2.52/1.42 NO 2.52/1.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.52/1.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.52/1.42 2.52/1.42 2.52/1.42 Outermost Termination of the given OTRS could be disproven: 2.52/1.42 2.52/1.42 (0) OTRS 2.52/1.42 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.52/1.42 (2) NO 2.52/1.42 2.52/1.42 2.52/1.42 ---------------------------------------- 2.52/1.42 2.52/1.42 (0) 2.52/1.42 Obligation: 2.52/1.42 Term rewrite system R: 2.52/1.42 The TRS R consists of the following rules: 2.52/1.42 2.52/1.42 zeros -> cons(0, n__zeros) 2.52/1.42 and(tt, X) -> activate(X) 2.52/1.42 length(nil) -> 0 2.52/1.42 length(cons(N, L)) -> s(length(activate(L))) 2.52/1.42 take(0, IL) -> nil 2.52/1.42 take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL))) 2.52/1.42 zeros -> n__zeros 2.52/1.42 take(X1, X2) -> n__take(X1, X2) 2.52/1.42 activate(n__zeros) -> zeros 2.52/1.42 activate(n__take(X1, X2)) -> take(X1, X2) 2.52/1.42 activate(X) -> X 2.52/1.42 2.52/1.42 2.52/1.42 2.52/1.42 Outermost Strategy. 2.52/1.42 2.52/1.42 ---------------------------------------- 2.52/1.42 2.52/1.42 (1) OutermostNonTerminationProof (COMPLETE) 2.52/1.42 Term rewrite system R: 2.52/1.42 The TRS R consists of the following rules: 2.52/1.42 2.52/1.42 zeros -> cons(0, n__zeros) 2.52/1.42 and(tt, X) -> activate(X) 2.52/1.42 length(nil) -> 0 2.52/1.42 length(cons(N, L)) -> s(length(activate(L))) 2.52/1.42 take(0, IL) -> nil 2.52/1.42 take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL))) 2.52/1.42 zeros -> n__zeros 2.52/1.42 take(X1, X2) -> n__take(X1, X2) 2.52/1.42 activate(n__zeros) -> zeros 2.52/1.42 activate(n__take(X1, X2)) -> take(X1, X2) 2.52/1.42 activate(X) -> X 2.52/1.42 2.52/1.42 2.52/1.42 2.52/1.42 Outermost Strategy. 2.52/1.42 2.52/1.42 ---------- Loop: ---------- 2.52/1.42 2.52/1.42 length(activate(n__zeros)) -> length(zeros) with rule activate(n__zeros) -> zeros at position [0] and matcher [ ] 2.52/1.42 2.52/1.42 length(zeros) -> length(cons(0, n__zeros)) with rule zeros -> cons(0, n__zeros) at position [0] and matcher [ ] 2.52/1.42 2.52/1.42 length(cons(0, n__zeros)) -> s(length(activate(n__zeros))) with rule length(cons(N, L)) -> s(length(activate(L))) at position [] and matcher [N / 0, L / n__zeros] 2.52/1.42 2.52/1.42 Now an instance of the first term with Matcher [ ] occurs in the last term at position [0]. 2.52/1.42 2.52/1.42 Context: s([]) 2.52/1.42 2.52/1.42 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.52/1.42 ---------------------------------------- 2.52/1.42 2.52/1.42 (2) 2.52/1.42 NO 2.72/1.45 EOF