/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 30 ms] (2) YES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, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 54, 55, 56, 57, 58, 59, 60, 61, 62, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106 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 13 labelled b_1(1)* 1 to 17 labelled d_1(1)* 1 to 20 labelled a_1(1)* 1 to 21 labelled b_1(2)* 1 to 25 labelled d_1(2)* 1 to 54 labelled a_1(1)* 1 to 55 labelled b_1(2)* 1 to 59 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 20 labelled a_1(1)* 5 to 21 labelled b_1(2)* 5 to 25 labelled d_1(2)* 5 to 54 labelled a_1(1)* 5 to 55 labelled b_1(2)* 5 to 59 labelled d_1(2)* 6 to 2 labelled d_1(0)* 6 to 20 labelled b_1(1), a_1(1)* 6 to 21 labelled b_1(2)* 6 to 25 labelled d_1(2)* 6 to 62 labelled a_1(2)* 6 to 91 labelled b_1(3)* 6 to 95 labelled d_1(3)* 6 to 59 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 54 labelled a_1(1)* 9 to 55 labelled b_1(2)* 9 to 59 labelled d_1(2)* 9 to 20 labelled a_1(1)* 9 to 21 labelled b_1(2)* 9 to 25 labelled d_1(2)* 10 to 2 labelled b_1(0)* 10 to 20 labelled a_1(1)* 10 to 21 labelled b_1(2)* 10 to 25 labelled d_1(2)* 10 to 59 labelled d_1(2)* 13 to 14 labelled b_1(1)* 14 to 15 labelled f_1(1)* 15 to 16 labelled b_1(1)* 15 to 62 labelled a_1(2)* 15 to 91 labelled b_1(3)* 15 to 95 labelled d_1(3)* 16 to 6 labelled b_1(1)* 16 to 20 labelled a_1(1)* 16 to 21 labelled b_1(2)* 16 to 25 labelled d_1(2)* 16 to 62 labelled a_1(2)* 16 to 91 labelled b_1(3)* 16 to 95 labelled d_1(3)* 16 to 59 labelled d_1(2)* 17 to 18 labelled b_1(1)* 18 to 19 labelled c_1(1)* 19 to 20 labelled b_1(1), a_1(1)* 19 to 21 labelled b_1(2)* 19 to 25 labelled d_1(2)* 19 to 62 labelled a_1(2)* 19 to 91 labelled b_1(3)* 19 to 95 labelled d_1(3)* 19 to 59 labelled d_1(2)* 20 to 2 labelled d_1(1)* 20 to 20 labelled b_1(1), a_1(1)* 20 to 21 labelled b_1(2)* 20 to 25 labelled d_1(1), d_1(2)* 20 to 62 labelled a_1(2)* 20 to 91 labelled b_1(3)* 20 to 95 labelled d_1(3), d_1(1)* 20 to 96 labelled d_1(1)* 20 to 59 labelled d_1(2), d_1(1)* 20 to 60 labelled d_1(1)* 21 to 22 labelled b_1(2)* 22 to 23 labelled f_1(2)* 23 to 24 labelled b_1(2)* 23 to 98 labelled a_1(3)* 23 to 99 labelled b_1(4)* 23 to 103 labelled d_1(4)* 24 to 20 labelled b_1(2), a_1(1)* 24 to 21 labelled b_1(2)* 24 to 25 labelled d_1(2)* 24 to 62 labelled a_1(2)* 24 to 98 labelled a_1(3)* 24 to 91 labelled b_1(3)* 24 to 99 labelled b_1(4)* 24 to 95 labelled d_1(3)* 24 to 103 labelled d_1(4)* 24 to 59 labelled d_1(2)* 25 to 26 labelled b_1(2)* 26 to 27 labelled c_1(2)* 27 to 28 labelled b_1(2)* 27 to 20 labelled a_1(1)* 27 to 21 labelled b_1(2)* 27 to 25 labelled d_1(2)* 27 to 98 labelled a_1(3)* 27 to 99 labelled b_1(4)* 27 to 103 labelled d_1(4)* 27 to 59 labelled d_1(2)* 28 to 2 labelled d_1(2)* 28 to 20 labelled b_1(1), a_1(1)* 28 to 21 labelled b_1(2)* 28 to 25 labelled d_1(2)* 28 to 62 labelled a_1(2)* 28 to 91 labelled b_1(3)* 28 to 95 labelled d_1(3), d_1(2)* 28 to 59 labelled d_1(2)* 54 to 26 labelled d_1(1)* 55 to 56 labelled b_1(2)* 56 to 57 labelled f_1(2)* 57 to 58 labelled b_1(2)* 58 to 54 labelled b_1(2)* 59 to 60 labelled b_1(2)* 60 to 61 labelled c_1(2)* 61 to 62 labelled b_1(2)* 62 to 26 labelled d_1(2)* 62 to 96 labelled d_1(2)* 62 to 60 labelled d_1(2)* 91 to 92 labelled b_1(3)* 92 to 93 labelled f_1(3)* 93 to 94 labelled b_1(3)* 94 to 62 labelled b_1(3)* 95 to 96 labelled b_1(3)* 96 to 97 labelled c_1(3)* 97 to 98 labelled b_1(3)* 98 to 26 labelled d_1(3)* 98 to 96 labelled d_1(3)* 98 to 104 labelled d_1(3)* 98 to 60 labelled d_1(3)* 99 to 100 labelled b_1(4)* 100 to 101 labelled f_1(4)* 101 to 102 labelled b_1(4)* 102 to 98 labelled b_1(4)* 103 to 104 labelled b_1(4)* 104 to 105 labelled c_1(4)* 105 to 106 labelled b_1(4)* 106 to 26 labelled d_1(4)* 106 to 96 labelled d_1(4)* 106 to 104 labelled d_1(4)* 106 to 60 labelled d_1(4) ---------------------------------------- (2) YES