3.39/1.64 YES 3.39/1.65 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.39/1.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.39/1.65 3.39/1.65 3.39/1.65 Quasi decreasingness of the given CTRS could be proven: 3.39/1.65 3.39/1.65 (0) CTRS 3.39/1.65 (1) CTRSToQTRSProof [SOUND, 0 ms] 3.39/1.65 (2) QTRS 3.39/1.65 (3) QTRSRRRProof [EQUIVALENT, 28 ms] 3.39/1.65 (4) QTRS 3.39/1.65 (5) RisEmptyProof [EQUIVALENT, 0 ms] 3.39/1.65 (6) YES 3.39/1.65 3.39/1.65 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (0) 3.39/1.65 Obligation: 3.39/1.65 Conditional term rewrite system: 3.39/1.65 The TRS R consists of the following rules: 3.39/1.65 3.39/1.65 a -> c 3.39/1.65 b -> c 3.39/1.65 3.39/1.65 The conditional TRS C consists of the following conditional rules: 3.39/1.65 3.39/1.65 f(x) -> g(y) <= x -> y 3.39/1.65 3.39/1.65 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (1) CTRSToQTRSProof (SOUND) 3.39/1.65 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (2) 3.39/1.65 Obligation: 3.39/1.65 Q restricted rewrite system: 3.39/1.65 The TRS R consists of the following rules: 3.39/1.65 3.39/1.65 f(x) -> U1(x) 3.39/1.65 U1(y) -> g(y) 3.39/1.65 a -> c 3.39/1.65 b -> c 3.39/1.65 3.39/1.65 Q is empty. 3.39/1.65 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (3) QTRSRRRProof (EQUIVALENT) 3.39/1.65 Used ordering: 3.39/1.65 Knuth-Bendix order [KBO] with precedence:f_1 > U1_1 > g_1 > b > a > c 3.39/1.65 3.39/1.65 and weight map: 3.39/1.65 3.39/1.65 a=1 3.39/1.65 c=1 3.39/1.65 b=1 3.39/1.65 f_1=1 3.39/1.65 U1_1=1 3.39/1.65 g_1=1 3.39/1.65 3.39/1.65 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.39/1.65 3.39/1.65 f(x) -> U1(x) 3.39/1.65 U1(y) -> g(y) 3.39/1.65 a -> c 3.39/1.65 b -> c 3.39/1.65 3.39/1.65 3.39/1.65 3.39/1.65 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (4) 3.39/1.65 Obligation: 3.39/1.65 Q restricted rewrite system: 3.39/1.65 R is empty. 3.39/1.65 Q is empty. 3.39/1.65 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (5) RisEmptyProof (EQUIVALENT) 3.39/1.65 The TRS R is empty. Hence, termination is trivially proven. 3.39/1.65 ---------------------------------------- 3.39/1.65 3.39/1.65 (6) 3.39/1.65 YES 3.39/1.68 EOF