2.63/1.22 NO 2.63/1.22 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.63/1.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.63/1.22 2.63/1.22 2.63/1.22 Outermost Termination of the given OTRS could be disproven: 2.63/1.22 2.63/1.22 (0) OTRS 2.63/1.22 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.63/1.22 (2) NO 2.63/1.22 2.63/1.22 2.63/1.22 ---------------------------------------- 2.63/1.22 2.63/1.22 (0) 2.63/1.22 Obligation: 2.63/1.22 Term rewrite system R: 2.63/1.22 The TRS R consists of the following rules: 2.63/1.22 2.63/1.22 splitAt(s(N), cons(X)) -> u(splitAt(N, XS)) 2.63/1.22 u(pair(YS, ZS)) -> pair(cons(X), ZS) 2.63/1.22 tail(cons(N)) -> XS 2.63/1.22 natsFrom(N) -> cons(N) 2.63/1.22 fst(pair(XS, YS)) -> XS 2.63/1.22 snd(pair(XS, YS)) -> YS 2.63/1.22 splitAt(0, XS) -> pair(nil, XS) 2.63/1.22 head(cons(N)) -> N 2.63/1.22 sel(N, XS) -> head(afterNth(N, XS)) 2.63/1.22 take(N, XS) -> fst(splitAt(N, XS)) 2.63/1.22 afterNth(N, XS) -> snd(splitAt(N, XS)) 2.63/1.22 2.63/1.22 2.63/1.22 2.63/1.22 Outermost Strategy. 2.63/1.22 2.63/1.22 ---------------------------------------- 2.63/1.22 2.63/1.22 (1) OutermostNonTerminationProof (COMPLETE) 2.63/1.22 Term rewrite system R: 2.63/1.22 The TRS R consists of the following rules: 2.63/1.22 2.63/1.22 splitAt(s(N), cons(X)) -> u(splitAt(N, XS)) 2.63/1.22 u(pair(YS, ZS)) -> pair(cons(X), ZS) 2.63/1.22 tail(cons(N)) -> XS 2.63/1.22 natsFrom(N) -> cons(N) 2.63/1.22 fst(pair(XS, YS)) -> XS 2.63/1.22 snd(pair(XS, YS)) -> YS 2.63/1.22 splitAt(0, XS) -> pair(nil, XS) 2.63/1.22 head(cons(N)) -> N 2.63/1.22 sel(N, XS) -> head(afterNth(N, XS)) 2.63/1.22 take(N, XS) -> fst(splitAt(N, XS)) 2.63/1.22 afterNth(N, XS) -> snd(splitAt(N, XS)) 2.63/1.22 2.63/1.22 2.63/1.22 2.63/1.22 Outermost Strategy. 2.63/1.22 2.63/1.22 ---------- Loop: ---------- 2.63/1.22 2.63/1.22 splitAt(s(N), cons(X)) -> u(splitAt(N, splitAt(s(N), cons(X)))) with rule splitAt(s(N''), cons(X'')) -> u(splitAt(N'', XS)) at position [] and matcher [N'' / N, X'' / X, XS / splitAt(s(N), cons(X))] 2.63/1.22 2.63/1.22 Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,1]. 2.63/1.22 2.63/1.22 Context: u(splitAt(N, [])) 2.63/1.22 2.63/1.22 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.63/1.22 ---------------------------------------- 2.63/1.22 2.63/1.22 (2) 2.63/1.22 NO 2.63/1.24 EOF