2)* 65 to 37 labelled c_1(2)* 65 to 61 labelled c_1(3)* 66 to 67 labelled a_1(3)* 66 to 64 labelled c_1(3)* 67 to 32 labelled c_1(3)* 140 to 141 labelled a_1(4)* 140 to 35 labelled c_1(2)* 140 to 62 labelled c_1(3)* 141 to 63 labelled c_1(4)* 141 to 65 labelled c_1(4) ---------------------------------------- (4) YES