14.58/4.61 YES 14.98/4.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.98/4.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.98/4.62 14.98/4.62 14.98/4.62 Termination w.r.t. Q of the given QTRS could be proven: 14.98/4.62 14.98/4.62 (0) QTRS 14.98/4.62 (1) QTRSRRRProof [EQUIVALENT, 179 ms] 14.98/4.62 (2) QTRS 14.98/4.62 (3) Overlay + Local Confluence [EQUIVALENT, 1 ms] 14.98/4.62 (4) QTRS 14.98/4.62 (5) DependencyPairsProof [EQUIVALENT, 4 ms] 14.98/4.62 (6) QDP 14.98/4.62 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 14.98/4.62 (8) TRUE 14.98/4.62 14.98/4.62 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (0) 14.98/4.62 Obligation: 14.98/4.62 Q restricted rewrite system: 14.98/4.62 The TRS R consists of the following rules: 14.98/4.62 14.98/4.62 0(x1) -> 1(x1) 14.98/4.62 0(0(x1)) -> 0(x1) 14.98/4.62 3(4(5(x1))) -> 4(3(5(x1))) 14.98/4.62 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.98/4.62 0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.98/4.62 14.98/4.62 Q is empty. 14.98/4.62 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (1) QTRSRRRProof (EQUIVALENT) 14.98/4.62 Used ordering: 14.98/4.62 Polynomial interpretation [POLO]: 14.98/4.62 14.98/4.62 POL(0(x_1)) = 12 + x_1 14.98/4.62 POL(1(x_1)) = 11 + x_1 14.98/4.62 POL(2(x_1)) = 24 + x_1 14.98/4.62 POL(3(x_1)) = x_1 14.98/4.62 POL(4(x_1)) = x_1 14.98/4.62 POL(5(x_1)) = x_1 14.98/4.62 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 14.98/4.62 14.98/4.62 0(x1) -> 1(x1) 14.98/4.62 0(0(x1)) -> 0(x1) 14.98/4.62 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.98/4.62 0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 14.98/4.62 14.98/4.62 14.98/4.62 14.98/4.62 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (2) 14.98/4.62 Obligation: 14.98/4.62 Q restricted rewrite system: 14.98/4.62 The TRS R consists of the following rules: 14.98/4.62 14.98/4.62 3(4(5(x1))) -> 4(3(5(x1))) 14.98/4.62 14.98/4.62 Q is empty. 14.98/4.62 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (3) Overlay + Local Confluence (EQUIVALENT) 14.98/4.62 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (4) 14.98/4.62 Obligation: 14.98/4.62 Q restricted rewrite system: 14.98/4.62 The TRS R consists of the following rules: 14.98/4.62 14.98/4.62 3(4(5(x1))) -> 4(3(5(x1))) 14.98/4.62 14.98/4.62 The set Q consists of the following terms: 14.98/4.62 14.98/4.62 3(4(5(x0))) 14.98/4.62 14.98/4.62 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (5) DependencyPairsProof (EQUIVALENT) 14.98/4.62 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (6) 14.98/4.62 Obligation: 14.98/4.62 Q DP problem: 14.98/4.62 The TRS P consists of the following rules: 14.98/4.62 14.98/4.62 3^1(4(5(x1))) -> 3^1(5(x1)) 14.98/4.62 14.98/4.62 The TRS R consists of the following rules: 14.98/4.62 14.98/4.62 3(4(5(x1))) -> 4(3(5(x1))) 14.98/4.62 14.98/4.62 The set Q consists of the following terms: 14.98/4.62 14.98/4.62 3(4(5(x0))) 14.98/4.62 14.98/4.62 We have to consider all minimal (P,Q,R)-chains. 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (7) DependencyGraphProof (EQUIVALENT) 14.98/4.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 14.98/4.62 ---------------------------------------- 14.98/4.62 14.98/4.62 (8) 14.98/4.62 TRUE 15.28/6.30 EOF