2.45/1.24 NO 2.45/1.24 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.45/1.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.45/1.24 2.45/1.24 2.45/1.24 Outermost Termination of the given OTRS could be disproven: 2.45/1.24 2.45/1.24 (0) OTRS 2.45/1.24 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.45/1.24 (2) NO 2.45/1.24 2.45/1.24 2.45/1.24 ---------------------------------------- 2.45/1.24 2.45/1.24 (0) 2.45/1.24 Obligation: 2.45/1.24 Term rewrite system R: 2.45/1.24 The TRS R consists of the following rules: 2.45/1.24 2.45/1.24 sel(0, cons) -> X 2.45/1.24 sel(s, cons) -> sel(X, Z) 2.45/1.24 dbl(0) -> 0 2.45/1.24 dbl(s) -> s 2.45/1.24 dbls(nil) -> nil 2.45/1.24 dbls(cons) -> cons 2.45/1.24 indx(nil) -> nil 2.45/1.24 indx(cons) -> cons 2.45/1.24 from -> cons 2.45/1.24 2.45/1.24 2.45/1.24 2.45/1.24 Outermost Strategy. 2.45/1.24 2.45/1.24 ---------------------------------------- 2.45/1.24 2.45/1.24 (1) OutermostNonTerminationProof (COMPLETE) 2.45/1.24 Term rewrite system R: 2.45/1.24 The TRS R consists of the following rules: 2.45/1.24 2.45/1.24 sel(0, cons) -> X 2.45/1.24 sel(s, cons) -> sel(X, Z) 2.45/1.24 dbl(0) -> 0 2.45/1.24 dbl(s) -> s 2.45/1.24 dbls(nil) -> nil 2.45/1.24 dbls(cons) -> cons 2.45/1.24 indx(nil) -> nil 2.45/1.24 indx(cons) -> cons 2.45/1.24 from -> cons 2.45/1.24 2.45/1.24 2.45/1.24 2.45/1.24 Outermost Strategy. 2.45/1.24 2.45/1.24 ---------- Loop: ---------- 2.45/1.24 2.45/1.24 sel(0, cons) -> sel(0, cons) with rule sel(0, cons) -> X at position [] and matcher [X / sel(0, cons)] 2.45/1.24 2.45/1.24 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.45/1.24 2.45/1.24 Context: [] 2.45/1.24 2.45/1.24 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.45/1.24 ---------------------------------------- 2.45/1.24 2.45/1.24 (2) 2.45/1.24 NO 2.45/1.27 EOF