11.11/3.65 YES 11.51/3.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.51/3.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.51/3.71 11.51/3.71 11.51/3.71 Termination w.r.t. Q of the given QTRS could be proven: 11.51/3.71 11.51/3.71 (0) QTRS 11.51/3.71 (1) QTRSRRRProof [EQUIVALENT, 184 ms] 11.51/3.71 (2) QTRS 11.51/3.71 (3) Overlay + Local Confluence [EQUIVALENT, 7 ms] 11.51/3.71 (4) QTRS 11.51/3.71 (5) DependencyPairsProof [EQUIVALENT, 18 ms] 11.51/3.71 (6) QDP 11.51/3.71 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 11.51/3.71 (8) TRUE 11.51/3.71 11.51/3.71 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (0) 11.51/3.71 Obligation: 11.51/3.71 Q restricted rewrite system: 11.51/3.71 The TRS R consists of the following rules: 11.51/3.71 11.51/3.71 0(x1) -> 1(x1) 11.51/3.71 0(0(x1)) -> 0(x1) 11.51/3.71 3(4(5(x1))) -> 4(3(5(x1))) 11.51/3.71 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(1(1(0(0(0(0(1(0(1(0(1(1(1(0(0(0(1(1(1(0(1(0(0(0(1(0(0(1(1(0(1(0(0(1(0(0(0(0(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(0(1(0(1(1(0(1(0(0(0(1(1(0(0(0(0(1(1(0(1(1(1(0(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(1(0(0(1(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(0(0(0(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(1(1(0(1(1(0(0(0(0(1(1(0(0(1(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.51/3.71 1(0(1(1(1(1(1(0(0(1(1(1(1(0(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(0(1(0(0(1(1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(1(0(1(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(0(1(0(1(0(1(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(0(1(0(0(0(1(1(0(0(1(1(1(1(1(1(1(0(1(0(1(1(0(1(0(0(0(1(0(1(0(1(0(0(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(0(1(0(1(0(0(0(0(1(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(0(1(1(0(0(1(1(1(1(0(1(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(0(0(1(0(1(1(1(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(1(0(1(0(0(1(1(1(0(0(0(0(1(1(0(1(1(1(1(1(1(1(0(0(1(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(0(0(1(1(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(1(0(0(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.51/3.71 11.51/3.71 Q is empty. 11.51/3.71 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (1) QTRSRRRProof (EQUIVALENT) 11.51/3.71 Used ordering: 11.51/3.71 Polynomial interpretation [POLO]: 11.51/3.71 11.51/3.71 POL(0(x_1)) = 2 + x_1 11.51/3.71 POL(1(x_1)) = x_1 11.51/3.71 POL(2(x_1)) = 3 + x_1 11.51/3.71 POL(3(x_1)) = x_1 11.51/3.71 POL(4(x_1)) = x_1 11.51/3.71 POL(5(x_1)) = x_1 11.51/3.71 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.51/3.71 11.51/3.71 0(x1) -> 1(x1) 11.51/3.71 0(0(x1)) -> 0(x1) 11.51/3.71 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(1(1(1(0(0(0(0(1(0(1(0(1(1(1(0(0(0(1(1(1(0(1(0(0(0(1(0(0(1(1(0(1(0(0(1(0(0(0(0(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(0(1(0(1(1(0(1(0(0(0(1(1(0(0(0(0(1(1(0(1(1(1(0(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(0(1(1(0(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(1(1(0(1(0(1(0(0(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(1(0(0(1(0(1(0(0(1(1(1(0(0(0(1(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(1(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(1(0(0(1(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(0(0(0(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(1(1(0(1(1(0(0(0(0(1(1(0(0(1(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.51/3.71 1(0(1(1(1(1(1(0(0(1(1(1(1(0(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(0(1(0(0(1(1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(1(0(1(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(0(1(0(1(0(1(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(0(1(0(0(0(1(1(0(0(1(1(1(1(1(1(1(0(1(0(1(1(0(1(0(0(0(1(0(1(0(1(0(0(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(0(1(0(1(0(0(0(0(1(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(0(1(1(0(0(1(1(1(1(0(1(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(0(0(1(0(1(1(1(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(1(0(1(0(0(1(1(1(0(0(0(0(1(1(0(1(1(1(1(1(1(1(0(0(1(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(0(0(1(1(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(1(1(0(0(0(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(1(0(0(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.51/3.71 11.51/3.71 11.51/3.71 11.51/3.71 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (2) 11.51/3.71 Obligation: 11.51/3.71 Q restricted rewrite system: 11.51/3.71 The TRS R consists of the following rules: 11.51/3.71 11.51/3.71 3(4(5(x1))) -> 4(3(5(x1))) 11.51/3.71 11.51/3.71 Q is empty. 11.51/3.71 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (3) Overlay + Local Confluence (EQUIVALENT) 11.51/3.71 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (4) 11.51/3.71 Obligation: 11.51/3.71 Q restricted rewrite system: 11.51/3.71 The TRS R consists of the following rules: 11.51/3.71 11.51/3.71 3(4(5(x1))) -> 4(3(5(x1))) 11.51/3.71 11.51/3.71 The set Q consists of the following terms: 11.51/3.71 11.51/3.71 3(4(5(x0))) 11.51/3.71 11.51/3.71 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (5) DependencyPairsProof (EQUIVALENT) 11.51/3.71 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (6) 11.51/3.71 Obligation: 11.51/3.71 Q DP problem: 11.51/3.71 The TRS P consists of the following rules: 11.51/3.71 11.51/3.71 3^1(4(5(x1))) -> 3^1(5(x1)) 11.51/3.71 11.51/3.71 The TRS R consists of the following rules: 11.51/3.71 11.51/3.71 3(4(5(x1))) -> 4(3(5(x1))) 11.51/3.71 11.51/3.71 The set Q consists of the following terms: 11.51/3.71 11.51/3.71 3(4(5(x0))) 11.51/3.71 11.51/3.71 We have to consider all minimal (P,Q,R)-chains. 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (7) DependencyGraphProof (EQUIVALENT) 11.51/3.71 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 11.51/3.71 ---------------------------------------- 11.51/3.71 11.51/3.71 (8) 11.51/3.71 TRUE 11.76/3.80 EOF