3.69/1.82 YES 3.69/1.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.69/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.69/1.84 3.69/1.84 3.69/1.84 Termination w.r.t. Q of the given QTRS could be proven: 3.69/1.84 3.69/1.84 (0) QTRS 3.69/1.84 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.69/1.84 (2) YES 3.69/1.84 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (0) 3.69/1.84 Obligation: 3.69/1.84 Q restricted rewrite system: 3.69/1.84 The TRS R consists of the following rules: 3.69/1.84 3.69/1.84 a(c(a(x1))) -> b(a(c(x1))) 3.69/1.84 a(c(c(x1))) -> a(b(b(x1))) 3.69/1.84 c(a(a(x1))) -> a(a(a(x1))) 3.69/1.84 b(c(c(x1))) -> a(c(a(x1))) 3.69/1.84 b(a(a(x1))) -> b(c(b(x1))) 3.69/1.84 3.69/1.84 Q is empty. 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.69/1.84 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 3.69/1.84 The following rules were used to construct the certificate: 3.69/1.84 3.69/1.84 a(c(a(x1))) -> b(a(c(x1))) 3.69/1.84 a(c(c(x1))) -> a(b(b(x1))) 3.69/1.84 c(a(a(x1))) -> a(a(a(x1))) 3.69/1.84 b(c(c(x1))) -> a(c(a(x1))) 3.69/1.84 b(a(a(x1))) -> b(c(b(x1))) 3.69/1.84 3.69/1.84 The certificate found is represented by the following graph. 3.69/1.84 The certificate consists of the following enumerated nodes: 3.69/1.84 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, 51, 52, 53, 54, 55, 56, 69, 70 3.69/1.84 3.69/1.84 Node 1 is start node and node 2 is final node. 3.69/1.84 3.69/1.84 Those nodes are connected through the following edges: 3.69/1.84 3.69/1.84 * 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 55 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 55 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 55 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 55 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 51 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 55 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 55 labelled b_1(2)* 22 to 49 labelled b_1(2)* 23 to 24 labelled c_1(1)* 23 to 51 labelled a_1(2)* 24 to 13 labelled b_1(1)* 24 to 53 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 69 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 53 labelled b_1(2)* 50 to 69 labelled b_1(3)* 51 to 52 labelled a_1(2)* 52 to 13 labelled a_1(2)* 53 to 54 labelled c_1(2)* 53 to 51 labelled a_1(2)* 54 to 2 labelled b_1(2)* 54 to 21 labelled b_1(2)* 54 to 15 labelled a_1(1)* 54 to 17 labelled b_1(1)* 54 to 25 labelled b_1(2)* 54 to 55 labelled b_1(2)* 54 to 14 labelled b_1(2)* 54 to 49 labelled b_1(2)* 55 to 56 labelled c_1(2)* 56 to 52 labelled b_1(2)* 56 to 53 labelled b_1(2)* 56 to 69 labelled b_1(3)* 69 to 70 labelled c_1(3)* 70 to 52 labelled b_1(3)* 70 to 53 labelled b_1(2)* 70 to 69 labelled b_1(3) 3.69/1.84 3.69/1.84 3.69/1.84 ---------------------------------------- 3.69/1.84 3.69/1.84 (2) 3.69/1.84 YES 3.69/1.87 EOF