/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(c(a(x1))) -> b(a(c(x1))) a(c(c(x1))) -> a(b(b(x1))) c(a(a(x1))) -> a(a(a(x1))) b(c(c(x1))) -> a(c(a(x1))) b(a(a(x1))) -> b(c(b(x1))) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. The following rules were used to construct the certificate: a(c(a(x1))) -> b(a(c(x1))) a(c(c(x1))) -> a(b(b(x1))) c(a(a(x1))) -> a(a(a(x1))) b(c(c(x1))) -> a(c(a(x1))) b(a(a(x1))) -> b(c(b(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, 49, 50, 55, 56, 57, 58, 59, 60, 71, 72 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled b_1(0)* 1 to 5 labelled a_1(0)* 1 to 7 labelled a_1(0)* 1 to 9 labelled a_1(0)* 1 to 11 labelled b_1(0)* 1 to 19 labelled b_1(1)* 1 to 23 labelled b_1(1)* 1 to 49 labelled b_1(2)* 1 to 59 labelled b_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 3 to 19 labelled b_1(1)* 3 to 21 labelled a_1(1)* 3 to 49 labelled b_1(2)* 4 to 2 labelled c_1(0)* 4 to 13 labelled a_1(1)* 5 to 6 labelled b_1(0)* 5 to 23 labelled b_1(1)* 5 to 59 labelled b_1(2)* 6 to 2 labelled b_1(0)* 6 to 15 labelled a_1(1)* 6 to 17 labelled b_1(1)* 6 to 25 labelled b_1(2)* 6 to 59 labelled b_1(2)* 6 to 49 labelled b_1(2)* 7 to 8 labelled a_1(0)* 8 to 2 labelled a_1(0)* 8 to 19 labelled b_1(1)* 8 to 21 labelled a_1(1)* 8 to 49 labelled b_1(2)* 9 to 10 labelled c_1(0)* 9 to 13 labelled a_1(1)* 10 to 2 labelled a_1(0)* 10 to 19 labelled b_1(1)* 10 to 21 labelled a_1(1)* 10 to 49 labelled b_1(2)* 11 to 12 labelled c_1(0)* 11 to 19 labelled a_1(1)* 12 to 2 labelled b_1(0)* 12 to 15 labelled a_1(1)* 12 to 17 labelled b_1(1)* 12 to 25 labelled b_1(2)* 12 to 59 labelled b_1(2)* 12 to 49 labelled b_1(2)* 13 to 14 labelled a_1(1)* 14 to 2 labelled a_1(1)* 14 to 19 labelled b_1(1)* 14 to 21 labelled a_1(1)* 14 to 49 labelled b_1(2)* 15 to 16 labelled c_1(1)* 15 to 13 labelled a_1(1)* 16 to 2 labelled a_1(1)* 16 to 19 labelled b_1(1)* 16 to 21 labelled a_1(1)* 16 to 49 labelled b_1(2)* 17 to 18 labelled c_1(1)* 17 to 55 labelled a_1(2)* 18 to 2 labelled b_1(1)* 18 to 15 labelled a_1(1)* 18 to 17 labelled b_1(1)* 18 to 25 labelled b_1(2)* 18 to 59 labelled b_1(2)* 18 to 49 labelled b_1(2)* 19 to 20 labelled a_1(1)* 19 to 19 labelled b_1(1)* 19 to 21 labelled a_1(1)* 19 to 49 labelled b_1(2)* 20 to 2 labelled c_1(1)* 20 to 13 labelled a_1(1)* 20 to 21 labelled c_1(1)* 21 to 22 labelled b_1(1)* 21 to 49 labelled b_1(2)* 22 to 2 labelled b_1(1)* 22 to 15 labelled a_1(1)* 22 to 17 labelled b_1(1)* 22 to 25 labelled b_1(2)* 22 to 59 labelled b_1(2)* 22 to 49 labelled b_1(2)* 23 to 24 labelled c_1(1)* 23 to 55 labelled a_1(2)* 24 to 13 labelled b_1(1)* 24 to 57 labelled b_1(2)* 24 to 20 labelled b_1(1)* 24 to 21 labelled b_1(1)* 24 to 15 labelled a_1(1)* 24 to 25 labelled b_1(2)* 24 to 71 labelled b_1(3)* 24 to 49 labelled b_1(2)* 25 to 26 labelled a_1(2)* 25 to 19 labelled b_1(1)* 25 to 21 labelled a_1(1)* 25 to 49 labelled b_1(2)* 26 to 2 labelled c_1(2)* 26 to 13 labelled a_1(1)* 26 to 21 labelled c_1(2)* 49 to 50 labelled c_1(2)* 50 to 13 labelled b_1(2)* 50 to 57 labelled b_1(2)* 50 to 71 labelled b_1(3)* 55 to 56 labelled a_1(2)* 56 to 13 labelled a_1(2)* 57 to 58 labelled c_1(2)* 57 to 55 labelled a_1(2)* 58 to 2 labelled b_1(2)* 58 to 21 labelled b_1(2)* 58 to 15 labelled a_1(1)* 58 to 17 labelled b_1(1)* 58 to 25 labelled b_1(2)* 58 to 59 labelled b_1(2)* 58 to 14 labelled b_1(2)* 58 to 49 labelled b_1(2)* 59 to 60 labelled c_1(2)* 60 to 56 labelled b_1(2)* 60 to 57 labelled b_1(2)* 60 to 71 labelled b_1(3)* 71 to 72 labelled c_1(3)* 72 to 56 labelled b_1(3)* 72 to 57 labelled b_1(2)* 72 to 71 labelled b_1(3) ---------------------------------------- (2) YES