2.66/1.21 NO 2.75/1.22 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.75/1.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.75/1.22 2.75/1.22 2.75/1.22 Outermost Termination of the given OTRS could be disproven: 2.75/1.22 2.75/1.22 (0) OTRS 2.75/1.22 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.75/1.22 (2) NO 2.75/1.22 2.75/1.22 2.75/1.22 ---------------------------------------- 2.75/1.22 2.75/1.22 (0) 2.75/1.22 Obligation: 2.75/1.22 Term rewrite system R: 2.75/1.22 The TRS R consists of the following rules: 2.75/1.22 2.75/1.22 from(X) -> cons(X, from(s(X))) 2.75/1.22 length(nil) -> 0 2.75/1.22 length(cons(X, Y)) -> s(length1(Y)) 2.75/1.22 length1(X) -> length(X) 2.75/1.22 2.75/1.22 2.75/1.22 2.75/1.22 Outermost Strategy. 2.75/1.22 2.75/1.22 ---------------------------------------- 2.75/1.22 2.75/1.22 (1) OutermostNonTerminationProof (COMPLETE) 2.75/1.22 Term rewrite system R: 2.75/1.22 The TRS R consists of the following rules: 2.75/1.22 2.75/1.22 from(X) -> cons(X, from(s(X))) 2.75/1.22 length(nil) -> 0 2.75/1.22 length(cons(X, Y)) -> s(length1(Y)) 2.75/1.22 length1(X) -> length(X) 2.75/1.22 2.75/1.22 2.75/1.22 2.75/1.22 Outermost Strategy. 2.75/1.22 2.75/1.22 ---------- Loop: ---------- 2.75/1.22 2.75/1.22 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 2.75/1.22 2.75/1.22 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 2.75/1.22 2.75/1.22 Context: cons(X, []) 2.75/1.22 2.75/1.22 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.75/1.22 ---------------------------------------- 2.75/1.22 2.75/1.22 (2) 2.75/1.22 NO 2.79/1.25 EOF