9.35/3.22 YES 9.35/3.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.35/3.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.35/3.26 9.35/3.26 9.35/3.26 Termination w.r.t. Q of the given QTRS could be proven: 9.35/3.26 9.35/3.26 (0) QTRS 9.35/3.26 (1) QTRSRRRProof [EQUIVALENT, 149 ms] 9.35/3.26 (2) QTRS 9.35/3.26 (3) AAECC Innermost [EQUIVALENT, 1 ms] 9.35/3.26 (4) QTRS 9.35/3.26 (5) DependencyPairsProof [EQUIVALENT, 24 ms] 9.35/3.26 (6) QDP 9.35/3.26 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 9.35/3.26 (8) TRUE 9.35/3.26 9.35/3.26 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (0) 9.35/3.26 Obligation: 9.35/3.26 Q restricted rewrite system: 9.35/3.26 The TRS R consists of the following rules: 9.35/3.26 9.35/3.26 0(1(2(3(x1)))) -> 4(4(2(3(x1)))) 9.35/3.26 5(3(3(5(4(x1))))) -> 5(1(0(2(x1)))) 9.35/3.26 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 9.35/3.26 5(3(3(5(5(4(x1)))))) -> 4(2(4(3(2(x1))))) 9.35/3.26 5(1(4(5(1(1(5(x1))))))) -> 1(4(0(2(3(2(5(x1))))))) 9.35/3.26 3(3(4(3(1(3(0(5(x1)))))))) -> 3(5(2(4(5(0(5(2(x1)))))))) 9.35/3.26 3(1(2(2(2(1(3(1(3(x1))))))))) -> 1(4(3(1(5(0(2(2(x1)))))))) 9.35/3.26 3(4(2(0(5(2(3(5(3(x1))))))))) -> 3(5(4(4(2(2(0(5(1(x1))))))))) 9.35/3.26 5(5(1(3(3(5(4(0(0(x1))))))))) -> 3(1(0(1(4(2(4(3(x1)))))))) 9.35/3.26 3(0(2(5(1(5(0(1(5(0(x1)))))))))) -> 1(2(2(0(0(4(3(4(4(x1))))))))) 9.35/3.26 3(5(5(4(4(4(2(0(0(3(x1)))))))))) -> 1(1(2(3(2(3(4(1(x1)))))))) 9.35/3.26 3(0(4(3(3(5(0(4(4(0(4(2(x1)))))))))))) -> 3(4(5(5(3(2(0(5(1(4(2(x1))))))))))) 9.35/3.26 5(2(0(4(5(0(2(1(1(1(2(0(x1)))))))))))) -> 3(0(0(2(2(4(5(1(3(1(0(x1))))))))))) 9.35/3.26 5(5(4(3(3(4(5(4(5(0(0(4(5(x1))))))))))))) -> 5(0(1(0(3(1(4(1(2(3(1(x1))))))))))) 9.35/3.26 5(2(1(3(0(2(2(4(5(2(2(0(0(1(x1)))))))))))))) -> 3(4(5(1(4(3(3(5(0(3(0(1(x1)))))))))))) 9.35/3.26 3(1(5(2(5(5(3(3(4(4(5(2(3(2(4(x1))))))))))))))) -> 3(0(5(4(4(4(2(0(0(1(4(3(2(4(x1)))))))))))))) 9.35/3.26 4(5(5(4(3(4(4(2(4(2(4(3(3(3(3(x1))))))))))))))) -> 4(5(0(0(4(4(5(4(4(3(4(0(0(0(x1)))))))))))))) 9.35/3.26 0(1(2(4(3(1(1(4(1(5(0(2(5(3(2(4(3(x1))))))))))))))))) -> 4(2(2(1(3(1(3(0(4(5(1(2(2(5(5(4(1(x1))))))))))))))))) 9.35/3.26 2(4(3(0(4(2(0(0(2(5(1(0(2(0(0(4(4(x1))))))))))))))))) -> 5(4(1(2(1(2(1(0(2(0(4(3(1(0(0(2(x1)))))))))))))))) 9.35/3.26 3(3(3(1(0(2(1(1(5(2(4(0(0(4(5(2(2(0(2(x1))))))))))))))))))) -> 3(2(2(3(1(5(5(5(3(0(3(1(4(3(2(3(1(x1))))))))))))))))) 9.35/3.26 5(3(2(2(5(2(1(3(0(2(4(3(2(5(3(3(0(5(4(x1))))))))))))))))))) -> 1(3(0(3(3(4(5(5(0(5(5(4(0(2(1(1(0(0(2(x1))))))))))))))))))) 9.35/3.26 5(4(5(5(5(2(0(1(2(1(0(1(2(1(5(3(1(3(1(x1))))))))))))))))))) -> 0(0(3(5(3(0(2(0(1(4(0(5(4(3(0(2(4(1(x1)))))))))))))))))) 9.35/3.26 4(0(4(0(5(1(0(3(2(5(3(1(3(0(2(5(3(5(0(0(x1)))))))))))))))))))) -> 1(5(3(5(2(0(5(4(4(5(0(1(4(4(3(1(3(2(5(1(x1)))))))))))))))))))) 9.35/3.26 5(4(2(1(3(2(5(4(2(2(0(0(5(5(1(0(5(1(3(0(x1)))))))))))))))))))) -> 4(4(2(4(0(1(3(2(5(1(3(4(4(0(0(1(1(1(2(0(x1)))))))))))))))))))) 9.35/3.26 3(0(4(5(4(1(4(3(5(5(3(5(4(0(1(4(3(5(0(3(2(x1))))))))))))))))))))) -> 1(2(4(1(1(2(5(4(2(4(0(4(2(5(1(4(2(1(3(1(2(x1))))))))))))))))))))) 9.35/3.26 9.35/3.26 Q is empty. 9.35/3.26 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (1) QTRSRRRProof (EQUIVALENT) 9.35/3.26 Used ordering: 9.35/3.26 Polynomial interpretation [POLO]: 9.35/3.26 9.35/3.26 POL(0(x_1)) = 6 + x_1 9.35/3.26 POL(1(x_1)) = 7 + x_1 9.35/3.26 POL(2(x_1)) = 6 + x_1 9.35/3.26 POL(3(x_1)) = 9 + x_1 9.35/3.26 POL(4(x_1)) = 5 + x_1 9.35/3.26 POL(5(x_1)) = 7 + x_1 9.35/3.26 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 9.35/3.26 9.35/3.26 0(1(2(3(x1)))) -> 4(4(2(3(x1)))) 9.35/3.26 5(3(3(5(4(x1))))) -> 5(1(0(2(x1)))) 9.35/3.26 5(3(3(5(5(4(x1)))))) -> 4(2(4(3(2(x1))))) 9.35/3.26 5(1(4(5(1(1(5(x1))))))) -> 1(4(0(2(3(2(5(x1))))))) 9.35/3.26 3(3(4(3(1(3(0(5(x1)))))))) -> 3(5(2(4(5(0(5(2(x1)))))))) 9.35/3.26 3(1(2(2(2(1(3(1(3(x1))))))))) -> 1(4(3(1(5(0(2(2(x1)))))))) 9.35/3.26 3(4(2(0(5(2(3(5(3(x1))))))))) -> 3(5(4(4(2(2(0(5(1(x1))))))))) 9.35/3.26 5(5(1(3(3(5(4(0(0(x1))))))))) -> 3(1(0(1(4(2(4(3(x1)))))))) 9.35/3.26 3(0(2(5(1(5(0(1(5(0(x1)))))))))) -> 1(2(2(0(0(4(3(4(4(x1))))))))) 9.35/3.26 3(5(5(4(4(4(2(0(0(3(x1)))))))))) -> 1(1(2(3(2(3(4(1(x1)))))))) 9.35/3.26 3(0(4(3(3(5(0(4(4(0(4(2(x1)))))))))))) -> 3(4(5(5(3(2(0(5(1(4(2(x1))))))))))) 9.35/3.26 5(2(0(4(5(0(2(1(1(1(2(0(x1)))))))))))) -> 3(0(0(2(2(4(5(1(3(1(0(x1))))))))))) 9.35/3.26 5(5(4(3(3(4(5(4(5(0(0(4(5(x1))))))))))))) -> 5(0(1(0(3(1(4(1(2(3(1(x1))))))))))) 9.35/3.26 5(2(1(3(0(2(2(4(5(2(2(0(0(1(x1)))))))))))))) -> 3(4(5(1(4(3(3(5(0(3(0(1(x1)))))))))))) 9.35/3.26 3(1(5(2(5(5(3(3(4(4(5(2(3(2(4(x1))))))))))))))) -> 3(0(5(4(4(4(2(0(0(1(4(3(2(4(x1)))))))))))))) 9.35/3.26 4(5(5(4(3(4(4(2(4(2(4(3(3(3(3(x1))))))))))))))) -> 4(5(0(0(4(4(5(4(4(3(4(0(0(0(x1)))))))))))))) 9.35/3.26 0(1(2(4(3(1(1(4(1(5(0(2(5(3(2(4(3(x1))))))))))))))))) -> 4(2(2(1(3(1(3(0(4(5(1(2(2(5(5(4(1(x1))))))))))))))))) 9.35/3.26 2(4(3(0(4(2(0(0(2(5(1(0(2(0(0(4(4(x1))))))))))))))))) -> 5(4(1(2(1(2(1(0(2(0(4(3(1(0(0(2(x1)))))))))))))))) 9.35/3.26 3(3(3(1(0(2(1(1(5(2(4(0(0(4(5(2(2(0(2(x1))))))))))))))))))) -> 3(2(2(3(1(5(5(5(3(0(3(1(4(3(2(3(1(x1))))))))))))))))) 9.35/3.26 5(3(2(2(5(2(1(3(0(2(4(3(2(5(3(3(0(5(4(x1))))))))))))))))))) -> 1(3(0(3(3(4(5(5(0(5(5(4(0(2(1(1(0(0(2(x1))))))))))))))))))) 9.35/3.26 5(4(5(5(5(2(0(1(2(1(0(1(2(1(5(3(1(3(1(x1))))))))))))))))))) -> 0(0(3(5(3(0(2(0(1(4(0(5(4(3(0(2(4(1(x1)))))))))))))))))) 9.35/3.26 4(0(4(0(5(1(0(3(2(5(3(1(3(0(2(5(3(5(0(0(x1)))))))))))))))))))) -> 1(5(3(5(2(0(5(4(4(5(0(1(4(4(3(1(3(2(5(1(x1)))))))))))))))))))) 9.35/3.26 5(4(2(1(3(2(5(4(2(2(0(0(5(5(1(0(5(1(3(0(x1)))))))))))))))))))) -> 4(4(2(4(0(1(3(2(5(1(3(4(4(0(0(1(1(1(2(0(x1)))))))))))))))))))) 9.35/3.26 3(0(4(5(4(1(4(3(5(5(3(5(4(0(1(4(3(5(0(3(2(x1))))))))))))))))))))) -> 1(2(4(1(1(2(5(4(2(4(0(4(2(5(1(4(2(1(3(1(2(x1))))))))))))))))))))) 9.35/3.26 9.35/3.26 9.35/3.26 9.35/3.26 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (2) 9.35/3.26 Obligation: 9.35/3.26 Q restricted rewrite system: 9.35/3.26 The TRS R consists of the following rules: 9.35/3.26 9.35/3.26 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 9.35/3.26 9.35/3.26 Q is empty. 9.35/3.26 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (3) AAECC Innermost (EQUIVALENT) 9.35/3.26 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 9.35/3.26 9.35/3.26 The TRS R 2 is 9.35/3.26 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 9.35/3.26 9.35/3.26 The signature Sigma is {2_1} 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (4) 9.35/3.26 Obligation: 9.35/3.26 Q restricted rewrite system: 9.35/3.26 The TRS R consists of the following rules: 9.35/3.26 9.35/3.26 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 9.35/3.26 9.35/3.26 The set Q consists of the following terms: 9.35/3.26 9.35/3.26 2(3(1(5(0(5(x0)))))) 9.35/3.26 9.35/3.26 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (5) DependencyPairsProof (EQUIVALENT) 9.35/3.26 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (6) 9.35/3.26 Obligation: 9.35/3.26 Q DP problem: 9.35/3.26 The TRS P consists of the following rules: 9.35/3.26 9.35/3.26 2^1(3(1(5(0(5(x1)))))) -> 2^1(1(3(5(0(5(x1)))))) 9.35/3.26 9.35/3.26 The TRS R consists of the following rules: 9.35/3.26 9.35/3.26 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 9.35/3.26 9.35/3.26 The set Q consists of the following terms: 9.35/3.26 9.35/3.26 2(3(1(5(0(5(x0)))))) 9.35/3.26 9.35/3.26 We have to consider all minimal (P,Q,R)-chains. 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (7) DependencyGraphProof (EQUIVALENT) 9.35/3.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 9.35/3.26 ---------------------------------------- 9.35/3.26 9.35/3.26 (8) 9.35/3.26 TRUE 9.67/3.37 EOF