9.64/3.33 YES 23.91/6.93 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 23.91/6.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.91/6.93 23.91/6.93 23.91/6.93 Termination w.r.t. Q of the given QTRS could be proven: 23.91/6.93 23.91/6.93 (0) QTRS 23.91/6.93 (1) QTRSRRRProof [EQUIVALENT, 234 ms] 23.91/6.93 (2) QTRS 23.91/6.93 (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] 23.91/6.93 (4) QTRS 23.91/6.93 (5) DependencyPairsProof [EQUIVALENT, 9 ms] 23.91/6.93 (6) QDP 23.91/6.93 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 23.91/6.93 (8) TRUE 23.91/6.93 23.91/6.93 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (0) 23.91/6.93 Obligation: 23.91/6.93 Q restricted rewrite system: 23.91/6.93 The TRS R consists of the following rules: 23.91/6.93 23.91/6.93 0(x1) -> 1(x1) 23.91/6.93 0(0(x1)) -> 0(x1) 23.91/6.93 3(4(5(x1))) -> 4(3(5(x1))) 23.91/6.93 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(0(1(0(1(1(0(0(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(1(1(1(1(0(0(1(1(0(0(1(0(0(0(1(1(0(1(0(0(0(0(1(0(0(0(0(0(1(0(1(0(1(0(0(0(0(0(1(0(0(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(1(1(0(0(1(1(1(1(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(1(1(0(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(0(0(1(0(0(0(1(0(0(1(0(1(0(1(1(1(1(1(1(0(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 23.91/6.93 1(0(1(1(1(1(1(0(0(1(1(0(1(1(0(0(1(0(1(0(1(1(0(1(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(0(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(0(0(1(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(1(0(1(1(1(0(0(1(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(0(1(0(0(1(0(1(0(0(0(0(0(0(0(1(1(0(1(0(1(0(0(1(1(1(0(1(0(0(1(1(1(0(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(0(0(0(0(1(1(1(0(0(1(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(1(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(1(0(0(1(1(1(0(0(0(0(0(0(1(0(1(0(1(0(0(0(0(1(0(1(0(1(0(1(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(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 23.91/6.93 23.91/6.93 Q is empty. 23.91/6.93 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (1) QTRSRRRProof (EQUIVALENT) 23.91/6.93 Used ordering: 23.91/6.93 Polynomial interpretation [POLO]: 23.91/6.93 23.91/6.93 POL(0(x_1)) = 7 + x_1 23.91/6.93 POL(1(x_1)) = 6 + x_1 23.91/6.93 POL(2(x_1)) = 16 + x_1 23.91/6.93 POL(3(x_1)) = x_1 23.91/6.93 POL(4(x_1)) = x_1 23.91/6.93 POL(5(x_1)) = x_1 23.91/6.93 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 23.91/6.93 23.91/6.93 0(x1) -> 1(x1) 23.91/6.93 0(0(x1)) -> 0(x1) 23.91/6.93 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(0(1(0(1(1(0(0(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(1(1(1(1(0(0(1(1(0(0(1(0(0(0(1(1(0(1(0(0(0(0(1(0(0(0(0(0(1(0(1(0(1(0(0(0(0(0(1(0(0(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(1(0(1(1(1(0(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(1(1(0(0(1(1(1(1(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(1(1(0(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(0(0(1(0(0(0(1(0(0(1(0(1(0(1(1(1(1(1(1(0(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 23.91/6.93 1(0(1(1(1(1(1(0(0(1(1(0(1(1(0(0(1(0(1(0(1(1(0(1(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(0(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(1(0(0(0(0(1(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(1(0(1(1(1(0(0(1(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(1(0(1(1(0(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(1(0(0(0(1(0(0(1(0(1(0(0(0(0(0(0(0(1(1(0(1(0(1(0(0(1(1(1(0(1(0(0(1(1(1(0(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(0(0(0(0(1(1(1(0(0(1(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(1(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(1(0(0(1(1(1(0(0(0(0(0(0(1(0(1(0(1(0(0(0(0(1(0(1(0(1(0(1(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(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 23.91/6.93 23.91/6.93 23.91/6.93 23.91/6.93 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (2) 23.91/6.93 Obligation: 23.91/6.93 Q restricted rewrite system: 23.91/6.93 The TRS R consists of the following rules: 23.91/6.93 23.91/6.93 3(4(5(x1))) -> 4(3(5(x1))) 23.91/6.93 23.91/6.93 Q is empty. 23.91/6.93 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (3) Overlay + Local Confluence (EQUIVALENT) 23.91/6.93 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (4) 23.91/6.93 Obligation: 23.91/6.93 Q restricted rewrite system: 23.91/6.93 The TRS R consists of the following rules: 23.91/6.93 23.91/6.93 3(4(5(x1))) -> 4(3(5(x1))) 23.91/6.93 23.91/6.93 The set Q consists of the following terms: 23.91/6.93 23.91/6.93 3(4(5(x0))) 23.91/6.93 23.91/6.93 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (5) DependencyPairsProof (EQUIVALENT) 23.91/6.93 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (6) 23.91/6.93 Obligation: 23.91/6.93 Q DP problem: 23.91/6.93 The TRS P consists of the following rules: 23.91/6.93 23.91/6.93 3^1(4(5(x1))) -> 3^1(5(x1)) 23.91/6.93 23.91/6.93 The TRS R consists of the following rules: 23.91/6.93 23.91/6.93 3(4(5(x1))) -> 4(3(5(x1))) 23.91/6.93 23.91/6.93 The set Q consists of the following terms: 23.91/6.93 23.91/6.93 3(4(5(x0))) 23.91/6.93 23.91/6.93 We have to consider all minimal (P,Q,R)-chains. 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (7) DependencyGraphProof (EQUIVALENT) 23.91/6.93 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 23.91/6.93 ---------------------------------------- 23.91/6.93 23.91/6.93 (8) 23.91/6.93 TRUE 24.25/7.06 EOF