2.48/1.43 NO 2.73/1.44 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.73/1.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.73/1.44 2.73/1.44 2.73/1.44 Outermost Termination of the given OTRS could be disproven: 2.73/1.44 2.73/1.44 (0) OTRS 2.73/1.44 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.73/1.44 (2) NO 2.73/1.44 2.73/1.44 2.73/1.44 ---------------------------------------- 2.73/1.44 2.73/1.44 (0) 2.73/1.44 Obligation: 2.73/1.44 Term rewrite system R: 2.73/1.44 The TRS R consists of the following rules: 2.73/1.44 2.73/1.44 h(X) -> g(X) 2.73/1.44 g(a) -> f(b) 2.73/1.44 f(X) -> h(a) 2.73/1.44 a -> b 2.73/1.44 2.73/1.44 2.73/1.44 2.73/1.44 Outermost Strategy. 2.73/1.44 2.73/1.44 ---------------------------------------- 2.73/1.44 2.73/1.44 (1) OutermostNonTerminationProof (COMPLETE) 2.73/1.44 Term rewrite system R: 2.73/1.44 The TRS R consists of the following rules: 2.73/1.44 2.73/1.44 h(X) -> g(X) 2.73/1.44 g(a) -> f(b) 2.73/1.44 f(X) -> h(a) 2.73/1.44 a -> b 2.73/1.44 2.73/1.44 2.73/1.44 2.73/1.44 Outermost Strategy. 2.73/1.44 2.73/1.44 ---------- Loop: ---------- 2.73/1.44 2.73/1.44 g(a) -> f(b) with rule g(a) -> f(b) at position [] and matcher [ ] 2.73/1.44 2.73/1.44 f(b) -> h(a) with rule f(X) -> h(a) at position [] and matcher [X / b] 2.73/1.44 2.73/1.44 h(a) -> g(a) with rule h(X) -> g(X) at position [] and matcher [X / a] 2.73/1.44 2.73/1.44 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.73/1.44 2.73/1.44 Context: [] 2.73/1.44 2.73/1.44 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.73/1.44 ---------------------------------------- 2.73/1.44 2.73/1.44 (2) 2.73/1.44 NO 2.75/1.48 EOF