8.15/2.92 YES 14.10/4.41 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.10/4.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.10/4.41 14.10/4.41 14.10/4.41 Termination w.r.t. Q of the given QTRS could be proven: 14.10/4.41 14.10/4.41 (0) QTRS 14.10/4.41 (1) QTRS Reverse [EQUIVALENT, 0 ms] 14.10/4.41 (2) QTRS 14.10/4.41 (3) QTRSRRRProof [EQUIVALENT, 101 ms] 14.10/4.41 (4) QTRS 14.10/4.41 (5) AAECC Innermost [EQUIVALENT, 0 ms] 14.10/4.41 (6) QTRS 14.10/4.41 (7) DependencyPairsProof [EQUIVALENT, 19 ms] 14.10/4.41 (8) QDP 14.10/4.41 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 14.10/4.41 (10) TRUE 14.10/4.41 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (0) 14.10/4.41 Obligation: 14.10/4.41 Q restricted rewrite system: 14.10/4.41 The TRS R consists of the following rules: 14.10/4.41 14.10/4.41 0(x1) -> 1(x1) 14.10/4.41 0(0(x1)) -> 0(x1) 14.10/4.41 3(4(5(x1))) -> 4(3(5(x1))) 14.10/4.41 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(1(1(0(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(1(1(1(1(1(1(0(1(0(0(1(1(0(0(0(0(1(0(1(1(0(0(1(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(0(0(0(1(0(1(0(0(1(0(1(0(1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(0(0(1(0(1(0(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(1(0(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(0(1(0(0(1(0(0(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(0(1(1(0(1(1(0(0(1(0(0(1(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(1(0(1(1(0(0(0(0(0(0(1(0(0(0(0(0(1(1(1(1(0(1(0(0(0(1(0(0(0(1(0(1(1(1(1(1(0(0(1(1(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(1(0(0(1(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(1(1(1(0(0(1(1(1(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(0(1(1(1(0(0(0(0(1(1(1(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(1(0(0(1(0(1(0(1(0(0(0(0(0(0(0(0(0(1(0(0(0(1(0(1(0(0(1(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 14.10/4.41 Q is empty. 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (1) QTRS Reverse (EQUIVALENT) 14.10/4.41 We applied the QTRS Reverse Processor [REVERSE]. 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (2) 14.10/4.41 Obligation: 14.10/4.41 Q restricted rewrite system: 14.10/4.41 The TRS R consists of the following rules: 14.10/4.41 14.10/4.41 0(x1) -> 1(x1) 14.10/4.41 0(0(x1)) -> 0(x1) 14.10/4.41 5(4(3(x1))) -> 5(3(4(x1))) 14.10/4.41 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(0(0(1(1(1(1(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(0(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(1(0(1(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(1(0(0(0(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(1(0(0(1(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(1(0(0(0(1(0(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(1(1(1(1(1(1(1(0(1(0(1(1(1(1(0(0(1(1(0(1(0(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 1(1(1(1(1(1(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(0(1(0(0(1(0(1(0(0(0(1(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(0(1(0(0(1(0(0(1(1(1(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(0(1(0(1(0(0(1(1(0(1(1(0(1(1(0(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(1(0(1(1(1(1(0(0(0(0(0(1(0(0(0(0(0(0(1(1(0(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(0(0(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(1(1(0(0(1(0(0(1(1(0(1(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 14.10/4.41 Q is empty. 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (3) QTRSRRRProof (EQUIVALENT) 14.10/4.41 Used ordering: 14.10/4.41 Polynomial interpretation [POLO]: 14.10/4.41 14.10/4.41 POL(0(x_1)) = 18 + x_1 14.10/4.41 POL(1(x_1)) = 17 + x_1 14.10/4.41 POL(2(x_1)) = 69 + x_1 14.10/4.41 POL(3(x_1)) = x_1 14.10/4.41 POL(4(x_1)) = x_1 14.10/4.41 POL(5(x_1)) = x_1 14.10/4.41 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 14.10/4.41 14.10/4.41 0(x1) -> 1(x1) 14.10/4.41 0(0(x1)) -> 0(x1) 14.10/4.41 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(0(0(1(1(1(1(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(0(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(1(0(1(1(0(1(0(0(1(1(1(0(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(1(0(0(0(1(1(0(1(0(0(0(0(1(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(1(0(0(1(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(1(0(0(0(1(0(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(1(1(1(1(1(1(1(0(1(0(1(1(1(1(0(0(1(1(0(1(0(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(0(1(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 1(1(1(1(1(1(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(0(1(0(0(1(0(1(0(0(0(1(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(0(1(0(0(1(0(0(1(1(1(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(0(1(0(1(0(0(1(1(0(1(1(0(1(1(0(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(1(0(1(1(1(1(0(0(0(0(0(1(0(0(0(0(0(0(1(1(0(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(0(0(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(1(1(0(0(1(0(0(1(1(0(1(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.10/4.41 14.10/4.41 14.10/4.41 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (4) 14.10/4.41 Obligation: 14.10/4.41 Q restricted rewrite system: 14.10/4.41 The TRS R consists of the following rules: 14.10/4.41 14.10/4.41 5(4(3(x1))) -> 5(3(4(x1))) 14.10/4.41 14.10/4.41 Q is empty. 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (5) AAECC Innermost (EQUIVALENT) 14.10/4.41 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 14.10/4.41 14.10/4.41 The TRS R 2 is 14.10/4.41 5(4(3(x1))) -> 5(3(4(x1))) 14.10/4.41 14.10/4.41 The signature Sigma is {5_1} 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (6) 14.10/4.41 Obligation: 14.10/4.41 Q restricted rewrite system: 14.10/4.41 The TRS R consists of the following rules: 14.10/4.41 14.10/4.41 5(4(3(x1))) -> 5(3(4(x1))) 14.10/4.41 14.10/4.41 The set Q consists of the following terms: 14.10/4.41 14.10/4.41 5(4(3(x0))) 14.10/4.41 14.10/4.41 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (7) DependencyPairsProof (EQUIVALENT) 14.10/4.41 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (8) 14.10/4.41 Obligation: 14.10/4.41 Q DP problem: 14.10/4.41 The TRS P consists of the following rules: 14.10/4.41 14.10/4.41 5^1(4(3(x1))) -> 5^1(3(4(x1))) 14.10/4.41 14.10/4.41 The TRS R consists of the following rules: 14.10/4.41 14.10/4.41 5(4(3(x1))) -> 5(3(4(x1))) 14.10/4.41 14.10/4.41 The set Q consists of the following terms: 14.10/4.41 14.10/4.41 5(4(3(x0))) 14.10/4.41 14.10/4.41 We have to consider all minimal (P,Q,R)-chains. 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (9) DependencyGraphProof (EQUIVALENT) 14.10/4.41 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 14.10/4.41 ---------------------------------------- 14.10/4.41 14.10/4.41 (10) 14.10/4.41 TRUE 14.31/4.51 EOF