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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(c(b(c(a(a(x1)))))) -> a(a(a(b(c(b(c(b(c(x1))))))))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(c(b(c(b(x1)))))) -> c(b(c(b(c(b(a(a(a(x1))))))))) Q is empty. ---------------------------------------- (3) 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(a(c(b(c(b(x1)))))) -> c(b(c(b(c(b(a(a(a(x1))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 67, 68, 69, 70, 71, 72, 73, 74, 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 Node 67 is start node and node 68 is final node. Those nodes are connected through the following edges: * 67 to 69 labelled c_1(0)* 68 to 68 labelled #_1(0)* 69 to 70 labelled b_1(0)* 70 to 71 labelled c_1(0)* 71 to 72 labelled b_1(0)* 72 to 73 labelled c_1(0)* 73 to 74 labelled b_1(0)* 74 to 75 labelled a_1(0)* 74 to 85 labelled c_1(1)* 75 to 76 labelled a_1(0)* 75 to 77 labelled c_1(1)* 76 to 68 labelled a_1(0)* 76 to 77 labelled c_1(1)* 77 to 78 labelled b_1(1)* 78 to 79 labelled c_1(1)* 79 to 80 labelled b_1(1)* 80 to 81 labelled c_1(1)* 81 to 82 labelled b_1(1)* 82 to 83 labelled a_1(1)* 82 to 93 labelled c_1(2)* 83 to 84 labelled a_1(1)* 83 to 77 labelled c_1(1)* 84 to 68 labelled a_1(1)* 84 to 77 labelled c_1(1)* 85 to 86 labelled b_1(1)* 86 to 87 labelled c_1(1)* 87 to 88 labelled b_1(1)* 88 to 89 labelled c_1(1)* 89 to 90 labelled b_1(1)* 90 to 91 labelled a_1(1)* 91 to 92 labelled a_1(1)* 91 to 101 labelled c_1(2)* 92 to 80 labelled a_1(1)* 93 to 94 labelled b_1(2)* 94 to 95 labelled c_1(2)* 95 to 96 labelled b_1(2)* 96 to 97 labelled c_1(2)* 97 to 98 labelled b_1(2)* 98 to 99 labelled a_1(2)* 99 to 100 labelled a_1(2)* 99 to 101 labelled c_1(2)* 100 to 80 labelled a_1(2)* 101 to 102 labelled b_1(2)* 102 to 103 labelled c_1(2)* 103 to 104 labelled b_1(2)* 104 to 105 labelled c_1(2)* 105 to 106 labelled b_1(2)* 106 to 107 labelled a_1(2)* 107 to 108 labelled a_1(2)* 107 to 109 labelled c_1(3)* 108 to 94 labelled a_1(2)* 109 to 110 labelled b_1(3)* 110 to 111 labelled c_1(3)* 111 to 112 labelled b_1(3)* 112 to 113 labelled c_1(3)* 113 to 114 labelled b_1(3)* 114 to 115 labelled a_1(3)* 114 to 125 labelled c_1(4)* 115 to 116 labelled a_1(3)* 116 to 98 labelled a_1(3)* 116 to 117 labelled c_1(3)* 117 to 118 labelled b_1(3)* 118 to 119 labelled c_1(3)* 119 to 120 labelled b_1(3)* 120 to 121 labelled c_1(3)* 121 to 122 labelled b_1(3)* 122 to 123 labelled a_1(3)* 123 to 124 labelled a_1(3)* 124 to 104 labelled a_1(3)* 125 to 126 labelled b_1(4)* 126 to 127 labelled c_1(4)* 127 to 128 labelled b_1(4)* 128 to 129 labelled c_1(4)* 129 to 130 labelled b_1(4)* 130 to 131 labelled a_1(4)* 131 to 132 labelled a_1(4)* 132 to 120 labelled a_1(4) ---------------------------------------- (4) YES