WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(cons(X,XS)) -> head(activate(XS)) activate(X) -> X activate(n__from(X)) -> from(X) activate(n__take(X1,X2)) -> take(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) head(cons(X,XS)) -> X sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) take(X1,X2) -> n__take(X1,X2) take(0(),XS) -> nil() take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS))) - Signature: {2nd/1,activate/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,n__from/1,n__take/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,from,head,sel,take} and constructors {0,cons ,n__from,n__take,nil,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(12) 0 :: [] -(0)-> "A"(3) 2nd :: ["A"(15)] -(12)-> "A"(0) activate :: ["A"(3)] -(5)-> "A"(3) cons :: ["A"(0) x "A"(15)] -(0)-> "A"(15) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) cons :: ["A"(0) x "A"(3)] -(0)-> "A"(3) cons :: ["A"(0) x "A"(10)] -(0)-> "A"(10) from :: ["A"(0)] -(4)-> "A"(5) head :: ["A"(0)] -(1)-> "A"(0) n__from :: ["A"(0)] -(0)-> "A"(3) n__from :: ["A"(0)] -(0)-> "A"(10) n__from :: ["A"(0)] -(0)-> "A"(15) n__take :: ["A"(3) x "A"(3)] -(0)-> "A"(3) nil :: [] -(0)-> "A"(5) s :: ["A"(12)] -(12)-> "A"(12) s :: ["A"(3)] -(3)-> "A"(3) s :: ["A"(0)] -(0)-> "A"(0) sel :: ["A"(12) x "A"(3)] -(2)-> "A"(0) take :: ["A"(3) x "A"(3)] -(4)-> "A"(3) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "cons_A" :: ["A"(0) x "A"(1)] -(0)-> "A"(1) "n__from_A" :: ["A"(0)] -(0)-> "A"(1) "n__take_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "s_A" :: ["A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))