3.43/1.62 YES 3.43/1.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.43/1.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.43/1.63 3.43/1.63 3.43/1.63 Quasi decreasingness of the given CTRS could be proven: 3.43/1.63 3.43/1.63 (0) CTRS 3.43/1.63 (1) CTRSToQTRSProof [SOUND, 0 ms] 3.43/1.63 (2) QTRS 3.43/1.63 (3) QTRSRRRProof [EQUIVALENT, 0 ms] 3.43/1.63 (4) QTRS 3.43/1.63 (5) RisEmptyProof [EQUIVALENT, 2 ms] 3.43/1.63 (6) YES 3.43/1.63 3.43/1.63 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (0) 3.43/1.63 Obligation: 3.43/1.63 Conditional term rewrite system: 3.43/1.63 The TRS R consists of the following rules: 3.43/1.63 3.43/1.63 a -> b 3.43/1.63 3.43/1.63 The conditional TRS C consists of the following conditional rules: 3.43/1.63 3.43/1.63 c -> d <= a -> a 3.43/1.63 3.43/1.63 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (1) CTRSToQTRSProof (SOUND) 3.43/1.63 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (2) 3.43/1.63 Obligation: 3.43/1.63 Q restricted rewrite system: 3.43/1.63 The TRS R consists of the following rules: 3.43/1.63 3.43/1.63 c -> U1(a) 3.43/1.63 U1(a) -> d 3.43/1.63 a -> b 3.43/1.63 3.43/1.63 Q is empty. 3.43/1.63 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (3) QTRSRRRProof (EQUIVALENT) 3.43/1.63 Used ordering: 3.43/1.63 Knuth-Bendix order [KBO] with precedence:a > b > c > U1_1 > d 3.43/1.63 3.43/1.63 and weight map: 3.43/1.63 3.43/1.63 c=2 3.43/1.63 a=1 3.43/1.63 d=2 3.43/1.63 b=1 3.43/1.63 U1_1=1 3.43/1.63 3.43/1.63 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.43/1.63 3.43/1.63 c -> U1(a) 3.43/1.63 U1(a) -> d 3.43/1.63 a -> b 3.43/1.63 3.43/1.63 3.43/1.63 3.43/1.63 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (4) 3.43/1.63 Obligation: 3.43/1.63 Q restricted rewrite system: 3.43/1.63 R is empty. 3.43/1.63 Q is empty. 3.43/1.63 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (5) RisEmptyProof (EQUIVALENT) 3.43/1.63 The TRS R is empty. Hence, termination is trivially proven. 3.43/1.63 ---------------------------------------- 3.43/1.63 3.43/1.63 (6) 3.43/1.63 YES 3.43/1.65 EOF