10.41/3.56 YES 10.75/3.64 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.75/3.64 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.75/3.64 10.75/3.64 10.75/3.64 Termination w.r.t. Q of the given QTRS could be proven: 10.75/3.64 10.75/3.64 (0) QTRS 10.75/3.64 (1) QTRSRRRProof [EQUIVALENT, 143 ms] 10.75/3.64 (2) QTRS 10.75/3.64 (3) DependencyPairsProof [EQUIVALENT, 5 ms] 10.75/3.64 (4) QDP 10.75/3.64 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 10.75/3.64 (6) TRUE 10.75/3.64 10.75/3.64 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (0) 10.75/3.64 Obligation: 10.75/3.64 Q restricted rewrite system: 10.75/3.64 The TRS R consists of the following rules: 10.75/3.64 10.75/3.64 0(1(2(2(x1)))) -> 0(1(0(1(x1)))) 10.75/3.64 0(0(0(0(0(x1))))) -> 2(0(2(0(x1)))) 10.75/3.64 3(2(3(4(0(4(1(0(x1)))))))) -> 2(3(2(2(5(3(1(x1))))))) 10.75/3.64 1(4(1(0(4(1(2(2(5(3(x1)))))))))) -> 1(4(4(2(5(3(1(5(2(x1))))))))) 10.75/3.64 1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1(1(4(1(0(4(2(3(2(1(x1)))))))))) 10.75/3.64 2(5(1(2(4(5(1(3(1(5(x1)))))))))) -> 2(4(3(0(3(4(2(4(5(x1))))))))) 10.75/3.64 2(3(2(4(3(2(3(4(4(0(0(0(x1)))))))))))) -> 2(4(2(0(2(2(2(2(4(3(0(x1))))))))))) 10.75/3.64 5(0(2(4(2(4(1(4(4(5(1(4(x1)))))))))))) -> 1(4(5(3(3(2(3(2(3(3(4(x1))))))))))) 10.75/3.64 1(0(1(3(5(5(1(2(5(2(3(5(4(x1))))))))))))) -> 1(0(3(4(1(2(3(4(5(3(3(5(4(x1))))))))))))) 10.75/3.64 1(4(4(2(5(3(1(5(1(2(1(5(0(x1))))))))))))) -> 3(5(2(5(4(1(5(2(4(1(3(2(x1)))))))))))) 10.75/3.64 4(1(2(5(1(1(0(0(5(4(1(3(1(x1))))))))))))) -> 4(1(1(2(2(3(5(1(4(2(3(1(x1)))))))))))) 10.75/3.64 5(5(3(2(0(3(4(0(0(3(1(4(3(x1))))))))))))) -> 5(5(3(5(0(3(1(5(2(3(1(3(4(x1))))))))))))) 10.75/3.64 0(5(3(2(4(0(2(1(2(3(3(4(3(3(x1)))))))))))))) -> 0(5(4(4(5(3(4(0(1(0(1(3(1(2(3(x1))))))))))))))) 10.75/3.64 4(3(0(5(5(2(5(2(3(5(3(0(2(2(4(x1))))))))))))))) -> 4(3(3(4(3(1(4(1(5(0(0(5(1(5(3(4(x1)))))))))))))))) 10.75/3.64 3(1(5(4(1(2(0(0(1(0(0(0(2(0(4(5(x1)))))))))))))))) -> 3(0(2(2(3(3(1(3(2(2(1(2(2(5(5(x1))))))))))))))) 10.75/3.64 4(1(1(0(5(4(2(0(4(0(5(1(2(0(3(1(x1)))))))))))))))) -> 2(4(3(1(4(1(4(0(1(1(0(5(4(0(5(0(x1)))))))))))))))) 10.75/3.64 4(0(2(2(4(4(1(1(1(1(0(4(1(5(1(2(0(1(x1)))))))))))))))))) -> 4(5(5(2(5(0(2(1(5(2(4(1(1(1(5(3(2(x1))))))))))))))))) 10.75/3.64 4(4(4(4(3(1(1(3(3(4(2(2(4(0(3(5(4(2(5(2(3(x1))))))))))))))))))))) -> 2(5(5(4(0(1(5(3(3(5(0(1(5(1(5(4(2(4(2(2(x1)))))))))))))))))))) 10.75/3.64 10.75/3.64 Q is empty. 10.75/3.64 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (1) QTRSRRRProof (EQUIVALENT) 10.75/3.64 Used ordering: 10.75/3.64 Polynomial interpretation [POLO]: 10.75/3.64 10.75/3.64 POL(0(x_1)) = 13 + x_1 10.75/3.64 POL(1(x_1)) = 9 + x_1 10.75/3.64 POL(2(x_1)) = 14 + x_1 10.75/3.64 POL(3(x_1)) = 11 + x_1 10.75/3.64 POL(4(x_1)) = 8 + x_1 10.75/3.64 POL(5(x_1)) = 10 + x_1 10.75/3.64 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.75/3.64 10.75/3.64 0(1(2(2(x1)))) -> 0(1(0(1(x1)))) 10.75/3.64 0(0(0(0(0(x1))))) -> 2(0(2(0(x1)))) 10.75/3.64 3(2(3(4(0(4(1(0(x1)))))))) -> 2(3(2(2(5(3(1(x1))))))) 10.75/3.64 1(4(1(0(4(1(2(2(5(3(x1)))))))))) -> 1(4(4(2(5(3(1(5(2(x1))))))))) 10.75/3.64 2(5(1(2(4(5(1(3(1(5(x1)))))))))) -> 2(4(3(0(3(4(2(4(5(x1))))))))) 10.75/3.64 2(3(2(4(3(2(3(4(4(0(0(0(x1)))))))))))) -> 2(4(2(0(2(2(2(2(4(3(0(x1))))))))))) 10.75/3.64 5(0(2(4(2(4(1(4(4(5(1(4(x1)))))))))))) -> 1(4(5(3(3(2(3(2(3(3(4(x1))))))))))) 10.75/3.64 1(0(1(3(5(5(1(2(5(2(3(5(4(x1))))))))))))) -> 1(0(3(4(1(2(3(4(5(3(3(5(4(x1))))))))))))) 10.75/3.64 1(4(4(2(5(3(1(5(1(2(1(5(0(x1))))))))))))) -> 3(5(2(5(4(1(5(2(4(1(3(2(x1)))))))))))) 10.75/3.64 4(1(2(5(1(1(0(0(5(4(1(3(1(x1))))))))))))) -> 4(1(1(2(2(3(5(1(4(2(3(1(x1)))))))))))) 10.75/3.64 5(5(3(2(0(3(4(0(0(3(1(4(3(x1))))))))))))) -> 5(5(3(5(0(3(1(5(2(3(1(3(4(x1))))))))))))) 10.75/3.64 0(5(3(2(4(0(2(1(2(3(3(4(3(3(x1)))))))))))))) -> 0(5(4(4(5(3(4(0(1(0(1(3(1(2(3(x1))))))))))))))) 10.75/3.64 4(3(0(5(5(2(5(2(3(5(3(0(2(2(4(x1))))))))))))))) -> 4(3(3(4(3(1(4(1(5(0(0(5(1(5(3(4(x1)))))))))))))))) 10.75/3.64 3(1(5(4(1(2(0(0(1(0(0(0(2(0(4(5(x1)))))))))))))))) -> 3(0(2(2(3(3(1(3(2(2(1(2(2(5(5(x1))))))))))))))) 10.75/3.64 4(1(1(0(5(4(2(0(4(0(5(1(2(0(3(1(x1)))))))))))))))) -> 2(4(3(1(4(1(4(0(1(1(0(5(4(0(5(0(x1)))))))))))))))) 10.75/3.64 4(0(2(2(4(4(1(1(1(1(0(4(1(5(1(2(0(1(x1)))))))))))))))))) -> 4(5(5(2(5(0(2(1(5(2(4(1(1(1(5(3(2(x1))))))))))))))))) 10.75/3.64 4(4(4(4(3(1(1(3(3(4(2(2(4(0(3(5(4(2(5(2(3(x1))))))))))))))))))))) -> 2(5(5(4(0(1(5(3(3(5(0(1(5(1(5(4(2(4(2(2(x1)))))))))))))))))))) 10.75/3.64 10.75/3.64 10.75/3.64 10.75/3.64 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (2) 10.75/3.64 Obligation: 10.75/3.64 Q restricted rewrite system: 10.75/3.64 The TRS R consists of the following rules: 10.75/3.64 10.75/3.64 1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1(1(4(1(0(4(2(3(2(1(x1)))))))))) 10.75/3.64 10.75/3.64 Q is empty. 10.75/3.64 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (3) DependencyPairsProof (EQUIVALENT) 10.75/3.64 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (4) 10.75/3.64 Obligation: 10.75/3.64 Q DP problem: 10.75/3.64 The TRS P consists of the following rules: 10.75/3.64 10.75/3.64 1^1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1^1(1(4(1(0(4(2(3(2(1(x1)))))))))) 10.75/3.64 1^1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1^1(4(1(0(4(2(3(2(1(x1))))))))) 10.75/3.64 1^1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1^1(0(4(2(3(2(1(x1))))))) 10.75/3.64 10.75/3.64 The TRS R consists of the following rules: 10.75/3.64 10.75/3.64 1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1(1(4(1(0(4(2(3(2(1(x1)))))))))) 10.75/3.64 10.75/3.64 Q is empty. 10.75/3.64 We have to consider all minimal (P,Q,R)-chains. 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (5) DependencyGraphProof (EQUIVALENT) 10.75/3.64 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes. 10.75/3.64 ---------------------------------------- 10.75/3.64 10.75/3.64 (6) 10.75/3.64 TRUE 10.93/3.71 EOF