/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 18 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, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 54, 55, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 88, 89 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 5 labelled c_1(0)* 3 to 7 labelled b_1(0)* 3 to 9 labelled a_1(0)* 3 to 10 labelled c_1(0)* 3 to 6 labelled a_1(0), c_1(1)* 3 to 11 labelled a_1(1)* 3 to 20 labelled c_1(1)* 3 to 58 labelled c_1(2)* 4 to 4 labelled #_1(0)* 5 to 6 labelled a_1(0), c_1(1)* 5 to 20 labelled c_1(1)* 6 to 4 labelled c_1(0)* 6 to 13 labelled a_1(1)* 6 to 11 labelled a_1(1)* 6 to 6 labelled c_1(1)* 6 to 54 labelled c_1(2)* 6 to 58 labelled c_1(2)* 6 to 56 labelled c_1(2)* 6 to 60 labelled c_1(2)* 7 to 8 labelled d_1(0)* 8 to 4 labelled a_1(0)* 8 to 6 labelled c_1(1)* 9 to 10 labelled a_1(0)* 9 to 20 labelled c_1(1)* 10 to 4 labelled b_1(0), a_1(0)* 10 to 14 labelled b_1(1)* 10 to 16 labelled a_1(1)* 10 to 17 labelled c_1(1)* 10 to 6 labelled c_1(1)* 10 to 18 labelled a_1(2)* 10 to 60 labelled c_1(2)* 10 to 65 labelled c_1(3)* 11 to 12 labelled a_1(1)* 11 to 54 labelled c_1(2)* 12 to 4 labelled a_1(1)* 12 to 14 labelled a_1(1)* 12 to 6 labelled c_1(1)* 13 to 4 labelled c_1(1)* 13 to 13 labelled a_1(1)* 13 to 11 labelled a_1(1)* 13 to 21 labelled c_1(1)* 13 to 6 labelled c_1(1)* 13 to 54 labelled c_1(2)* 13 to 58 labelled c_1(2)* 13 to 55 labelled c_1(1)* 13 to 59 labelled c_1(1)* 13 to 56 labelled c_1(2)* 13 to 57 labelled c_1(1)* 13 to 60 labelled c_1(2)* 14 to 15 labelled d_1(1)* 15 to 4 labelled a_1(1)* 15 to 6 labelled c_1(1)* 16 to 17 labelled a_1(1)* 16 to 56 labelled c_1(2)* 17 to 4 labelled b_1(1)* 17 to 14 labelled b_1(1)* 17 to 16 labelled a_1(1)* 17 to 17 labelled c_1(1)* 17 to 18 labelled a_1(2)* 17 to 60 labelled c_1(2)* 17 to 65 labelled c_1(3)* 18 to 19 labelled a_1(2)* 18 to 54 labelled c_1(2)* 19 to 4 labelled a_1(2)* 19 to 6 labelled c_1(1)* 19 to 14 labelled a_1(2)* 20 to 21 labelled a_1(1)* 20 to 54 labelled c_1(2)* 21 to 13 labelled c_1(1)* 21 to 11 labelled c_1(1)* 21 to 16 labelled c_1(1)* 21 to 18 labelled c_1(1)* 21 to 61 labelled c_1(1)* 21 to 66 labelled c_1(1)* 54 to 55 labelled a_1(2)* 54 to 54 labelled c_1(2)* 54 to 6 labelled c_1(1)* 54 to 56 labelled c_1(2)* 54 to 67 labelled c_1(3)* 54 to 65 labelled c_1(3)* 55 to 13 labelled c_1(2), a_1(1)* 55 to 11 labelled c_1(2), a_1(1)* 55 to 12 labelled c_1(2)* 55 to 17 labelled c_1(2)* 55 to 4 labelled c_1(2)* 55 to 14 labelled c_1(2)* 55 to 18 labelled a_1(2)* 55 to 59 labelled c_1(2)* 55 to 19 labelled c_1(2)* 55 to 55 labelled a_1(2)* 55 to 6 labelled c_1(1)* 55 to 54 labelled c_1(2)* 55 to 58 labelled c_1(2)* 55 to 65 labelled c_1(3)* 55 to 56 labelled c_1(2)* 55 to 67 labelled c_1(3)* 55 to 60 labelled c_1(2)* 56 to 57 labelled a_1(2)* 56 to 54 labelled c_1(2)* 56 to 69 labelled c_1(3)* 57 to 16 labelled c_1(2)* 57 to 18 labelled c_1(2)* 57 to 61 labelled c_1(2)* 57 to 66 labelled c_1(2)* 58 to 59 labelled a_1(2)* 58 to 54 labelled c_1(2)* 58 to 67 labelled c_1(3)* 58 to 65 labelled c_1(3)* 59 to 55 labelled c_1(2)* 60 to 61 labelled a_1(2)* 61 to 57 labelled c_1(2)* 65 to 66 labelled a_1(3)* 65 to 54 labelled c_1(2)* 65 to 67 labelled c_1(3)* 65 to 65 labelled c_1(3)* 66 to 55 labelled c_1(3)* 67 to 68 labelled a_1(3)* 67 to 69 labelled c_1(3)* 67 to 6 labelled c_1(1)* 67 to 54 labelled c_1(2)* 67 to 65 labelled c_1(3)* 67 to 67 labelled c_1(3)* 67 to 88 labelled c_1(4)* 68 to 18 labelled c_1(3)* 68 to 4 labelled c_1(3)* 68 to 14 labelled c_1(3)* 68 to 13 labelled a_1(1)* 68 to 11 labelled a_1(1)* 68 to 59 labelled c_1(3)* 68 to 57 labelled c_1(3)* 68 to 66 labelled c_1(3)* 68 to 68 labelled c_1(3)* 68 to 55 labelled a_1(2)* 68 to 6 labelled c_1(1)* 68 to 54 labelled c_1(2)* 68 to 58 labelled c_1(2)* 68 to 65 labelled c_1(3)* 68 to 67 labelled c_1(3)* 68 to 60 labelled c_1(2)* 68 to 56 labelled c_1(2)* 68 to 61 labelled c_1(3)* 69 to 70 labelled a_1(3)* 69 to 67 labelled c_1(3)* 70 to 19 labelled c_1(3)* 88 to 89 labelled a_1(4)* 88 to 54 labelled c_1(2)* 88 to 65 labelled c_1(3)* 89 to 66 labelled c_1(4)* 89 to 68 labelled c_1(4) ---------------------------------------- (4) YES