16.88/5.10 YES 17.08/5.14 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.08/5.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.08/5.14 17.08/5.14 17.08/5.14 Termination w.r.t. Q of the given QTRS could be proven: 17.08/5.14 17.08/5.14 (0) QTRS 17.08/5.14 (1) QTRSRRRProof [EQUIVALENT, 356 ms] 17.08/5.14 (2) QTRS 17.08/5.14 (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] 17.08/5.14 (4) QTRS 17.08/5.14 (5) DependencyPairsProof [EQUIVALENT, 11 ms] 17.08/5.14 (6) QDP 17.08/5.14 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 17.08/5.14 (8) TRUE 17.08/5.14 17.08/5.14 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (0) 17.08/5.14 Obligation: 17.08/5.14 Q restricted rewrite system: 17.08/5.14 The TRS R consists of the following rules: 17.08/5.14 17.08/5.14 0(x1) -> 1(x1) 17.08/5.14 0(0(x1)) -> 0(x1) 17.08/5.14 3(4(5(x1))) -> 4(3(5(x1))) 17.08/5.14 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(1(1(0(0(1(0(1(1(1(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(1(0(1(0(1(0(0(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(1(0(0(0(1(1(0(0(0(1(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(0(0(1(1(0(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(1(0(1(1(0(1(1(1(1(1(1(0(1(1(1(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(1(0(1(1(0(0(0(1(0(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(1(0(0(1(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(0(1(0(0(0(1(0(1(0(1(1(0(0(0(1(0(0(0(1(0(1(0(0(0(0(1(1(1(1(0(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.08/5.14 1(0(1(0(0(1(0(0(0(1(1(0(0(1(0(1(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(0(1(0(1(0(0(0(1(1(1(1(1(1(1(0(0(1(1(0(0(1(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(1(1(0(1(1(0(1(1(1(0(0(1(1(0(1(1(1(0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(1(0(1(0(1(1(1(0(0(0(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(1(1(1(1(0(1(0(1(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(1(0(0(1(0(1(0(1(0(0(0(0(1(0(0(0(0(0(1(1(1(0(0(1(1(1(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(0(1(0(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(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.08/5.14 17.08/5.14 Q is empty. 17.08/5.14 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (1) QTRSRRRProof (EQUIVALENT) 17.08/5.14 Used ordering: 17.08/5.14 Polynomial interpretation [POLO]: 17.08/5.14 17.08/5.14 POL(0(x_1)) = 5 + x_1 17.08/5.14 POL(1(x_1)) = 4 + x_1 17.08/5.14 POL(2(x_1)) = 7 + x_1 17.08/5.14 POL(3(x_1)) = x_1 17.08/5.14 POL(4(x_1)) = x_1 17.08/5.14 POL(5(x_1)) = x_1 17.08/5.14 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 17.08/5.14 17.08/5.14 0(x1) -> 1(x1) 17.08/5.14 0(0(x1)) -> 0(x1) 17.08/5.14 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(0(1(0(0(1(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(1(1(0(0(1(0(1(1(1(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(1(0(1(0(1(0(0(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(1(0(0(0(1(1(0(0(0(1(1(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(0(0(1(1(0(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(1(0(1(1(0(1(1(1(1(1(1(0(1(1(1(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(1(0(1(1(0(0(0(1(0(0(0(1(0(0(0(0(1(1(0(1(1(1(0(0(0(0(0(1(1(1(1(0(0(1(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(0(1(0(0(0(1(0(1(0(1(1(0(0(0(1(0(0(0(1(0(1(0(0(0(0(1(1(1(1(0(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.08/5.14 1(0(1(0(0(1(0(0(0(1(1(0(0(1(0(1(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(1(0(1(0(1(0(0(0(1(1(1(1(1(1(1(0(0(1(1(0(0(1(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(0(0(1(0(0(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(1(1(0(1(1(0(1(1(1(0(0(1(1(0(1(1(1(0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(1(0(1(0(1(1(1(0(0(0(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(1(1(1(1(0(1(0(1(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(1(0(0(1(0(1(0(1(0(0(0(0(1(0(0(0(0(0(1(1(1(0(0(1(1(1(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(0(1(0(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(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 17.08/5.14 17.08/5.14 17.08/5.14 17.08/5.14 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (2) 17.08/5.14 Obligation: 17.08/5.14 Q restricted rewrite system: 17.08/5.14 The TRS R consists of the following rules: 17.08/5.14 17.08/5.14 3(4(5(x1))) -> 4(3(5(x1))) 17.08/5.14 17.08/5.14 Q is empty. 17.08/5.14 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (3) Overlay + Local Confluence (EQUIVALENT) 17.08/5.14 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (4) 17.08/5.14 Obligation: 17.08/5.14 Q restricted rewrite system: 17.08/5.14 The TRS R consists of the following rules: 17.08/5.14 17.08/5.14 3(4(5(x1))) -> 4(3(5(x1))) 17.08/5.14 17.08/5.14 The set Q consists of the following terms: 17.08/5.14 17.08/5.14 3(4(5(x0))) 17.08/5.14 17.08/5.14 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (5) DependencyPairsProof (EQUIVALENT) 17.08/5.14 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (6) 17.08/5.14 Obligation: 17.08/5.14 Q DP problem: 17.08/5.14 The TRS P consists of the following rules: 17.08/5.14 17.08/5.14 3^1(4(5(x1))) -> 3^1(5(x1)) 17.08/5.14 17.08/5.14 The TRS R consists of the following rules: 17.08/5.14 17.08/5.14 3(4(5(x1))) -> 4(3(5(x1))) 17.08/5.14 17.08/5.14 The set Q consists of the following terms: 17.08/5.14 17.08/5.14 3(4(5(x0))) 17.08/5.14 17.08/5.14 We have to consider all minimal (P,Q,R)-chains. 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (7) DependencyGraphProof (EQUIVALENT) 17.08/5.14 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 17.08/5.14 ---------------------------------------- 17.08/5.14 17.08/5.14 (8) 17.08/5.14 TRUE 17.22/5.20 EOF