8.97/3.17 YES 10.54/3.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 10.54/3.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.54/3.54 10.54/3.54 10.54/3.54 Termination w.r.t. Q of the given QTRS could be proven: 10.54/3.54 10.54/3.54 (0) QTRS 10.54/3.54 (1) QTRS Reverse [EQUIVALENT, 0 ms] 10.54/3.54 (2) QTRS 10.54/3.54 (3) QTRSRRRProof [EQUIVALENT, 142 ms] 10.54/3.54 (4) QTRS 10.54/3.54 (5) AAECC Innermost [EQUIVALENT, 0 ms] 10.54/3.54 (6) QTRS 10.54/3.54 (7) DependencyPairsProof [EQUIVALENT, 1 ms] 10.54/3.54 (8) QDP 10.54/3.54 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 10.54/3.54 (10) TRUE 10.54/3.54 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (0) 10.54/3.54 Obligation: 10.54/3.54 Q restricted rewrite system: 10.54/3.54 The TRS R consists of the following rules: 10.54/3.54 10.54/3.54 0(x1) -> 1(x1) 10.54/3.54 0(0(x1)) -> 0(x1) 10.54/3.54 3(4(5(x1))) -> 4(3(5(x1))) 10.54/3.54 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(1(1(1(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(0(0(0(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(0(1(1(0(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(0(0(0(1(0(0(1(0(1(1(1(1(0(0(0(0(1(1(0(1(0(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(1(0(0(1(1(1(1(0(1(1(0(1(0(0(1(1(0(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(1(0(1(0(1(1(1(0(0(1(1(0(1(0(0(0(1(1(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(1(1(0(0(1(1(1(1(1(0(1(1(1(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(0(0(1(1(1(0(0(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(0(1(1(0(1(0(0(0(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(0(1(1(0(1(0(0(1(1(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(1(0(1(0(0(1(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(0(1(0(1(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(1(0(1(0(0(1(1(1(0(1(1(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(1(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(1(1(1(0(0(0(0(1(0(0(0(1(1(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 10.54/3.54 Q is empty. 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (1) QTRS Reverse (EQUIVALENT) 10.54/3.54 We applied the QTRS Reverse Processor [REVERSE]. 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (2) 10.54/3.54 Obligation: 10.54/3.54 Q restricted rewrite system: 10.54/3.54 The TRS R consists of the following rules: 10.54/3.54 10.54/3.54 0(x1) -> 1(x1) 10.54/3.54 0(0(x1)) -> 0(x1) 10.54/3.54 5(4(3(x1))) -> 5(3(4(x1))) 10.54/3.54 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(0(1(1(1(1(0(1(0(0(1(0(1(1(0(0(1(1(1(1(1(1(1(1(1(1(0(1(0(1(0(0(0(1(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(1(1(1(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(0(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(0(1(1(1(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(1(0(1(0(0(0(0(1(0(1(1(0(1(0(0(1(1(1(0(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(1(0(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(1(1(1(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(0(0(1(1(0(0(0(1(1(1(1(0(0(1(1(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(1(1(0(1(0(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(1(1(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(1(1(0(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(1(0(0(1(1(1(0(0(1(0(1(1(1(0(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(1(0(1(0(0(1(0(1(0(1(1(1(0(0(1(0(0(0(0(0(1(1(1(0(0(1(0(1(0(0(0(0(0(1(0(1(1(0(0(1(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(1(1(1(0(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(0(0(0(1(0(0(0(1(0(1(0(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(1(1(1(1(1(0(0(0(1(0(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 10.54/3.54 Q is empty. 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (3) QTRSRRRProof (EQUIVALENT) 10.54/3.54 Used ordering: 10.54/3.54 Polynomial interpretation [POLO]: 10.54/3.54 10.54/3.54 POL(0(x_1)) = 1 + x_1 10.54/3.54 POL(1(x_1)) = x_1 10.54/3.54 POL(2(x_1)) = 1 + x_1 10.54/3.54 POL(3(x_1)) = x_1 10.54/3.54 POL(4(x_1)) = x_1 10.54/3.54 POL(5(x_1)) = x_1 10.54/3.54 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.54/3.54 10.54/3.54 0(x1) -> 1(x1) 10.54/3.54 0(0(x1)) -> 0(x1) 10.54/3.54 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(0(0(1(1(1(1(0(1(0(0(1(0(1(1(0(0(1(1(1(1(1(1(1(1(1(1(0(1(0(1(0(0(0(1(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(1(1(1(1(1(1(0(0(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(0(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(0(1(1(1(0(0(1(1(1(1(0(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(1(0(1(0(0(0(0(1(0(1(1(0(1(0(0(1(1(1(0(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(1(0(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(1(1(1(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(0(0(1(1(0(0(0(1(1(1(1(0(0(1(1(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(1(1(0(1(0(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(0(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(1(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(1(1(1(0(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(1(1(0(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(1(0(0(1(1(1(0(0(1(0(1(1(1(0(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(1(0(1(0(0(1(0(1(0(1(1(1(0(0(1(0(0(0(0(0(1(1(1(0(0(1(0(1(0(0(0(0(0(1(0(1(1(0(0(1(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(1(1(1(0(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(0(1(1(1(0(1(0(1(0(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(0(0(0(1(0(0(0(1(0(1(0(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(1(1(1(1(1(0(0(0(1(0(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.54/3.54 10.54/3.54 10.54/3.54 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (4) 10.54/3.54 Obligation: 10.54/3.54 Q restricted rewrite system: 10.54/3.54 The TRS R consists of the following rules: 10.54/3.54 10.54/3.54 5(4(3(x1))) -> 5(3(4(x1))) 10.54/3.54 10.54/3.54 Q is empty. 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (5) AAECC Innermost (EQUIVALENT) 10.54/3.54 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 10.54/3.54 10.54/3.54 The TRS R 2 is 10.54/3.54 5(4(3(x1))) -> 5(3(4(x1))) 10.54/3.54 10.54/3.54 The signature Sigma is {5_1} 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (6) 10.54/3.54 Obligation: 10.54/3.54 Q restricted rewrite system: 10.54/3.54 The TRS R consists of the following rules: 10.54/3.54 10.54/3.54 5(4(3(x1))) -> 5(3(4(x1))) 10.54/3.54 10.54/3.54 The set Q consists of the following terms: 10.54/3.54 10.54/3.54 5(4(3(x0))) 10.54/3.54 10.54/3.54 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (7) DependencyPairsProof (EQUIVALENT) 10.54/3.54 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (8) 10.54/3.54 Obligation: 10.54/3.54 Q DP problem: 10.54/3.54 The TRS P consists of the following rules: 10.54/3.54 10.54/3.54 5^1(4(3(x1))) -> 5^1(3(4(x1))) 10.54/3.54 10.54/3.54 The TRS R consists of the following rules: 10.54/3.54 10.54/3.54 5(4(3(x1))) -> 5(3(4(x1))) 10.54/3.54 10.54/3.54 The set Q consists of the following terms: 10.54/3.54 10.54/3.54 5(4(3(x0))) 10.54/3.54 10.54/3.54 We have to consider all minimal (P,Q,R)-chains. 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (9) DependencyGraphProof (EQUIVALENT) 10.54/3.54 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 10.54/3.54 ---------------------------------------- 10.54/3.54 10.54/3.54 (10) 10.54/3.54 TRUE 10.73/3.62 EOF