10.94/3.73 YES 11.34/3.74 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.34/3.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.34/3.74 11.34/3.74 11.34/3.74 Termination w.r.t. Q of the given QTRS could be proven: 11.34/3.74 11.34/3.74 (0) QTRS 11.34/3.74 (1) QTRSRRRProof [EQUIVALENT, 173 ms] 11.34/3.74 (2) QTRS 11.34/3.74 (3) Overlay + Local Confluence [EQUIVALENT, 5 ms] 11.34/3.74 (4) QTRS 11.34/3.74 (5) DependencyPairsProof [EQUIVALENT, 3 ms] 11.34/3.74 (6) QDP 11.34/3.74 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 11.34/3.74 (8) TRUE 11.34/3.74 11.34/3.74 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (0) 11.34/3.74 Obligation: 11.34/3.74 Q restricted rewrite system: 11.34/3.74 The TRS R consists of the following rules: 11.34/3.74 11.34/3.74 0(x1) -> 1(x1) 11.34/3.74 0(0(x1)) -> 0(x1) 11.34/3.74 3(4(5(x1))) -> 4(3(5(x1))) 11.34/3.74 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(0(0(1(0(1(0(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(0(1(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(0(0(1(1(0(1(1(1(1(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(0(0(1(0(1(1(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(0(1(1(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(1(0(0(1(0(0(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(0(1(1(1(1(1(0(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(1(0(1(0(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(0(0(1(1(1(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(0(0(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(0(1(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.34/3.74 1(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(1(1(0(1(1(1(0(1(1(0(0(1(0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(0(1(1(1(0(1(1(1(0(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(1(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(1(1(1(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(1(0(1(0(1(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(1(1(1(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(0(0(1(1(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(0(1(0(1(0(0(1(1(0(1(0(1(0(0(1(1(1(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(1(0(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(1(1(0(1(0(1(1(0(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.34/3.74 11.34/3.74 Q is empty. 11.34/3.74 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (1) QTRSRRRProof (EQUIVALENT) 11.34/3.74 Used ordering: 11.34/3.74 Polynomial interpretation [POLO]: 11.34/3.74 11.34/3.74 POL(0(x_1)) = 98 + x_1 11.34/3.74 POL(1(x_1)) = 97 + x_1 11.34/3.74 POL(2(x_1)) = 443 + x_1 11.34/3.74 POL(3(x_1)) = x_1 11.34/3.74 POL(4(x_1)) = x_1 11.34/3.74 POL(5(x_1)) = x_1 11.34/3.74 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.34/3.74 11.34/3.74 0(x1) -> 1(x1) 11.34/3.74 0(0(x1)) -> 0(x1) 11.34/3.74 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(0(0(1(0(1(0(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(0(1(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(0(0(1(1(0(1(1(1(1(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(0(0(1(0(1(1(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(0(1(1(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(1(0(0(1(0(0(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(0(1(1(1(1(1(0(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(1(0(1(0(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(0(0(1(1(1(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(0(0(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(0(1(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.34/3.74 1(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(1(1(0(1(1(1(0(1(1(0(0(1(0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(0(1(1(1(0(1(1(1(0(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(1(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(1(1(1(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(1(0(1(0(1(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(1(1(1(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(0(0(1(1(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(0(1(0(1(0(0(1(1(0(1(0(1(0(0(1(1(1(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(1(0(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(1(1(0(1(0(1(1(0(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.34/3.74 11.34/3.74 11.34/3.74 11.34/3.74 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (2) 11.34/3.74 Obligation: 11.34/3.74 Q restricted rewrite system: 11.34/3.74 The TRS R consists of the following rules: 11.34/3.74 11.34/3.74 3(4(5(x1))) -> 4(3(5(x1))) 11.34/3.74 11.34/3.74 Q is empty. 11.34/3.74 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (3) Overlay + Local Confluence (EQUIVALENT) 11.34/3.74 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (4) 11.34/3.74 Obligation: 11.34/3.74 Q restricted rewrite system: 11.34/3.74 The TRS R consists of the following rules: 11.34/3.74 11.34/3.74 3(4(5(x1))) -> 4(3(5(x1))) 11.34/3.74 11.34/3.74 The set Q consists of the following terms: 11.34/3.74 11.34/3.74 3(4(5(x0))) 11.34/3.74 11.34/3.74 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (5) DependencyPairsProof (EQUIVALENT) 11.34/3.74 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (6) 11.34/3.74 Obligation: 11.34/3.74 Q DP problem: 11.34/3.74 The TRS P consists of the following rules: 11.34/3.74 11.34/3.74 3^1(4(5(x1))) -> 3^1(5(x1)) 11.34/3.74 11.34/3.74 The TRS R consists of the following rules: 11.34/3.74 11.34/3.74 3(4(5(x1))) -> 4(3(5(x1))) 11.34/3.74 11.34/3.74 The set Q consists of the following terms: 11.34/3.74 11.34/3.74 3(4(5(x0))) 11.34/3.74 11.34/3.74 We have to consider all minimal (P,Q,R)-chains. 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (7) DependencyGraphProof (EQUIVALENT) 11.34/3.74 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 11.34/3.74 ---------------------------------------- 11.34/3.74 11.34/3.74 (8) 11.34/3.74 TRUE 13.03/5.58 EOF