2.66/1.22 NO 2.66/1.23 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.66/1.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.66/1.23 2.66/1.23 2.66/1.23 Outermost Termination of the given OTRS could be disproven: 2.66/1.23 2.66/1.23 (0) OTRS 2.66/1.23 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.66/1.23 (2) NO 2.66/1.23 2.66/1.23 2.66/1.23 ---------------------------------------- 2.66/1.23 2.66/1.23 (0) 2.66/1.23 Obligation: 2.66/1.23 Term rewrite system R: 2.66/1.23 The TRS R consists of the following rules: 2.66/1.23 2.66/1.23 g(b) -> g(f(f(f(f(b))))) 2.66/1.23 f(f(b)) -> b 2.66/1.23 f(b) -> b 2.66/1.23 g(f(b)) -> c 2.66/1.23 2.66/1.23 2.66/1.23 2.66/1.23 Outermost Strategy. 2.66/1.23 2.66/1.23 ---------------------------------------- 2.66/1.23 2.66/1.23 (1) OutermostNonTerminationProof (COMPLETE) 2.66/1.23 Term rewrite system R: 2.66/1.23 The TRS R consists of the following rules: 2.66/1.23 2.66/1.23 g(b) -> g(f(f(f(f(b))))) 2.66/1.23 f(f(b)) -> b 2.66/1.23 f(b) -> b 2.66/1.23 g(f(b)) -> c 2.66/1.23 2.66/1.23 2.66/1.23 2.66/1.23 Outermost Strategy. 2.66/1.23 2.66/1.23 ---------- Loop: ---------- 2.66/1.23 2.66/1.23 g(f(f(f(f(b))))) -> g(f(f(b))) with rule f(f(b)) -> b at position [0,0,0] and matcher [ ] 2.66/1.23 2.66/1.23 g(f(f(b))) -> g(b) with rule f(f(b)) -> b at position [0] and matcher [ ] 2.66/1.23 2.66/1.23 g(b) -> g(f(f(f(f(b))))) with rule g(b) -> g(f(f(f(f(b))))) at position [] and matcher [ ] 2.66/1.23 2.66/1.23 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.66/1.23 2.66/1.23 Context: [] 2.66/1.23 2.66/1.23 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.66/1.23 ---------------------------------------- 2.66/1.23 2.66/1.23 (2) 2.66/1.23 NO 2.69/1.27 EOF