2.55/1.21 NO 2.55/1.22 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.55/1.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.55/1.22 2.55/1.22 2.55/1.22 Outermost Termination of the given OTRS could be disproven: 2.55/1.22 2.55/1.22 (0) OTRS 2.55/1.22 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.55/1.22 (2) NO 2.55/1.22 2.55/1.22 2.55/1.22 ---------------------------------------- 2.55/1.22 2.55/1.22 (0) 2.55/1.22 Obligation: 2.55/1.22 Term rewrite system R: 2.55/1.22 The TRS R consists of the following rules: 2.55/1.22 2.55/1.22 U12(tt) -> s(length(L)) 2.55/1.22 zeros -> cons(0) 2.55/1.22 U11(tt) -> U12(tt) 2.55/1.22 length(nil) -> 0 2.55/1.22 length(cons(N)) -> U11(tt) 2.55/1.22 2.55/1.22 2.55/1.22 2.55/1.22 Outermost Strategy. 2.55/1.22 2.55/1.22 ---------------------------------------- 2.55/1.22 2.55/1.22 (1) OutermostNonTerminationProof (COMPLETE) 2.55/1.22 Term rewrite system R: 2.55/1.22 The TRS R consists of the following rules: 2.55/1.22 2.55/1.22 U12(tt) -> s(length(L)) 2.55/1.22 zeros -> cons(0) 2.55/1.22 U11(tt) -> U12(tt) 2.55/1.22 length(nil) -> 0 2.55/1.22 length(cons(N)) -> U11(tt) 2.55/1.22 2.55/1.22 2.55/1.22 2.55/1.22 Outermost Strategy. 2.55/1.22 2.55/1.22 ---------- Loop: ---------- 2.55/1.22 2.55/1.22 U12(tt) -> s(length(U12(tt))) with rule U12(tt) -> s(length(L)) at position [] and matcher [L / U12(tt)] 2.55/1.22 2.55/1.22 Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0]. 2.55/1.22 2.55/1.22 Context: s(length([])) 2.55/1.22 2.55/1.22 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.55/1.22 ---------------------------------------- 2.55/1.22 2.55/1.22 (2) 2.55/1.22 NO 2.65/1.25 EOF