2.85/1.24 NO 2.85/1.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.85/1.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.85/1.25 2.85/1.25 2.85/1.25 Outermost Termination of the given OTRS could be disproven: 2.85/1.25 2.85/1.25 (0) OTRS 2.85/1.25 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.85/1.25 (2) NO 2.85/1.25 2.85/1.25 2.85/1.25 ---------------------------------------- 2.85/1.25 2.85/1.25 (0) 2.85/1.25 Obligation: 2.85/1.25 Term rewrite system R: 2.85/1.25 The TRS R consists of the following rules: 2.85/1.25 2.85/1.25 f(g(x, y), x, z) -> f(z, z, z) 2.85/1.25 g(x, y) -> x 2.85/1.25 g(x, y) -> y 2.85/1.25 2.85/1.25 2.85/1.25 2.85/1.25 Outermost Strategy. 2.85/1.25 2.85/1.25 ---------------------------------------- 2.85/1.25 2.85/1.25 (1) OutermostNonTerminationProof (COMPLETE) 2.85/1.25 Term rewrite system R: 2.85/1.25 The TRS R consists of the following rules: 2.85/1.25 2.85/1.25 f(g(x, y), x, z) -> f(z, z, z) 2.85/1.25 g(x, y) -> x 2.85/1.25 g(x, y) -> y 2.85/1.25 2.85/1.25 2.85/1.25 2.85/1.25 Outermost Strategy. 2.85/1.25 2.85/1.25 ---------- Loop: ---------- 2.85/1.25 2.85/1.25 f(g(x', y), g(x', y), g(x', y)) -> f(g(x', y), x', g(x', y)) with rule g(x'', y') -> x'' at position [1] and matcher [x'' / x', y' / y] 2.85/1.25 2.85/1.25 f(g(x', y), x', g(x', y)) -> f(g(x', y), g(x', y), g(x', y)) with rule f(g(x, y'), x, z) -> f(z, z, z) at position [] and matcher [x / x', y' / y, z / g(x', y)] 2.85/1.25 2.85/1.25 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.85/1.25 2.85/1.25 Context: [] 2.85/1.25 2.85/1.25 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.85/1.25 ---------------------------------------- 2.85/1.25 2.85/1.25 (2) 2.85/1.25 NO 2.85/1.28 EOF