9.81/3.24 YES 9.98/3.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.98/3.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.98/3.28 9.98/3.28 9.98/3.28 Termination w.r.t. Q of the given QTRS could be proven: 9.98/3.28 9.98/3.28 (0) QTRS 9.98/3.28 (1) QTRSRRRProof [EQUIVALENT, 110 ms] 9.98/3.28 (2) QTRS 9.98/3.28 (3) DependencyPairsProof [EQUIVALENT, 37 ms] 9.98/3.28 (4) QDP 9.98/3.28 (5) DependencyGraphProof [EQUIVALENT, 1 ms] 9.98/3.28 (6) TRUE 9.98/3.28 9.98/3.28 9.98/3.28 ---------------------------------------- 9.98/3.28 9.98/3.28 (0) 9.98/3.28 Obligation: 9.98/3.28 Q restricted rewrite system: 9.98/3.28 The TRS R consists of the following rules: 9.98/3.28 9.98/3.28 0(1(0(2(x1)))) -> 3(4(4(x1))) 9.98/3.28 2(0(0(3(x1)))) -> 3(4(1(x1))) 9.98/3.28 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 9.98/3.28 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 9.98/3.28 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 9.98/3.28 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 9.98/3.28 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 9.98/3.28 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 9.98/3.28 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 9.98/3.28 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 9.98/3.28 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 9.98/3.28 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 9.98/3.28 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 9.98/3.28 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 9.98/3.28 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 9.98/3.28 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 9.98/3.28 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 9.98/3.28 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 9.98/3.28 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 9.98/3.28 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 9.98/3.28 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 9.98/3.28 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 9.98/3.28 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 9.98/3.28 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 9.98/3.28 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 9.98/3.28 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 9.98/3.28 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 9.98/3.28 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 9.98/3.28 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 9.98/3.28 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(x1))))))))))))))))))))) 9.98/3.28 9.98/3.28 Q is empty. 9.98/3.28 9.98/3.28 ---------------------------------------- 9.98/3.28 9.98/3.28 (1) QTRSRRRProof (EQUIVALENT) 9.98/3.28 Used ordering: 9.98/3.28 Polynomial interpretation [POLO]: 9.98/3.28 9.98/3.28 POL(0(x_1)) = 130 + x_1 9.98/3.28 POL(1(x_1)) = 129 + x_1 9.98/3.28 POL(2(x_1)) = 120 + x_1 9.98/3.28 POL(3(x_1)) = 132 + x_1 9.98/3.28 POL(4(x_1)) = 151 + x_1 9.98/3.28 POL(5(x_1)) = 122 + x_1 9.98/3.28 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 9.98/3.28 9.98/3.28 0(1(0(2(x1)))) -> 3(4(4(x1))) 9.98/3.28 2(0(0(3(x1)))) -> 3(4(1(x1))) 9.98/3.28 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 9.98/3.28 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 9.98/3.28 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 9.98/3.28 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 9.98/3.28 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 9.98/3.28 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 9.98/3.28 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 9.98/3.28 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 9.98/3.28 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 9.98/3.28 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 9.98/3.28 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 9.98/3.28 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 9.98/3.28 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 9.98/3.28 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 9.98/3.28 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 9.98/3.28 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 9.98/3.28 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 9.98/3.28 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 9.98/3.28 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 9.98/3.28 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 9.98/3.28 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 9.98/3.28 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 9.98/3.28 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 9.98/3.28 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 9.98/3.28 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 9.98/3.28 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(x1))))))))))))))))))))) 9.98/3.28 9.98/3.28 9.98/3.28 9.98/3.28 9.98/3.28 ---------------------------------------- 9.98/3.28 9.98/3.28 (2) 9.98/3.28 Obligation: 9.98/3.28 Q restricted rewrite system: 9.98/3.28 The TRS R consists of the following rules: 9.98/3.28 9.98/3.28 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 9.98/3.28 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 9.98/3.28 9.98/3.28 Q is empty. 9.98/3.28 9.98/3.28 ---------------------------------------- 9.98/3.28 9.98/3.28 (3) DependencyPairsProof (EQUIVALENT) 9.98/3.28 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.98/3.28 ---------------------------------------- 9.98/3.28 9.98/3.28 (4) 9.98/3.28 Obligation: 9.98/3.28 Q DP problem: 9.98/3.28 The TRS P consists of the following rules: 9.98/3.28 9.98/3.28 2^1(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3^1(4(4(2(0(2(3(3(5(2(x1)))))))))) 9.98/3.28 2^1(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 2^1(0(2(3(3(5(2(x1))))))) 9.98/3.28 2^1(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 2^1(3(3(5(2(x1))))) 9.98/3.28 2^1(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3^1(3(5(2(x1)))) 9.98/3.28 2^1(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3^1(5(2(x1))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 2^1(0(1(4(4(3(3(3(5(3(4(1(2(x1))))))))))))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 3^1(3(3(5(3(4(1(2(x1)))))))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 3^1(3(5(3(4(1(2(x1))))))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 3^1(5(3(4(1(2(x1)))))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 3^1(4(1(2(x1)))) 9.98/3.28 3^1(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 2^1(x1) 9.98/3.28 9.98/3.28 The TRS R consists of the following rules: 9.98/3.29 9.98/3.29 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 9.98/3.29 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 9.98/3.29 9.98/3.29 Q is empty. 9.98/3.29 We have to consider all minimal (P,Q,R)-chains. 9.98/3.29 ---------------------------------------- 9.98/3.29 9.98/3.29 (5) DependencyGraphProof (EQUIVALENT) 9.98/3.29 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 11 less nodes. 9.98/3.29 ---------------------------------------- 9.98/3.29 9.98/3.29 (6) 9.98/3.29 TRUE 9.98/3.34 EOF