9.37/3.37 YES 9.75/3.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.75/3.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.75/3.42 9.75/3.42 9.75/3.42 Termination w.r.t. Q of the given QTRS could be proven: 9.75/3.42 9.75/3.42 (0) QTRS 9.75/3.42 (1) QTRS Reverse [EQUIVALENT, 0 ms] 9.75/3.42 (2) QTRS 9.75/3.42 (3) QTRSRRRProof [EQUIVALENT, 137 ms] 9.75/3.42 (4) QTRS 9.75/3.42 (5) AAECC Innermost [EQUIVALENT, 0 ms] 9.75/3.42 (6) QTRS 9.75/3.42 (7) DependencyPairsProof [EQUIVALENT, 20 ms] 9.75/3.42 (8) QDP 9.75/3.42 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 9.75/3.42 (10) TRUE 9.75/3.42 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (0) 9.75/3.42 Obligation: 9.75/3.42 Q restricted rewrite system: 9.75/3.42 The TRS R consists of the following rules: 9.75/3.42 9.75/3.42 0(x1) -> 1(x1) 9.75/3.42 0(0(x1)) -> 0(x1) 9.75/3.42 3(4(5(x1))) -> 4(3(5(x1))) 9.75/3.42 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(0(0(1(1(0(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(1(1(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(0(1(1(0(0(0(0(1(1(1(1(0(0(0(1(1(1(0(1(1(0(1(1(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(0(1(0(0(0(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(0(1(0(0(1(0(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(0(1(0(0(1(0(1(1(0(1(0(0(1(0(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(1(0(1(0(1(1(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(1(0(1(0(1(0(1(1(0(0(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(1(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(0(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 9.75/3.42 Q is empty. 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (1) QTRS Reverse (EQUIVALENT) 9.75/3.42 We applied the QTRS Reverse Processor [REVERSE]. 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (2) 9.75/3.42 Obligation: 9.75/3.42 Q restricted rewrite system: 9.75/3.42 The TRS R consists of the following rules: 9.75/3.42 9.75/3.42 0(x1) -> 1(x1) 9.75/3.42 0(0(x1)) -> 0(x1) 9.75/3.42 5(4(3(x1))) -> 5(3(4(x1))) 9.75/3.42 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(1(1(0(1(0(1(0(1(0(0(1(0(1(1(0(1(0(0(1(0(1(0(0(0(0(0(1(1(1(1(0(1(0(0(1(0(1(0(0(1(0(1(0(0(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(1(0(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(1(0(0(1(1(1(1(0(0(1(1(0(0(0(1(1(0(0(0(1(0(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 0(0(0(0(1(0(1(1(1(1(0(1(0(1(1(1(0(0(1(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(0(0(1(0(0(0(0(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(0(1(0(1(0(0(0(1(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 9.75/3.42 Q is empty. 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (3) QTRSRRRProof (EQUIVALENT) 9.75/3.42 Used ordering: 9.75/3.42 Polynomial interpretation [POLO]: 9.75/3.42 9.75/3.42 POL(0(x_1)) = 23 + x_1 9.75/3.42 POL(1(x_1)) = x_1 9.75/3.42 POL(2(x_1)) = 12 + x_1 9.75/3.42 POL(3(x_1)) = x_1 9.75/3.42 POL(4(x_1)) = x_1 9.75/3.42 POL(5(x_1)) = x_1 9.75/3.42 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 9.75/3.42 9.75/3.42 0(x1) -> 1(x1) 9.75/3.42 0(0(x1)) -> 0(x1) 9.75/3.42 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(1(1(0(1(0(1(0(1(0(0(1(0(1(1(0(1(0(0(1(0(1(0(0(0(0(0(1(1(1(1(0(1(0(0(1(0(1(0(0(1(0(1(0(0(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(1(0(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(1(0(0(1(1(1(1(0(0(1(1(0(0(0(1(1(0(0(0(1(0(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 0(0(0(0(1(0(1(1(1(1(0(1(0(1(1(1(0(0(1(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(0(0(1(0(0(0(0(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(0(1(0(1(0(0(0(1(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.75/3.42 9.75/3.42 9.75/3.42 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (4) 9.75/3.42 Obligation: 9.75/3.42 Q restricted rewrite system: 9.75/3.42 The TRS R consists of the following rules: 9.75/3.42 9.75/3.42 5(4(3(x1))) -> 5(3(4(x1))) 9.75/3.42 9.75/3.42 Q is empty. 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (5) AAECC Innermost (EQUIVALENT) 9.75/3.42 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 9.75/3.42 9.75/3.42 The TRS R 2 is 9.75/3.42 5(4(3(x1))) -> 5(3(4(x1))) 9.75/3.42 9.75/3.42 The signature Sigma is {5_1} 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (6) 9.75/3.42 Obligation: 9.75/3.42 Q restricted rewrite system: 9.75/3.42 The TRS R consists of the following rules: 9.75/3.42 9.75/3.42 5(4(3(x1))) -> 5(3(4(x1))) 9.75/3.42 9.75/3.42 The set Q consists of the following terms: 9.75/3.42 9.75/3.42 5(4(3(x0))) 9.75/3.42 9.75/3.42 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (7) DependencyPairsProof (EQUIVALENT) 9.75/3.42 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (8) 9.75/3.42 Obligation: 9.75/3.42 Q DP problem: 9.75/3.42 The TRS P consists of the following rules: 9.75/3.42 9.75/3.42 5^1(4(3(x1))) -> 5^1(3(4(x1))) 9.75/3.42 9.75/3.42 The TRS R consists of the following rules: 9.75/3.42 9.75/3.42 5(4(3(x1))) -> 5(3(4(x1))) 9.75/3.42 9.75/3.42 The set Q consists of the following terms: 9.75/3.42 9.75/3.42 5(4(3(x0))) 9.75/3.42 9.75/3.42 We have to consider all minimal (P,Q,R)-chains. 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (9) DependencyGraphProof (EQUIVALENT) 9.75/3.42 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 9.75/3.42 ---------------------------------------- 9.75/3.42 9.75/3.42 (10) 9.75/3.42 TRUE 10.11/3.53 EOF