YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES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: b(a(b(a(a(x1))))) -> a(a(a(b(a(b(a(b(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: b(a(b(a(a(x1))))) -> a(a(a(b(a(b(a(b(x1)))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 3, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144 Node 1 is start node and node 3 is final node. Those nodes are connected through the following edges: * 1 to 75 labelled a_1(0)* 3 to 3 labelled #_1(0)* 75 to 76 labelled a_1(0)* 76 to 77 labelled a_1(0)* 77 to 78 labelled b_1(0)* 77 to 89 labelled a_1(1)* 78 to 79 labelled a_1(0)* 79 to 80 labelled b_1(0)* 79 to 82 labelled a_1(1)* 80 to 81 labelled a_1(0)* 81 to 3 labelled b_1(0)* 81 to 82 labelled a_1(1)* 82 to 83 labelled a_1(1)* 83 to 84 labelled a_1(1)* 84 to 85 labelled b_1(1)* 84 to 96 labelled a_1(2)* 85 to 86 labelled a_1(1)* 86 to 87 labelled b_1(1)* 86 to 82 labelled a_1(1)* 87 to 88 labelled a_1(1)* 88 to 3 labelled b_1(1)* 88 to 82 labelled a_1(1)* 89 to 90 labelled a_1(1)* 90 to 91 labelled a_1(1)* 91 to 92 labelled b_1(1)* 92 to 93 labelled a_1(1)* 93 to 94 labelled b_1(1)* 93 to 103 labelled a_1(2)* 94 to 95 labelled a_1(1)* 95 to 82 labelled b_1(1)* 96 to 97 labelled a_1(2)* 97 to 98 labelled a_1(2)* 98 to 99 labelled b_1(2)* 99 to 100 labelled a_1(2)* 100 to 101 labelled b_1(2)* 100 to 103 labelled a_1(2)* 101 to 102 labelled a_1(2)* 102 to 82 labelled b_1(2)* 103 to 104 labelled a_1(2)* 104 to 105 labelled a_1(2)* 105 to 106 labelled b_1(2)* 106 to 107 labelled a_1(2)* 107 to 108 labelled b_1(2)* 107 to 110 labelled a_1(3)* 108 to 109 labelled a_1(2)* 109 to 84 labelled b_1(2)* 110 to 111 labelled a_1(3)* 111 to 112 labelled a_1(3)* 112 to 113 labelled b_1(3)* 112 to 124 labelled a_1(4)* 113 to 114 labelled a_1(3)* 114 to 115 labelled b_1(3)* 115 to 116 labelled a_1(3)* 116 to 97 labelled b_1(3)* 116 to 117 labelled a_1(3)* 117 to 118 labelled a_1(3)* 118 to 119 labelled a_1(3)* 119 to 120 labelled b_1(3)* 120 to 121 labelled a_1(3)* 121 to 122 labelled b_1(3)* 121 to 131 labelled a_1(3)* 122 to 123 labelled a_1(3)* 123 to 103 labelled b_1(3)* 124 to 125 labelled a_1(4)* 125 to 126 labelled a_1(4)* 126 to 127 labelled b_1(4)* 127 to 128 labelled a_1(4)* 128 to 129 labelled b_1(4)* 128 to 138 labelled a_1(4)* 129 to 130 labelled a_1(4)* 130 to 117 labelled b_1(4)* 131 to 132 labelled a_1(3)* 132 to 133 labelled a_1(3)* 133 to 134 labelled b_1(3)* 134 to 135 labelled a_1(3)* 135 to 136 labelled b_1(3)* 136 to 137 labelled a_1(3)* 137 to 105 labelled b_1(3)* 138 to 139 labelled a_1(4)* 139 to 140 labelled a_1(4)* 140 to 141 labelled b_1(4)* 141 to 142 labelled a_1(4)* 142 to 143 labelled b_1(4)* 143 to 144 labelled a_1(4)* 144 to 119 labelled b_1(4) ---------------------------------------- (2) YES