8.88/3.08 YES 8.88/3.11 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 8.88/3.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.88/3.11 8.88/3.11 8.88/3.11 Termination w.r.t. Q of the given QTRS could be proven: 8.88/3.11 8.88/3.11 (0) QTRS 8.88/3.11 (1) QTRS Reverse [EQUIVALENT, 0 ms] 8.88/3.11 (2) QTRS 8.88/3.11 (3) QTRSRRRProof [EQUIVALENT, 143 ms] 8.88/3.11 (4) QTRS 8.88/3.11 (5) AAECC Innermost [EQUIVALENT, 0 ms] 8.88/3.11 (6) QTRS 8.88/3.11 (7) DependencyPairsProof [EQUIVALENT, 2 ms] 8.88/3.11 (8) QDP 8.88/3.11 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 8.88/3.11 (10) TRUE 8.88/3.11 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (0) 8.88/3.11 Obligation: 8.88/3.11 Q restricted rewrite system: 8.88/3.11 The TRS R consists of the following rules: 8.88/3.11 8.88/3.11 0(x1) -> 1(x1) 8.88/3.11 0(0(x1)) -> 0(x1) 8.88/3.11 3(4(5(x1))) -> 4(3(5(x1))) 8.88/3.11 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(1(0(0(1(0(1(0(0(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(1(1(0(0(1(1(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(1(1(1(1(0(1(0(0(0(1(1(0(0(0(0(1(1(0(1(0(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(1(1(1(0(0(1(1(0(1(0(1(0(0(1(1(0(1(0(1(1(1(1(0(0(1(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(0(1(1(1(1(0(0(0(1(1(0(1(0(0(0(0(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(1(1(1(0(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(1(1(0(0(1(0(1(0(1(1(0(0(0(0(0(0(0(0(1(0(0(0(0(1(1(1(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 0(1(1(1(1(0(0(1(0(1(0(0(1(0(0(1(0(1(1(1(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(0(0(0(0(1(1(1(1(0(0(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(1(0(0(1(1(0(1(0(1(0(1(1(0(0(1(0(0(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(0(0(1(1(1(0(1(1(1(1(0(1(0(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(0(0(1(0(1(0(0(0(1(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(1(0(1(1(1(0(1(1(0(1(0(0(0(1(0(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(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 8.88/3.11 Q is empty. 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (1) QTRS Reverse (EQUIVALENT) 8.88/3.11 We applied the QTRS Reverse Processor [REVERSE]. 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (2) 8.88/3.11 Obligation: 8.88/3.11 Q restricted rewrite system: 8.88/3.11 The TRS R consists of the following rules: 8.88/3.11 8.88/3.11 0(x1) -> 1(x1) 8.88/3.11 0(0(x1)) -> 0(x1) 8.88/3.11 5(4(3(x1))) -> 5(3(4(x1))) 8.88/3.11 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(0(1(1(0(0(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(1(1(1(0(0(0(1(0(1(0(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(0(1(1(0(0(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(0(1(0(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(1(1(0(1(0(1(1(0(0(1(0(1(0(1(1(0(0(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(0(0(0(0(1(0(1(1(1(0(0(1(1(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(0(0(1(0(1(0(0(1(1(0(1(0(0(1(0(1(0(0(1(1(1(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 1(1(1(0(1(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(0(1(1(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(0(1(1(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(0(0(0(0(0(0(1(1(0(1(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(1(0(1(0(1(0(0(1(0(0(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(1(0(0(0(0(0(1(1(1(1(1(1(1(1(1(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(1(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 8.88/3.11 Q is empty. 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (3) QTRSRRRProof (EQUIVALENT) 8.88/3.11 Used ordering: 8.88/3.11 Polynomial interpretation [POLO]: 8.88/3.11 8.88/3.11 POL(0(x_1)) = 4 + x_1 8.88/3.11 POL(1(x_1)) = 3 + x_1 8.88/3.11 POL(2(x_1)) = 9 + x_1 8.88/3.11 POL(3(x_1)) = x_1 8.88/3.11 POL(4(x_1)) = x_1 8.88/3.11 POL(5(x_1)) = x_1 8.88/3.11 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 8.88/3.11 8.88/3.11 0(x1) -> 1(x1) 8.88/3.11 0(0(x1)) -> 0(x1) 8.88/3.11 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(0(0(1(1(0(0(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(1(1(1(0(0(0(1(0(1(0(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(0(1(1(0(0(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(0(1(0(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(1(1(0(1(0(1(1(0(0(1(0(1(0(1(1(0(0(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(0(0(0(0(1(0(1(1(1(0(0(1(1(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(0(0(1(0(1(0(0(1(1(0(1(0(0(1(0(1(0(0(1(1(1(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 1(1(1(0(1(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(0(1(1(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(0(1(1(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(0(0(0(0(0(0(1(1(0(1(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(0(1(0(1(0(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(1(0(1(0(1(0(0(1(0(0(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(1(0(0(0(0(0(1(1(1(1(1(1(1(1(1(0(0(1(1(1(1(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(1(0(0(1(0(1(0(0(1(1(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 8.88/3.11 8.88/3.11 8.88/3.11 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (4) 8.88/3.11 Obligation: 8.88/3.11 Q restricted rewrite system: 8.88/3.11 The TRS R consists of the following rules: 8.88/3.11 8.88/3.11 5(4(3(x1))) -> 5(3(4(x1))) 8.88/3.11 8.88/3.11 Q is empty. 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (5) AAECC Innermost (EQUIVALENT) 8.88/3.11 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 8.88/3.11 8.88/3.11 The TRS R 2 is 8.88/3.11 5(4(3(x1))) -> 5(3(4(x1))) 8.88/3.11 8.88/3.11 The signature Sigma is {5_1} 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (6) 8.88/3.11 Obligation: 8.88/3.11 Q restricted rewrite system: 8.88/3.11 The TRS R consists of the following rules: 8.88/3.11 8.88/3.11 5(4(3(x1))) -> 5(3(4(x1))) 8.88/3.11 8.88/3.11 The set Q consists of the following terms: 8.88/3.11 8.88/3.11 5(4(3(x0))) 8.88/3.11 8.88/3.11 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (7) DependencyPairsProof (EQUIVALENT) 8.88/3.11 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (8) 8.88/3.11 Obligation: 8.88/3.11 Q DP problem: 8.88/3.11 The TRS P consists of the following rules: 8.88/3.11 8.88/3.11 5^1(4(3(x1))) -> 5^1(3(4(x1))) 8.88/3.11 8.88/3.11 The TRS R consists of the following rules: 8.88/3.11 8.88/3.11 5(4(3(x1))) -> 5(3(4(x1))) 8.88/3.11 8.88/3.11 The set Q consists of the following terms: 8.88/3.11 8.88/3.11 5(4(3(x0))) 8.88/3.11 8.88/3.11 We have to consider all minimal (P,Q,R)-chains. 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (9) DependencyGraphProof (EQUIVALENT) 8.88/3.11 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 8.88/3.11 ---------------------------------------- 8.88/3.11 8.88/3.11 (10) 8.88/3.11 TRUE 9.27/3.20 EOF