/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 48 ms] (2) YES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, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 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 11 labelled b_1(1)* 1 to 15 labelled d_1(1)* 1 to 18 labelled a_1(1)* 1 to 19 labelled b_1(2)* 1 to 23 labelled d_1(2)* 1 to 27 labelled a_1(1)* 1 to 28 labelled b_1(2)* 1 to 32 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 18 labelled a_1(1)* 5 to 19 labelled b_1(2)* 5 to 23 labelled d_1(2)* 5 to 27 labelled a_1(1)* 5 to 28 labelled b_1(2)* 5 to 32 labelled d_1(2)* 6 to 2 labelled d_1(0)* 6 to 18 labelled b_1(1), a_1(1)* 6 to 19 labelled b_1(2)* 6 to 23 labelled d_1(2)* 6 to 35 labelled a_1(2)* 6 to 36 labelled b_1(3)* 6 to 40 labelled d_1(3)* 6 to 32 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 27 labelled a_1(1)* 9 to 28 labelled b_1(2)* 9 to 32 labelled d_1(2)* 9 to 18 labelled a_1(1)* 9 to 19 labelled b_1(2)* 9 to 23 labelled d_1(2)* 10 to 2 labelled b_1(0)* 10 to 18 labelled a_1(1)* 10 to 19 labelled b_1(2)* 10 to 23 labelled d_1(2)* 10 to 32 labelled d_1(2)* 11 to 12 labelled b_1(1)* 12 to 13 labelled f_1(1)* 13 to 14 labelled b_1(1)* 13 to 35 labelled a_1(2)* 13 to 36 labelled b_1(3)* 13 to 40 labelled d_1(3)* 14 to 6 labelled b_1(1)* 14 to 18 labelled a_1(1)* 14 to 19 labelled b_1(2)* 14 to 23 labelled d_1(2)* 14 to 35 labelled a_1(2)* 14 to 36 labelled b_1(3)* 14 to 40 labelled d_1(3)* 14 to 32 labelled d_1(2)* 15 to 16 labelled b_1(1)* 16 to 17 labelled c_1(1)* 17 to 18 labelled b_1(1), a_1(1)* 17 to 19 labelled b_1(2)* 17 to 23 labelled d_1(2)* 17 to 35 labelled a_1(2)* 17 to 36 labelled b_1(3)* 17 to 40 labelled d_1(3)* 17 to 32 labelled d_1(2)* 18 to 2 labelled d_1(1)* 18 to 18 labelled b_1(1), a_1(1)* 18 to 19 labelled b_1(2)* 18 to 23 labelled d_1(1), d_1(2)* 18 to 35 labelled a_1(2)* 18 to 36 labelled b_1(3)* 18 to 40 labelled d_1(3), d_1(1)* 18 to 41 labelled d_1(1)* 18 to 32 labelled d_1(2), d_1(1)* 18 to 33 labelled d_1(1)* 19 to 20 labelled b_1(2)* 20 to 21 labelled f_1(2)* 21 to 22 labelled b_1(2)* 21 to 43 labelled a_1(3)* 21 to 44 labelled b_1(4)* 21 to 48 labelled d_1(4)* 22 to 18 labelled b_1(2), a_1(1)* 22 to 19 labelled b_1(2)* 22 to 23 labelled d_1(2)* 22 to 35 labelled a_1(2)* 22 to 43 labelled a_1(3)* 22 to 36 labelled b_1(3)* 22 to 44 labelled b_1(4)* 22 to 40 labelled d_1(3)* 22 to 48 labelled d_1(4)* 22 to 32 labelled d_1(2)* 23 to 24 labelled b_1(2)* 24 to 25 labelled c_1(2)* 25 to 26 labelled b_1(2)* 25 to 18 labelled a_1(1)* 25 to 19 labelled b_1(2)* 25 to 23 labelled d_1(2)* 25 to 43 labelled a_1(3)* 25 to 44 labelled b_1(4)* 25 to 48 labelled d_1(4)* 25 to 32 labelled d_1(2)* 26 to 2 labelled d_1(2)* 26 to 18 labelled b_1(1), a_1(1)* 26 to 19 labelled b_1(2)* 26 to 23 labelled d_1(2)* 26 to 35 labelled a_1(2)* 26 to 36 labelled b_1(3)* 26 to 40 labelled d_1(3), d_1(2)* 26 to 32 labelled d_1(2)* 27 to 24 labelled d_1(1)* 28 to 29 labelled b_1(2)* 29 to 30 labelled f_1(2)* 30 to 31 labelled b_1(2)* 31 to 27 labelled b_1(2)* 32 to 33 labelled b_1(2)* 33 to 34 labelled c_1(2)* 34 to 35 labelled b_1(2)* 35 to 24 labelled d_1(2)* 35 to 41 labelled d_1(2)* 35 to 33 labelled d_1(2)* 36 to 37 labelled b_1(3)* 37 to 38 labelled f_1(3)* 38 to 39 labelled b_1(3)* 39 to 35 labelled b_1(3)* 40 to 41 labelled b_1(3)* 41 to 42 labelled c_1(3)* 42 to 43 labelled b_1(3)* 43 to 24 labelled d_1(3)* 43 to 41 labelled d_1(3)* 43 to 49 labelled d_1(3)* 43 to 33 labelled d_1(3)* 44 to 45 labelled b_1(4)* 45 to 46 labelled f_1(4)* 46 to 47 labelled b_1(4)* 47 to 43 labelled b_1(4)* 48 to 49 labelled b_1(4)* 49 to 50 labelled c_1(4)* 50 to 51 labelled b_1(4)* 51 to 24 labelled d_1(4)* 51 to 41 labelled d_1(4)* 51 to 49 labelled d_1(4)* 51 to 33 labelled d_1(4) ---------------------------------------- (2) YES