2.68/1.27 NO 2.68/1.27 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.68/1.27 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.68/1.27 2.68/1.27 2.68/1.27 Outermost Termination of the given OTRS could be disproven: 2.68/1.27 2.68/1.27 (0) OTRS 2.68/1.27 (1) OutermostNonTerminationProof [COMPLETE, 78 ms] 2.68/1.27 (2) NO 2.68/1.27 2.68/1.27 2.68/1.27 ---------------------------------------- 2.68/1.27 2.68/1.27 (0) 2.68/1.27 Obligation: 2.68/1.27 Term rewrite system R: 2.68/1.27 The TRS R consists of the following rules: 2.68/1.27 2.68/1.27 g(X) -> h(activate(X)) 2.68/1.27 c -> d 2.68/1.27 h(n__d) -> g(n__c) 2.68/1.27 d -> n__d 2.68/1.27 c -> n__c 2.68/1.27 activate(n__d) -> d 2.68/1.27 activate(n__c) -> c 2.68/1.27 activate(X) -> X 2.68/1.27 2.68/1.27 2.68/1.27 2.68/1.27 Outermost Strategy. 2.68/1.27 2.68/1.27 ---------------------------------------- 2.68/1.27 2.68/1.27 (1) OutermostNonTerminationProof (COMPLETE) 2.68/1.27 Term rewrite system R: 2.68/1.27 The TRS R consists of the following rules: 2.68/1.27 2.68/1.27 g(X) -> h(activate(X)) 2.68/1.27 c -> d 2.68/1.27 h(n__d) -> g(n__c) 2.68/1.27 d -> n__d 2.68/1.27 c -> n__c 2.68/1.27 activate(n__d) -> d 2.68/1.27 activate(n__c) -> c 2.68/1.27 activate(X) -> X 2.68/1.27 2.68/1.27 2.68/1.27 2.68/1.27 Outermost Strategy. 2.68/1.27 2.68/1.27 ---------- Loop: ---------- 2.68/1.27 2.68/1.27 h(activate(n__c)) -> h(c) with rule activate(n__c) -> c at position [0] and matcher [ ] 2.68/1.27 2.68/1.27 h(c) -> h(d) with rule c -> d at position [0] and matcher [ ] 2.68/1.27 2.68/1.27 h(d) -> h(n__d) with rule d -> n__d at position [0] and matcher [ ] 2.68/1.27 2.68/1.27 h(n__d) -> g(n__c) with rule h(n__d) -> g(n__c) at position [] and matcher [ ] 2.68/1.27 2.68/1.27 g(n__c) -> h(activate(n__c)) with rule g(X) -> h(activate(X)) at position [] and matcher [X / n__c] 2.68/1.27 2.68/1.27 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.68/1.27 2.68/1.27 Context: [] 2.68/1.27 2.68/1.27 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.68/1.27 ---------------------------------------- 2.68/1.27 2.68/1.27 (2) 2.68/1.27 NO 2.88/1.30 EOF