16.93/5.16 YES 17.18/5.22 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.18/5.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.18/5.22 17.18/5.22 17.18/5.22 Termination w.r.t. Q of the given QTRS could be proven: 17.18/5.22 17.18/5.22 (0) QTRS 17.18/5.22 (1) QTRS Reverse [EQUIVALENT, 0 ms] 17.18/5.22 (2) QTRS 17.18/5.22 (3) QTRSRRRProof [EQUIVALENT, 463 ms] 17.18/5.22 (4) QTRS 17.18/5.22 (5) DependencyPairsProof [EQUIVALENT, 28 ms] 17.18/5.22 (6) QDP 17.18/5.22 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 17.18/5.22 (8) TRUE 17.18/5.22 17.18/5.22 17.18/5.22 ---------------------------------------- 17.18/5.22 17.18/5.22 (0) 17.18/5.22 Obligation: 17.18/5.22 Q restricted rewrite system: 17.18/5.22 The TRS R consists of the following rules: 17.18/5.22 17.18/5.22 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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1(1(0(0(1(1(0(0(1(1(1(1(0(1(1(0(0(0(1(0(1(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(0(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 1(1(0(0(1(1(0(0(1(1(1(1(0(1(1(0(0(0(1(0(1(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(1(1(1(1(1(0(0(0(0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(1(1(1(0(1(0(0(1(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0(0(0(1(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(1(1(0(1(1(1(1(1(1(1(0(0(0(0(0(1(1(1(1(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 17.18/5.24 Q is empty. 17.18/5.24 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (3) QTRSRRRProof (EQUIVALENT) 17.18/5.24 Used ordering: 17.18/5.24 Polynomial interpretation [POLO]: 17.18/5.24 17.18/5.24 POL(0(x_1)) = x_1 17.18/5.24 POL(1(x_1)) = 1 + x_1 17.18/5.24 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 17.18/5.24 17.18/5.24 0(1(1(1(1(1(0(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(0(0(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(0(1(0(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(1(0(1(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(0(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(0(1(1(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0(1(0(1(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(0(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(0(1(1(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(0(0(1(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(1(1(0(1(1(1(1(1(1(1(0(0(0(0(0(1(1(1(1(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 17.18/5.24 17.18/5.24 17.18/5.24 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (4) 17.18/5.24 Obligation: 17.18/5.24 Q restricted rewrite system: 17.18/5.24 The TRS R consists of the following rules: 17.18/5.24 17.18/5.24 0(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 17.18/5.24 Q is empty. 17.18/5.24 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (5) DependencyPairsProof (EQUIVALENT) 17.18/5.24 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (6) 17.18/5.24 Obligation: 17.18/5.24 Q DP problem: 17.18/5.24 The TRS P consists of the following rules: 17.18/5.24 17.18/5.24 0^1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0^1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0^1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 0^1(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 17.18/5.24 The TRS R consists of the following rules: 17.18/5.24 17.18/5.24 0(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.18/5.24 17.18/5.24 Q is empty. 17.18/5.24 We have to consider all minimal (P,Q,R)-chains. 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (7) DependencyGraphProof (EQUIVALENT) 17.18/5.24 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes. 17.18/5.24 ---------------------------------------- 17.18/5.24 17.18/5.24 (8) 17.18/5.24 TRUE 17.49/5.31 EOF