2.60/1.31 NO 2.60/1.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.60/1.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.60/1.32 2.60/1.32 2.60/1.32 Outermost Termination of the given OTRS could be disproven: 2.60/1.32 2.60/1.32 (0) OTRS 2.60/1.32 (1) OutermostNonTerminationProof [COMPLETE, 58 ms] 2.60/1.32 (2) NO 2.60/1.32 2.60/1.32 2.60/1.32 ---------------------------------------- 2.60/1.32 2.60/1.32 (0) 2.60/1.32 Obligation: 2.60/1.32 Term rewrite system R: 2.60/1.32 The TRS R consists of the following rules: 2.60/1.32 2.60/1.32 f(n__b, X, n__c) -> f(X, c, X) 2.60/1.32 c -> b 2.60/1.32 b -> n__b 2.60/1.32 c -> n__c 2.60/1.32 activate(n__b) -> b 2.60/1.32 activate(n__c) -> c 2.60/1.32 activate(X) -> X 2.60/1.32 2.60/1.32 2.60/1.32 2.60/1.32 Outermost Strategy. 2.60/1.32 2.60/1.32 ---------------------------------------- 2.60/1.32 2.60/1.32 (1) OutermostNonTerminationProof (COMPLETE) 2.60/1.32 Term rewrite system R: 2.60/1.32 The TRS R consists of the following rules: 2.60/1.32 2.60/1.32 f(n__b, X, n__c) -> f(X, c, X) 2.60/1.32 c -> b 2.60/1.32 b -> n__b 2.60/1.32 c -> n__c 2.60/1.32 activate(n__b) -> b 2.60/1.32 activate(n__c) -> c 2.60/1.32 activate(X) -> X 2.60/1.32 2.60/1.32 2.60/1.32 2.60/1.32 Outermost Strategy. 2.60/1.32 2.60/1.32 ---------- Loop: ---------- 2.60/1.32 2.60/1.32 f(c, c, c) -> f(c, c, n__c) with rule c -> n__c at position [2] and matcher [ ] 2.60/1.32 2.60/1.32 f(c, c, n__c) -> f(b, c, n__c) with rule c -> b at position [0] and matcher [ ] 2.60/1.32 2.60/1.32 f(b, c, n__c) -> f(n__b, c, n__c) with rule b -> n__b at position [0] and matcher [ ] 2.60/1.32 2.60/1.32 f(n__b, c, n__c) -> f(c, c, c) with rule f(n__b, X, n__c) -> f(X, c, X) at position [] and matcher [X / c] 2.60/1.32 2.60/1.32 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.60/1.32 2.60/1.32 Context: [] 2.60/1.32 2.60/1.32 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.60/1.32 ---------------------------------------- 2.60/1.32 2.60/1.32 (2) 2.60/1.32 NO 2.94/1.36 EOF