3.37/1.71 YES 3.37/1.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.37/1.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.37/1.73 3.37/1.73 3.37/1.73 Termination w.r.t. Q of the given QTRS could be proven: 3.37/1.73 3.37/1.73 (0) QTRS 3.37/1.73 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 20 ms] 3.37/1.73 (2) YES 3.37/1.73 3.37/1.73 3.37/1.73 ---------------------------------------- 3.37/1.73 3.37/1.73 (0) 3.37/1.73 Obligation: 3.37/1.73 Q restricted rewrite system: 3.37/1.73 The TRS R consists of the following rules: 3.37/1.73 3.37/1.73 a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1)))))))) 3.37/1.73 3.37/1.73 Q is empty. 3.37/1.73 3.37/1.73 ---------------------------------------- 3.37/1.73 3.37/1.73 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.37/1.73 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. 3.37/1.73 The following rules were used to construct the certificate: 3.37/1.73 3.37/1.73 a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1)))))))) 3.37/1.73 3.37/1.73 The certificate found is represented by the following graph. 3.37/1.73 The certificate consists of the following enumerated nodes: 3.37/1.73 1, 2, 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, 53, 55, 56, 57, 58, 59, 60, 75, 76, 77, 78, 79, 80, 81, 96, 97, 98, 99, 100, 101, 102, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 3.37/1.73 3.37/1.73 Node 1 is start node and node 2 is final node. 3.37/1.73 3.37/1.73 Those nodes are connected through the following edges: 3.37/1.73 3.37/1.73 * 1 to 5 labelled b_1(0)* 2 to 2 labelled #_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 7 to 26 labelled b_1(1)* 8 to 9 labelled a_1(0)* 8 to 19 labelled b_1(1)* 9 to 10 labelled a_1(0)* 9 to 19 labelled b_1(1)* 10 to 11 labelled a_1(0)* 10 to 12 labelled b_1(1)* 11 to 2 labelled a_1(0)* 11 to 12 labelled b_1(1)* 12 to 13 labelled b_1(1)* 13 to 14 labelled b_1(1)* 14 to 15 labelled a_1(1)* 14 to 53 labelled b_1(2)* 15 to 16 labelled a_1(1)* 15 to 33 labelled b_1(2)* 16 to 17 labelled a_1(1)* 16 to 33 labelled b_1(2)* 17 to 18 labelled a_1(1)* 17 to 12 labelled b_1(1)* 18 to 2 labelled a_1(1)* 18 to 12 labelled b_1(1)* 19 to 20 labelled b_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled a_1(1)* 22 to 23 labelled a_1(1)* 22 to 96 labelled b_1(2)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 24 to 75 labelled b_1(2)* 25 to 13 labelled a_1(1)* 26 to 27 labelled b_1(1)* 27 to 28 labelled b_1(1)* 28 to 29 labelled a_1(1)* 29 to 30 labelled a_1(1)* 30 to 31 labelled a_1(1)* 31 to 32 labelled a_1(1)* 32 to 20 labelled a_1(1)* 33 to 34 labelled b_1(2)* 34 to 35 labelled b_1(2)* 35 to 36 labelled a_1(2)* 36 to 37 labelled a_1(2)* 36 to 145 labelled b_1(3)* 37 to 38 labelled a_1(2)* 38 to 39 labelled a_1(2)* 38 to 75 labelled b_1(2)* 39 to 13 labelled a_1(2)* 53 to 55 labelled b_1(2)* 55 to 56 labelled b_1(2)* 56 to 57 labelled a_1(2)* 57 to 58 labelled a_1(2)* 58 to 59 labelled a_1(2)* 59 to 60 labelled a_1(2)* 60 to 34 labelled a_1(2)* 75 to 76 labelled b_1(2)* 76 to 77 labelled b_1(2)* 77 to 78 labelled a_1(2)* 78 to 79 labelled a_1(2)* 78 to 159 labelled b_1(3)* 79 to 80 labelled a_1(2)* 80 to 81 labelled a_1(2)* 80 to 152 labelled b_1(3)* 81 to 53 labelled a_1(2)* 96 to 97 labelled b_1(2)* 97 to 98 labelled b_1(2)* 98 to 99 labelled a_1(2)* 99 to 100 labelled a_1(2)* 100 to 101 labelled a_1(2)* 101 to 102 labelled a_1(2)* 102 to 76 labelled a_1(2)* 145 to 146 labelled b_1(3)* 146 to 147 labelled b_1(3)* 147 to 148 labelled a_1(3)* 148 to 149 labelled a_1(3)* 149 to 150 labelled a_1(3)* 150 to 151 labelled a_1(3)* 151 to 76 labelled a_1(3)* 152 to 153 labelled b_1(3)* 153 to 154 labelled b_1(3)* 154 to 155 labelled a_1(3)* 155 to 156 labelled a_1(3)* 156 to 157 labelled a_1(3)* 157 to 158 labelled a_1(3)* 158 to 56 labelled a_1(3)* 159 to 160 labelled b_1(3)* 160 to 161 labelled b_1(3)* 161 to 162 labelled a_1(3)* 162 to 163 labelled a_1(3)* 163 to 164 labelled a_1(3)* 164 to 165 labelled a_1(3)* 165 to 153 labelled a_1(3) 3.37/1.73 3.37/1.73 3.37/1.73 ---------------------------------------- 3.37/1.73 3.37/1.73 (2) 3.37/1.73 YES 3.37/1.75 EOF