WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__natsFrom(X)) -> natsFrom(X) afterNth(N,XS) -> snd(splitAt(N,XS)) fst(pair(XS,YS)) -> XS head(cons(N,XS)) -> N natsFrom(N) -> cons(N,n__natsFrom(s(N))) natsFrom(X) -> n__natsFrom(X) sel(N,XS) -> head(afterNth(N,XS)) snd(pair(XS,YS)) -> YS splitAt(0(),XS) -> pair(nil(),XS) splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS)) tail(cons(N,XS)) -> activate(XS) take(N,XS) -> fst(splitAt(N,XS)) u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS) - Signature: {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2 ,n__natsFrom/1,nil/0,pair/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(8) activate :: ["A"(0)] -(2)-> "A"(0) afterNth :: ["A"(8) x "A"(0)] -(3)-> "A"(0) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) fst :: ["A"(0)] -(1)-> "A"(0) head :: ["A"(0)] -(1)-> "A"(0) n__natsFrom :: ["A"(0)] -(0)-> "A"(0) natsFrom :: ["A"(0)] -(1)-> "A"(0) nil :: [] -(0)-> "A"(0) pair :: ["A"(0) x "A"(0)] -(0)-> "A"(0) s :: ["A"(8)] -(8)-> "A"(8) s :: ["A"(0)] -(0)-> "A"(0) sel :: ["A"(8) x "A"(0)] -(5)-> "A"(0) snd :: ["A"(0)] -(1)-> "A"(0) splitAt :: ["A"(8) x "A"(0)] -(1)-> "A"(0) tail :: ["A"(0)] -(3)-> "A"(0) take :: ["A"(8) x "A"(0)] -(3)-> "A"(0) u :: ["A"(0) x "A"(0) x "A"(0) x "A"(0)] -(3)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "cons_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "n__natsFrom_A" :: ["A"(0)] -(0)-> "A"(0) "nil_A" :: [] -(0)-> "A"(0) "pair_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^1))