2.62/1.32 NO 2.62/1.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.62/1.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.62/1.32 2.62/1.32 2.62/1.32 Outermost Termination of the given OTRS could be disproven: 2.62/1.32 2.62/1.32 (0) OTRS 2.62/1.32 (1) OutermostNonTerminationProof [COMPLETE, 51 ms] 2.62/1.32 (2) NO 2.62/1.32 2.62/1.32 2.62/1.32 ---------------------------------------- 2.62/1.32 2.62/1.32 (0) 2.62/1.32 Obligation: 2.62/1.32 Term rewrite system R: 2.62/1.32 The TRS R consists of the following rules: 2.62/1.32 2.62/1.32 f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) 2.62/1.32 g(s(x)) -> s(g(x)) 2.62/1.32 g(0) -> 0 2.62/1.32 2.62/1.32 2.62/1.32 2.62/1.32 Outermost Strategy. 2.62/1.32 2.62/1.32 ---------------------------------------- 2.62/1.32 2.62/1.32 (1) OutermostNonTerminationProof (COMPLETE) 2.62/1.32 Term rewrite system R: 2.62/1.32 The TRS R consists of the following rules: 2.62/1.32 2.62/1.32 f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) 2.62/1.32 g(s(x)) -> s(g(x)) 2.62/1.32 g(0) -> 0 2.62/1.32 2.62/1.32 2.62/1.32 2.62/1.32 Outermost Strategy. 2.62/1.32 2.62/1.32 ---------- Loop: ---------- 2.62/1.32 2.62/1.32 f(g(s(0)), g(s(0)), g(s(0))) -> f(g(s(0)), s(g(0)), g(s(0))) with rule g(s(x')) -> s(g(x')) at position [1] and matcher [x' / 0] 2.62/1.32 2.62/1.32 f(g(s(0)), s(g(0)), g(s(0))) -> f(g(s(0)), s(0), g(s(0))) with rule g(0) -> 0 at position [1,0] and matcher [ ] 2.62/1.32 2.62/1.32 f(g(s(0)), s(0), g(s(0))) -> f(g(s(0)), g(s(0)), g(s(0))) with rule f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) at position [] and matcher [x / s(0), y / g(s(0))] 2.62/1.32 2.62/1.32 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.62/1.32 2.62/1.32 Context: [] 2.62/1.32 2.62/1.32 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.62/1.32 ---------------------------------------- 2.62/1.32 2.62/1.32 (2) 2.62/1.32 NO 2.93/1.35 EOF