8.18/2.83 YES 17.85/5.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.85/5.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.85/5.31 17.85/5.31 17.85/5.31 Termination w.r.t. Q of the given QTRS could be proven: 17.85/5.31 17.85/5.31 (0) QTRS 17.85/5.31 (1) QTRSRRRProof [EQUIVALENT, 152 ms] 17.85/5.31 (2) QTRS 17.85/5.31 (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] 17.85/5.31 (4) QTRS 17.85/5.31 (5) DependencyPairsProof [EQUIVALENT, 0 ms] 17.85/5.31 (6) QDP 17.85/5.31 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 17.85/5.31 (8) TRUE 17.85/5.31 17.85/5.31 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (0) 17.85/5.31 Obligation: 17.85/5.31 Q restricted rewrite system: 17.85/5.31 The TRS R consists of the following rules: 17.85/5.31 17.85/5.31 0(x1) -> 1(x1) 17.85/5.31 0(0(x1)) -> 0(x1) 17.85/5.31 3(4(5(x1))) -> 4(3(5(x1))) 17.85/5.31 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(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(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(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(1(1(1(0(0(1(1(0(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(1(1(1(0(0(1(1(0(1(0(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(0(0(1(1(0(0(0(1(1(0(0(0(1(0(0(0(1(0(0(0(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(1(1(0(0(1(0(0(1(0(1(0(0(1(1(0(0(1(0(1(0(1(1(0(0(0(1(0(1(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.85/5.31 0(0(0(1(1(0(1(0(0(0(0(0(0(1(0(0(1(0(0(1(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(0(0(0(0(1(0(0(0(1(0(1(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(1(0(1(1(1(1(0(1(0(1(1(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(1(1(0(0(0(0(0(0(1(0(0(1(0(0(1(0(1(0(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(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(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.85/5.31 17.85/5.31 Q is empty. 17.85/5.31 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (1) QTRSRRRProof (EQUIVALENT) 17.85/5.31 Used ordering: 17.85/5.31 Polynomial interpretation [POLO]: 17.85/5.31 17.85/5.31 POL(0(x_1)) = 35 + x_1 17.85/5.31 POL(1(x_1)) = x_1 17.85/5.31 POL(2(x_1)) = 18 + x_1 17.85/5.31 POL(3(x_1)) = x_1 17.85/5.31 POL(4(x_1)) = x_1 17.85/5.31 POL(5(x_1)) = x_1 17.85/5.31 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 17.85/5.31 17.85/5.31 0(x1) -> 1(x1) 17.85/5.31 0(0(x1)) -> 0(x1) 17.85/5.31 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(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(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(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(1(1(1(0(0(1(1(0(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(1(1(1(0(0(1(1(0(1(0(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(0(0(1(1(0(0(0(1(1(0(0(0(1(0(0(0(1(0(0(0(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(1(1(0(0(1(0(0(1(0(1(0(0(1(1(0(0(1(0(1(0(1(1(0(0(0(1(0(1(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.85/5.31 0(0(0(1(1(0(1(0(0(0(0(0(0(1(0(0(1(0(0(1(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(1(0(0(0(0(1(0(0(0(1(0(1(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(1(0(1(1(1(1(0(1(0(1(1(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(1(1(0(0(0(0(0(0(1(0(0(1(0(0(1(0(1(0(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(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(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.85/5.31 17.85/5.31 17.85/5.31 17.85/5.31 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (2) 17.85/5.31 Obligation: 17.85/5.31 Q restricted rewrite system: 17.85/5.31 The TRS R consists of the following rules: 17.85/5.31 17.85/5.31 3(4(5(x1))) -> 4(3(5(x1))) 17.85/5.31 17.85/5.31 Q is empty. 17.85/5.31 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (3) Overlay + Local Confluence (EQUIVALENT) 17.85/5.31 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (4) 17.85/5.31 Obligation: 17.85/5.31 Q restricted rewrite system: 17.85/5.31 The TRS R consists of the following rules: 17.85/5.31 17.85/5.31 3(4(5(x1))) -> 4(3(5(x1))) 17.85/5.31 17.85/5.31 The set Q consists of the following terms: 17.85/5.31 17.85/5.31 3(4(5(x0))) 17.85/5.31 17.85/5.31 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (5) DependencyPairsProof (EQUIVALENT) 17.85/5.31 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (6) 17.85/5.31 Obligation: 17.85/5.31 Q DP problem: 17.85/5.31 The TRS P consists of the following rules: 17.85/5.31 17.85/5.31 3^1(4(5(x1))) -> 3^1(5(x1)) 17.85/5.31 17.85/5.31 The TRS R consists of the following rules: 17.85/5.31 17.85/5.31 3(4(5(x1))) -> 4(3(5(x1))) 17.85/5.31 17.85/5.31 The set Q consists of the following terms: 17.85/5.31 17.85/5.31 3(4(5(x0))) 17.85/5.31 17.85/5.31 We have to consider all minimal (P,Q,R)-chains. 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (7) DependencyGraphProof (EQUIVALENT) 17.85/5.31 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 17.85/5.31 ---------------------------------------- 17.85/5.31 17.85/5.31 (8) 17.85/5.31 TRUE 18.38/5.44 EOF