WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(x,xs) -> member(x,xs) member(x,Nil()) -> False() member(x',Cons(x,xs)) -> member[Ite][True][Ite](!EQ(x',x),x',Cons(x,xs)) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) member[Ite][True][Ite](False(),x',Cons(x,xs)) -> member(x',xs) member[Ite][True][Ite](True(),x,xs) -> True() - Signature: {!EQ/2,goal/2,member/2,member[Ite][True][Ite]/3,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,goal,member,member[Ite][True][Ite] ,notEmpty} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- !EQ :: ["A"(0) x "A"(0)] -(0)-> "A"(14) 0 :: [] -(0)-> "A"(0) Cons :: ["A"(3) x "A"(3)] -(3)-> "A"(3) Cons :: ["A"(7) x "A"(7)] -(7)-> "A"(7) False :: [] -(0)-> "A"(7) False :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(3) Nil :: [] -(0)-> "A"(7) S :: ["A"(0)] -(0)-> "A"(0) True :: [] -(0)-> "A"(7) True :: [] -(0)-> "A"(15) goal :: ["A"(15) x "A"(13)] -(16)-> "A"(2) member :: ["A"(9) x "A"(3)] -(13)-> "A"(12) member[Ite][True][Ite] :: ["A"(7) x "A"(9) x "A"(3)] -(11)-> "A"(12) notEmpty :: ["A"(7)] -(10)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))