YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 625 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 9 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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(0(0(1(1(0(1(1(0(0(0(0(0(0(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(1(0(0(0(0(0(1(1(1(1(1(1(1(0(1(1(1(0(1(1(0(0(1(1(0(0(0(0(0(0(0(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: 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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-> 0(1(0(0(0(0(0(1(1(0(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(0(1(1(1(1(1(0(1(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(0(1(1(0(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(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(1(0(1(0(1(1(1(0(1(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(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(0(0(1(1(0(1(0(1(1(0(1(1(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(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(1(0(0(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(1(0(1(0(1(1(1(0(1(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(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The TRS R consists of the following rules: 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes. ---------------------------------------- (8) TRUE