WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__first(X1,X2)) -> first(X1,X2) activate(n__from(X)) -> from(X) first(X1,X2) -> n__first(X1,X2) first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,first/2,from/1} / {0/0,cons/2,n__first/2,n__from/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,first,from} and constructors {0,cons,n__first ,n__from,nil,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(13) activate :: ["A"(14)] -(8)-> "A"(0) cons :: ["A"(0) x "A"(14)] -(14)-> "A"(14) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) first :: ["A"(13) x "A"(14)] -(3)-> "A"(0) from :: ["A"(7)] -(4)-> "A"(0) n__first :: ["A"(14) x "A"(14)] -(0)-> "A"(14) n__first :: ["A"(4) x "A"(4)] -(0)-> "A"(4) n__first :: ["A"(0) x "A"(0)] -(0)-> "A"(0) n__from :: ["A"(14)] -(14)-> "A"(14) n__from :: ["A"(0)] -(0)-> "A"(0) n__from :: ["A"(2)] -(2)-> "A"(2) nil :: [] -(0)-> "A"(0) s :: ["A"(0)] -(13)-> "A"(13) s :: ["A"(0)] -(0)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "n__first_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(1) "n__from_A" :: ["A"(0)] -(1)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "s_A" :: ["A"(0)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))