/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 22 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(d(x1)) -> d(b(c(b(d(x1))))) a(x1) -> b(b(f(b(b(x1))))) b(d(b(x1))) -> a(d(x1)) d(f(x1)) -> b(d(x1)) Q is empty. ---------------------------------------- (1) 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(d(x1)) -> d(b(c(b(d(x1))))) a(x1) -> b(b(f(b(b(x1))))) b(d(b(x1))) -> a(d(x1)) d(f(x1)) -> b(d(x1)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 22, 23, 24, 25, 26, 27, 28, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled d_1(0)* 1 to 7 labelled b_1(0)* 1 to 6 labelled a_1(0), b_1(0)* 1 to 21 labelled b_1(1)* 1 to 25 labelled d_1(1)* 1 to 28 labelled a_1(1)* 1 to 38 labelled b_1(2)* 1 to 42 labelled d_1(2)* 1 to 46 labelled a_1(1)* 1 to 47 labelled b_1(2)* 1 to 51 labelled d_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled c_1(0)* 5 to 6 labelled b_1(0)* 5 to 28 labelled a_1(1)* 5 to 38 labelled b_1(2)* 5 to 42 labelled d_1(2)* 5 to 46 labelled a_1(1)* 5 to 47 labelled b_1(2)* 5 to 51 labelled d_1(2)* 6 to 2 labelled d_1(0)* 6 to 28 labelled b_1(1), a_1(1)* 6 to 38 labelled b_1(2)* 6 to 42 labelled d_1(2)* 6 to 54 labelled a_1(2)* 6 to 65 labelled b_1(3)* 6 to 69 labelled d_1(3)* 6 to 51 labelled d_1(2)* 7 to 8 labelled b_1(0)* 8 to 9 labelled f_1(0)* 9 to 10 labelled b_1(0)* 9 to 46 labelled a_1(1)* 9 to 47 labelled b_1(2)* 9 to 51 labelled d_1(2)* 9 to 28 labelled a_1(1)* 9 to 38 labelled b_1(2)* 9 to 42 labelled d_1(2)* 10 to 2 labelled b_1(0)* 10 to 28 labelled a_1(1)* 10 to 38 labelled b_1(2)* 10 to 42 labelled d_1(2)* 10 to 51 labelled d_1(2)* 21 to 22 labelled b_1(1)* 22 to 23 labelled f_1(1)* 23 to 24 labelled b_1(1)* 23 to 54 labelled a_1(2)* 23 to 65 labelled b_1(3)* 23 to 69 labelled d_1(3)* 24 to 6 labelled b_1(1)* 24 to 28 labelled a_1(1)* 24 to 38 labelled b_1(2)* 24 to 42 labelled d_1(2)* 24 to 54 labelled a_1(2)* 24 to 65 labelled b_1(3)* 24 to 69 labelled d_1(3)* 24 to 51 labelled d_1(2)* 25 to 26 labelled b_1(1)* 26 to 27 labelled c_1(1)* 27 to 28 labelled b_1(1), a_1(1)* 27 to 38 labelled b_1(2)* 27 to 42 labelled d_1(2)* 27 to 54 labelled a_1(2)* 27 to 65 labelled b_1(3)* 27 to 69 labelled d_1(3)* 27 to 51 labelled d_1(2)* 28 to 2 labelled d_1(1)* 28 to 28 labelled b_1(1), a_1(1)* 28 to 38 labelled b_1(2)* 28 to 42 labelled d_1(1), d_1(2)* 28 to 54 labelled a_1(2)* 28 to 65 labelled b_1(3)* 28 to 69 labelled d_1(3), d_1(1)* 28 to 70 labelled d_1(1)* 28 to 51 labelled d_1(2), d_1(1)* 28 to 52 labelled d_1(1)* 38 to 39 labelled b_1(2)* 39 to 40 labelled f_1(2)* 40 to 41 labelled b_1(2)* 40 to 72 labelled a_1(3)* 40 to 73 labelled b_1(4)* 40 to 77 labelled d_1(4)* 41 to 28 labelled b_1(2), a_1(1)* 41 to 38 labelled b_1(2)* 41 to 42 labelled d_1(2)* 41 to 54 labelled a_1(2)* 41 to 72 labelled a_1(3)* 41 to 65 labelled b_1(3)* 41 to 73 labelled b_1(4)* 41 to 69 labelled d_1(3)* 41 to 77 labelled d_1(4)* 41 to 51 labelled d_1(2)* 42 to 43 labelled b_1(2)* 43 to 44 labelled c_1(2)* 44 to 45 labelled b_1(2)* 44 to 28 labelled a_1(1)* 44 to 38 labelled b_1(2)* 44 to 42 labelled d_1(2)* 44 to 72 labelled a_1(3)* 44 to 73 labelled b_1(4)* 44 to 77 labelled d_1(4)* 44 to 51 labelled d_1(2)* 45 to 2 labelled d_1(2)* 45 to 28 labelled b_1(1), a_1(1)* 45 to 38 labelled b_1(2)* 45 to 42 labelled d_1(2)* 45 to 54 labelled a_1(2)* 45 to 65 labelled b_1(3)* 45 to 69 labelled d_1(3), d_1(2)* 45 to 51 labelled d_1(2)* 46 to 43 labelled d_1(1)* 47 to 48 labelled b_1(2)* 48 to 49 labelled f_1(2)* 49 to 50 labelled b_1(2)* 50 to 46 labelled b_1(2)* 51 to 52 labelled b_1(2)* 52 to 53 labelled c_1(2)* 53 to 54 labelled b_1(2)* 54 to 43 labelled d_1(2)* 54 to 70 labelled d_1(2)* 54 to 52 labelled d_1(2)* 65 to 66 labelled b_1(3)* 66 to 67 labelled f_1(3)* 67 to 68 labelled b_1(3)* 68 to 54 labelled b_1(3)* 69 to 70 labelled b_1(3)* 70 to 71 labelled c_1(3)* 71 to 72 labelled b_1(3)* 72 to 43 labelled d_1(3)* 72 to 70 labelled d_1(3)* 72 to 78 labelled d_1(3)* 72 to 52 labelled d_1(3)* 73 to 74 labelled b_1(4)* 74 to 75 labelled f_1(4)* 75 to 76 labelled b_1(4)* 76 to 72 labelled b_1(4)* 77 to 78 labelled b_1(4)* 78 to 79 labelled c_1(4)* 79 to 80 labelled b_1(4)* 80 to 43 labelled d_1(4)* 80 to 70 labelled d_1(4)* 80 to 78 labelled d_1(4)* 80 to 52 labelled d_1(4) ---------------------------------------- (2) YES