2.57/1.24 NO 2.57/1.24 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.57/1.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.57/1.24 2.57/1.24 2.57/1.24 Outermost Termination of the given OTRS could be disproven: 2.57/1.24 2.57/1.24 (0) OTRS 2.57/1.24 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.57/1.24 (2) NO 2.57/1.24 2.57/1.24 2.57/1.24 ---------------------------------------- 2.57/1.24 2.57/1.24 (0) 2.57/1.24 Obligation: 2.57/1.24 Term rewrite system R: 2.57/1.24 The TRS R consists of the following rules: 2.57/1.24 2.57/1.24 sel(s(X), cons(Y)) -> sel(X, Z) 2.57/1.24 sel1(s(X), cons(Y)) -> sel1(X, Z) 2.57/1.24 first1(s(X), cons(Y)) -> cons1(quote, first1(X, Z)) 2.57/1.24 quote -> sel1(X, Z) 2.57/1.24 quote1 -> first1(X, Z) 2.57/1.24 sel(0, cons(X)) -> X 2.57/1.24 first(0, Z) -> nil 2.57/1.24 first(s(X), cons(Y)) -> cons(Y) 2.57/1.24 from(X) -> cons(X) 2.57/1.24 sel1(0, cons(X)) -> quote 2.57/1.24 first1(0, Z) -> nil1 2.57/1.24 quote -> 01 2.57/1.24 quote1 -> cons1(quote, quote1) 2.57/1.24 quote1 -> nil1 2.57/1.24 quote -> s1(quote) 2.57/1.24 unquote(01) -> 0 2.57/1.24 unquote(s1(X)) -> s(unquote(X)) 2.57/1.24 unquote1(nil1) -> nil 2.57/1.24 unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)) 2.57/1.24 fcons(X, Z) -> cons(X) 2.57/1.24 2.57/1.24 2.57/1.24 2.57/1.24 Outermost Strategy. 2.57/1.24 2.57/1.24 ---------------------------------------- 2.57/1.24 2.57/1.24 (1) OutermostNonTerminationProof (COMPLETE) 2.57/1.24 Term rewrite system R: 2.57/1.24 The TRS R consists of the following rules: 2.57/1.24 2.57/1.24 sel(s(X), cons(Y)) -> sel(X, Z) 2.57/1.24 sel1(s(X), cons(Y)) -> sel1(X, Z) 2.57/1.24 first1(s(X), cons(Y)) -> cons1(quote, first1(X, Z)) 2.57/1.24 quote -> sel1(X, Z) 2.57/1.24 quote1 -> first1(X, Z) 2.57/1.24 sel(0, cons(X)) -> X 2.57/1.24 first(0, Z) -> nil 2.57/1.24 first(s(X), cons(Y)) -> cons(Y) 2.57/1.24 from(X) -> cons(X) 2.57/1.24 sel1(0, cons(X)) -> quote 2.57/1.24 first1(0, Z) -> nil1 2.57/1.24 quote -> 01 2.57/1.24 quote1 -> cons1(quote, quote1) 2.57/1.24 quote1 -> nil1 2.57/1.24 quote -> s1(quote) 2.57/1.24 unquote(01) -> 0 2.57/1.24 unquote(s1(X)) -> s(unquote(X)) 2.57/1.24 unquote1(nil1) -> nil 2.57/1.24 unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)) 2.57/1.24 fcons(X, Z) -> cons(X) 2.57/1.24 2.57/1.24 2.57/1.24 2.57/1.24 Outermost Strategy. 2.57/1.24 2.57/1.24 ---------- Loop: ---------- 2.57/1.24 2.57/1.24 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))] 2.57/1.24 2.57/1.24 Now an instance of the first term with Matcher [ ] occurs in the last term at position [1]. 2.57/1.24 2.57/1.24 Context: sel(X, []) 2.57/1.24 2.57/1.24 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.57/1.24 ---------------------------------------- 2.57/1.24 2.57/1.24 (2) 2.57/1.24 NO 2.57/1.27 EOF