2.60/1.33 NO 2.60/1.34 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.60/1.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.60/1.34 2.60/1.34 2.60/1.34 Outermost Termination of the given OTRS could be disproven: 2.60/1.34 2.60/1.34 (0) OTRS 2.60/1.34 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.60/1.34 (2) NO 2.60/1.34 2.60/1.34 2.60/1.34 ---------------------------------------- 2.60/1.34 2.60/1.34 (0) 2.60/1.34 Obligation: 2.60/1.34 Term rewrite system R: 2.60/1.34 The TRS R consists of the following rules: 2.60/1.34 2.60/1.34 f(g(x)) -> f(g(g(x))) 2.60/1.34 g(g(g(x))) -> a 2.60/1.34 2.60/1.34 2.60/1.34 2.60/1.34 Outermost Strategy. 2.60/1.34 2.60/1.34 ---------------------------------------- 2.60/1.34 2.60/1.34 (1) OutermostNonTerminationProof (COMPLETE) 2.60/1.34 Term rewrite system R: 2.60/1.34 The TRS R consists of the following rules: 2.60/1.34 2.60/1.34 f(g(x)) -> f(g(g(x))) 2.60/1.34 g(g(g(x))) -> a 2.60/1.34 2.60/1.34 2.60/1.34 2.60/1.34 Outermost Strategy. 2.60/1.34 2.60/1.34 ---------- Loop: ---------- 2.60/1.34 2.60/1.34 f(g(x)) -> f(g(g(x))) with rule f(g(x')) -> f(g(g(x'))) at position [] and matcher [x' / x] 2.60/1.34 2.60/1.34 Now an instance of the first term with Matcher [x / g(x)] occurs in the last term at position []. 2.60/1.34 2.60/1.34 Context: [] 2.60/1.34 2.60/1.34 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.60/1.34 ---------------------------------------- 2.60/1.34 2.60/1.34 (2) 2.60/1.34 NO 2.89/1.36 EOF