2.63/1.23 NO 2.63/1.24 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.63/1.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.63/1.24 2.63/1.24 2.63/1.24 Outermost Termination of the given OTRS could be disproven: 2.63/1.24 2.63/1.24 (0) OTRS 2.63/1.24 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.63/1.24 (2) NO 2.63/1.24 2.63/1.24 2.63/1.24 ---------------------------------------- 2.63/1.24 2.63/1.24 (0) 2.63/1.24 Obligation: 2.63/1.24 Term rewrite system R: 2.63/1.24 The TRS R consists of the following rules: 2.63/1.24 2.63/1.24 first(0, X) -> nil 2.63/1.24 first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) 2.63/1.24 from(X) -> cons(X, from(s(X))) 2.63/1.24 2.63/1.24 2.63/1.24 2.63/1.24 Outermost Strategy. 2.63/1.24 2.63/1.24 ---------------------------------------- 2.63/1.24 2.63/1.24 (1) OutermostNonTerminationProof (COMPLETE) 2.63/1.24 Term rewrite system R: 2.63/1.24 The TRS R consists of the following rules: 2.63/1.24 2.63/1.24 first(0, X) -> nil 2.63/1.24 first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) 2.63/1.24 from(X) -> cons(X, from(s(X))) 2.63/1.24 2.63/1.24 2.63/1.24 2.63/1.24 Outermost Strategy. 2.63/1.24 2.63/1.24 ---------- Loop: ---------- 2.63/1.24 2.63/1.24 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 2.63/1.24 2.63/1.24 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 2.63/1.24 2.63/1.24 Context: cons(X, []) 2.63/1.24 2.63/1.24 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.63/1.24 ---------------------------------------- 2.63/1.24 2.63/1.24 (2) 2.63/1.24 NO 2.63/1.27 EOF