2.32/1.29 NO 2.32/1.30 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.32/1.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.32/1.30 2.32/1.30 2.32/1.30 Outermost Termination of the given OTRS could be disproven: 2.32/1.30 2.32/1.30 (0) OTRS 2.32/1.30 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.32/1.30 (2) NO 2.32/1.30 2.32/1.30 2.32/1.30 ---------------------------------------- 2.32/1.30 2.32/1.30 (0) 2.32/1.30 Obligation: 2.32/1.30 Term rewrite system R: 2.32/1.30 The TRS R consists of the following rules: 2.32/1.30 2.32/1.30 sel(s(X), cons(Y)) -> sel(X, Z) 2.32/1.30 f(X) -> cons(X) 2.32/1.30 g(0) -> s(0) 2.32/1.30 g(s(X)) -> s(s(g(X))) 2.32/1.30 sel(0, cons(X)) -> X 2.32/1.30 2.32/1.30 2.32/1.30 2.32/1.30 Outermost Strategy. 2.32/1.30 2.32/1.30 ---------------------------------------- 2.32/1.30 2.32/1.30 (1) OutermostNonTerminationProof (COMPLETE) 2.32/1.30 Term rewrite system R: 2.32/1.30 The TRS R consists of the following rules: 2.32/1.30 2.32/1.30 sel(s(X), cons(Y)) -> sel(X, Z) 2.32/1.30 f(X) -> cons(X) 2.32/1.30 g(0) -> s(0) 2.32/1.30 g(s(X)) -> s(s(g(X))) 2.32/1.30 sel(0, cons(X)) -> X 2.32/1.30 2.32/1.30 2.32/1.30 2.32/1.30 Outermost Strategy. 2.32/1.30 2.32/1.30 ---------- Loop: ---------- 2.32/1.30 2.32/1.30 sel(s(X), cons(Y)) -> sel(X, sel(s(X), cons(Y))) with rule sel(s(X''), cons(Y'')) -> sel(X'', Z) at position [] and matcher [X'' / X, Y'' / Y, Z / sel(s(X), cons(Y))] 2.32/1.30 2.32/1.30 Now an instance of the first term with Matcher [ ] occurs in the last term at position [1]. 2.32/1.30 2.32/1.30 Context: sel(X, []) 2.32/1.30 2.32/1.30 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.32/1.30 ---------------------------------------- 2.32/1.30 2.32/1.30 (2) 2.32/1.30 NO 2.54/1.33 EOF