14.24/4.55 YES 20.18/6.07 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 20.18/6.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.18/6.07 20.18/6.07 20.18/6.07 Termination w.r.t. Q of the given QTRS could be proven: 20.18/6.07 20.18/6.07 (0) QTRS 20.18/6.07 (1) QTRSRRRProof [EQUIVALENT, 182 ms] 20.18/6.07 (2) QTRS 20.18/6.07 (3) Overlay + Local Confluence [EQUIVALENT, 10 ms] 20.18/6.07 (4) QTRS 20.18/6.07 (5) DependencyPairsProof [EQUIVALENT, 28 ms] 20.18/6.07 (6) QDP 20.18/6.07 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 20.18/6.07 (8) TRUE 20.18/6.07 20.18/6.07 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (0) 20.18/6.07 Obligation: 20.18/6.07 Q restricted rewrite system: 20.18/6.07 The TRS R consists of the following rules: 20.18/6.07 20.18/6.07 0(x1) -> 1(x1) 20.18/6.07 0(0(x1)) -> 0(x1) 20.18/6.07 3(4(5(x1))) -> 4(3(5(x1))) 20.18/6.07 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 20.18/6.07 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 20.18/6.07 20.18/6.07 Q is empty. 20.18/6.07 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (1) QTRSRRRProof (EQUIVALENT) 20.18/6.07 Used ordering: 20.18/6.07 Polynomial interpretation [POLO]: 20.18/6.07 20.18/6.07 POL(0(x_1)) = 6 + x_1 20.18/6.07 POL(1(x_1)) = 5 + x_1 20.18/6.07 POL(2(x_1)) = 9 + x_1 20.18/6.07 POL(3(x_1)) = x_1 20.18/6.07 POL(4(x_1)) = x_1 20.18/6.07 POL(5(x_1)) = x_1 20.18/6.07 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 20.18/6.07 20.18/6.07 0(x1) -> 1(x1) 20.18/6.07 0(0(x1)) -> 0(x1) 20.18/6.07 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 20.18/6.07 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 20.18/6.07 20.18/6.07 20.18/6.07 20.18/6.07 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (2) 20.18/6.07 Obligation: 20.18/6.07 Q restricted rewrite system: 20.18/6.07 The TRS R consists of the following rules: 20.18/6.07 20.18/6.07 3(4(5(x1))) -> 4(3(5(x1))) 20.18/6.07 20.18/6.07 Q is empty. 20.18/6.07 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (3) Overlay + Local Confluence (EQUIVALENT) 20.18/6.07 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (4) 20.18/6.07 Obligation: 20.18/6.07 Q restricted rewrite system: 20.18/6.07 The TRS R consists of the following rules: 20.18/6.07 20.18/6.07 3(4(5(x1))) -> 4(3(5(x1))) 20.18/6.07 20.18/6.07 The set Q consists of the following terms: 20.18/6.07 20.18/6.07 3(4(5(x0))) 20.18/6.07 20.18/6.07 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (5) DependencyPairsProof (EQUIVALENT) 20.18/6.07 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 20.18/6.07 ---------------------------------------- 20.18/6.07 20.18/6.07 (6) 20.18/6.07 Obligation: 20.18/6.07 Q DP problem: 20.18/6.07 The TRS P consists of the following rules: 20.18/6.07 20.18/6.07 3^1(4(5(x1))) -> 3^1(5(x1)) 20.18/6.07 20.18/6.07 The TRS R consists of the following rules: 20.18/6.07 20.18/6.07 3(4(5(x1))) -> 4(3(5(x1))) 20.18/6.07 20.18/6.07 The set Q consists of the following terms: 20.18/6.07 20.18/6.07 3(4(5(x0))) 20.18/6.07 20.18/6.07 We have to consider all minimal (P,Q,R)-chains. 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (7) DependencyGraphProof (EQUIVALENT) 20.18/6.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 20.18/6.08 ---------------------------------------- 20.18/6.08 20.18/6.08 (8) 20.18/6.08 TRUE 20.72/6.24 EOF