2.52/1.29 NO 2.52/1.30 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.52/1.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.52/1.30 2.52/1.30 2.52/1.30 Outermost Termination of the given OTRS could be disproven: 2.52/1.30 2.52/1.30 (0) OTRS 2.52/1.30 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.52/1.30 (2) NO 2.52/1.30 2.52/1.30 2.52/1.30 ---------------------------------------- 2.52/1.30 2.52/1.30 (0) 2.52/1.30 Obligation: 2.52/1.30 Term rewrite system R: 2.52/1.30 The TRS R consists of the following rules: 2.52/1.30 2.52/1.30 sel(s(N), cons(X)) -> sel(N, XS) 2.52/1.30 fib(N) -> sel(N, fib1(s(0), s(0))) 2.52/1.30 fib1(X, Y) -> cons(X) 2.52/1.30 add(0, X) -> X 2.52/1.30 add(s(X), Y) -> s(add(X, Y)) 2.52/1.30 sel(0, cons(X)) -> X 2.52/1.30 2.52/1.30 2.52/1.30 2.52/1.30 Outermost Strategy. 2.52/1.30 2.52/1.30 ---------------------------------------- 2.52/1.30 2.52/1.30 (1) OutermostNonTerminationProof (COMPLETE) 2.52/1.30 Term rewrite system R: 2.52/1.30 The TRS R consists of the following rules: 2.52/1.30 2.52/1.30 sel(s(N), cons(X)) -> sel(N, XS) 2.52/1.30 fib(N) -> sel(N, fib1(s(0), s(0))) 2.52/1.30 fib1(X, Y) -> cons(X) 2.52/1.30 add(0, X) -> X 2.52/1.30 add(s(X), Y) -> s(add(X, Y)) 2.52/1.30 sel(0, cons(X)) -> X 2.52/1.30 2.52/1.30 2.52/1.30 2.52/1.30 Outermost Strategy. 2.52/1.30 2.52/1.30 ---------- Loop: ---------- 2.52/1.30 2.52/1.30 sel(s(N), cons(X)) -> sel(N, sel(s(N), cons(X))) with rule sel(s(N''), cons(X'')) -> sel(N'', XS) at position [] and matcher [N'' / N, X'' / X, XS / sel(s(N), cons(X))] 2.52/1.30 2.52/1.30 Now an instance of the first term with Matcher [ ] occurs in the last term at position [1]. 2.52/1.30 2.52/1.30 Context: sel(N, []) 2.52/1.30 2.52/1.30 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.52/1.30 ---------------------------------------- 2.52/1.30 2.52/1.30 (2) 2.52/1.30 NO 2.55/1.31 EOF