2.46/1.29 NO 2.46/1.30 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.46/1.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.46/1.30 2.46/1.30 2.46/1.30 Outermost Termination of the given OTRS could be disproven: 2.46/1.30 2.46/1.30 (0) OTRS 2.46/1.30 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.46/1.30 (2) NO 2.46/1.30 2.46/1.30 2.46/1.30 ---------------------------------------- 2.46/1.30 2.46/1.30 (0) 2.46/1.30 Obligation: 2.46/1.30 Term rewrite system R: 2.46/1.30 The TRS R consists of the following rules: 2.46/1.30 2.46/1.30 f(g(x), x, y) -> f(y, y, g(y)) 2.46/1.30 g(g(x)) -> g(x) 2.46/1.30 2.46/1.30 2.46/1.30 2.46/1.30 Outermost Strategy. 2.46/1.30 2.46/1.30 ---------------------------------------- 2.46/1.30 2.46/1.30 (1) OutermostNonTerminationProof (COMPLETE) 2.46/1.30 Term rewrite system R: 2.46/1.30 The TRS R consists of the following rules: 2.46/1.30 2.46/1.30 f(g(x), x, y) -> f(y, y, g(y)) 2.46/1.30 g(g(x)) -> g(x) 2.46/1.30 2.46/1.30 2.46/1.30 2.46/1.30 Outermost Strategy. 2.46/1.30 2.46/1.30 ---------- Loop: ---------- 2.46/1.30 2.46/1.30 f(g(g(x')), g(g(x')), g(g(x''))) -> f(g(g(x')), g(x'), g(g(x''))) with rule g(g(x''')) -> g(x''') at position [1] and matcher [x''' / x'] 2.46/1.30 2.46/1.30 f(g(g(x')), g(x'), g(g(x''))) -> f(g(g(x'')), g(g(x'')), g(g(g(x'')))) with rule f(g(x), x, y) -> f(y, y, g(y)) at position [] and matcher [x / g(x'), y / g(g(x''))] 2.46/1.30 2.46/1.30 Now an instance of the first term with Matcher [x' / x'', x'' / g(x'')] occurs in the last term at position []. 2.46/1.30 2.46/1.30 Context: [] 2.46/1.30 2.46/1.30 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.46/1.30 ---------------------------------------- 2.46/1.30 2.46/1.30 (2) 2.46/1.30 NO 2.73/1.33 EOF