2.36/1.25 NO 2.36/1.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.36/1.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.36/1.25 2.36/1.25 2.36/1.25 Outermost Termination of the given OTRS could be disproven: 2.36/1.25 2.36/1.25 (0) OTRS 2.36/1.25 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.36/1.25 (2) NO 2.36/1.25 2.36/1.25 2.36/1.25 ---------------------------------------- 2.36/1.25 2.36/1.25 (0) 2.36/1.25 Obligation: 2.36/1.25 Term rewrite system R: 2.36/1.25 The TRS R consists of the following rules: 2.36/1.25 2.36/1.25 f(X) -> g(n__h(f(X))) 2.36/1.25 h(X) -> n__h(X) 2.36/1.25 activate(n__h(X)) -> h(X) 2.36/1.25 activate(X) -> X 2.36/1.25 2.36/1.25 2.36/1.25 2.36/1.25 Outermost Strategy. 2.36/1.25 2.36/1.25 ---------------------------------------- 2.36/1.25 2.36/1.25 (1) OutermostNonTerminationProof (COMPLETE) 2.36/1.25 Term rewrite system R: 2.36/1.25 The TRS R consists of the following rules: 2.36/1.25 2.36/1.25 f(X) -> g(n__h(f(X))) 2.36/1.25 h(X) -> n__h(X) 2.36/1.25 activate(n__h(X)) -> h(X) 2.36/1.25 activate(X) -> X 2.36/1.25 2.36/1.25 2.36/1.25 2.36/1.25 Outermost Strategy. 2.36/1.25 2.36/1.25 ---------- Loop: ---------- 2.36/1.25 2.36/1.25 f(X) -> g(n__h(f(X))) with rule f(X') -> g(n__h(f(X'))) at position [] and matcher [X' / X] 2.36/1.25 2.36/1.25 Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0]. 2.36/1.25 2.36/1.25 Context: g(n__h([])) 2.36/1.25 2.36/1.25 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.36/1.25 ---------------------------------------- 2.36/1.25 2.36/1.25 (2) 2.36/1.25 NO 2.58/1.29 EOF