9.21/3.21 YES 9.62/3.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.62/3.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.62/3.26 9.62/3.26 9.62/3.26 Termination w.r.t. Q of the given QTRS could be proven: 9.62/3.26 9.62/3.26 (0) QTRS 9.62/3.26 (1) QTRSRRRProof [EQUIVALENT, 145 ms] 9.62/3.26 (2) QTRS 9.62/3.26 (3) Overlay + Local Confluence [EQUIVALENT, 9 ms] 9.62/3.26 (4) QTRS 9.62/3.26 (5) DependencyPairsProof [EQUIVALENT, 15 ms] 9.62/3.26 (6) QDP 9.62/3.26 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 9.62/3.26 (8) TRUE 9.62/3.26 9.62/3.26 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (0) 9.62/3.26 Obligation: 9.62/3.26 Q restricted rewrite system: 9.62/3.26 The TRS R consists of the following rules: 9.62/3.26 9.62/3.26 0(x1) -> 1(x1) 9.62/3.26 0(0(x1)) -> 0(x1) 9.62/3.26 3(4(5(x1))) -> 4(3(5(x1))) 9.62/3.26 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.62/3.26 1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.62/3.26 9.62/3.26 Q is empty. 9.62/3.26 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (1) QTRSRRRProof (EQUIVALENT) 9.62/3.26 Used ordering: 9.62/3.26 Polynomial interpretation [POLO]: 9.62/3.26 9.62/3.26 POL(0(x_1)) = 72 + x_1 9.62/3.26 POL(1(x_1)) = 71 + x_1 9.62/3.26 POL(2(x_1)) = 333 + x_1 9.62/3.26 POL(3(x_1)) = x_1 9.62/3.26 POL(4(x_1)) = x_1 9.62/3.26 POL(5(x_1)) = x_1 9.62/3.26 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 9.62/3.26 9.62/3.26 0(x1) -> 1(x1) 9.62/3.26 0(0(x1)) -> 0(x1) 9.62/3.26 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.62/3.26 1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 9.62/3.26 9.62/3.26 9.62/3.26 9.62/3.26 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (2) 9.62/3.26 Obligation: 9.62/3.26 Q restricted rewrite system: 9.62/3.26 The TRS R consists of the following rules: 9.62/3.26 9.62/3.26 3(4(5(x1))) -> 4(3(5(x1))) 9.62/3.26 9.62/3.26 Q is empty. 9.62/3.26 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (3) Overlay + Local Confluence (EQUIVALENT) 9.62/3.26 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (4) 9.62/3.26 Obligation: 9.62/3.26 Q restricted rewrite system: 9.62/3.26 The TRS R consists of the following rules: 9.62/3.26 9.62/3.26 3(4(5(x1))) -> 4(3(5(x1))) 9.62/3.26 9.62/3.26 The set Q consists of the following terms: 9.62/3.26 9.62/3.26 3(4(5(x0))) 9.62/3.26 9.62/3.26 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (5) DependencyPairsProof (EQUIVALENT) 9.62/3.26 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (6) 9.62/3.26 Obligation: 9.62/3.26 Q DP problem: 9.62/3.26 The TRS P consists of the following rules: 9.62/3.26 9.62/3.26 3^1(4(5(x1))) -> 3^1(5(x1)) 9.62/3.26 9.62/3.26 The TRS R consists of the following rules: 9.62/3.26 9.62/3.26 3(4(5(x1))) -> 4(3(5(x1))) 9.62/3.26 9.62/3.26 The set Q consists of the following terms: 9.62/3.26 9.62/3.26 3(4(5(x0))) 9.62/3.26 9.62/3.26 We have to consider all minimal (P,Q,R)-chains. 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (7) DependencyGraphProof (EQUIVALENT) 9.62/3.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 9.62/3.26 ---------------------------------------- 9.62/3.26 9.62/3.26 (8) 9.62/3.26 TRUE 11.19/3.67 EOF