WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: loop(Cons(x,xs),Nil(),pp,ss) -> False() loop(Cons(x',xs'),Cons(x,xs),pp,ss) -> loop[Ite](!EQ(x',x),Cons(x',xs'),Cons(x,xs),pp,ss) loop(Nil(),s,pp,ss) -> True() match1(p,s) -> loop(p,s,p,s) - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) loop[Ite](False(),p,s,pp,Cons(x,xs)) -> loop(pp,xs,pp,xs) loop[Ite](True(),Cons(x',xs'),Cons(x,xs),pp,ss) -> loop(xs',xs,pp,ss) - Signature: {!EQ/2,loop/4,loop[Ite]/5,match1/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,loop,loop[Ite],match1} 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, 0) x "A"(0, 0)] -(0)-> "A"(14, 14) 0 :: [] -(0)-> "A"(0, 0) Cons :: ["A"(0, 0) x "A"(0, 0)] -(0)-> "A"(0, 0) Cons :: ["A"(9, 0) x "A"(9, 0)] -(9)-> "A"(9, 0) Cons :: ["A"(0, 0) x "A"(13, 13)] -(13)-> "A"(0, 13) False :: [] -(0)-> "A"(7, 7) False :: [] -(0)-> "A"(15, 11) False :: [] -(0)-> "A"(15, 15) Nil :: [] -(0)-> "A"(9, 0) Nil :: [] -(0)-> "A"(0, 0) S :: ["A"(0, 0)] -(0)-> "A"(0, 0) True :: [] -(0)-> "A"(7, 7) True :: [] -(0)-> "A"(15, 11) True :: [] -(0)-> "A"(15, 15) loop :: ["A"(0, 0) x "A"(9, 0) x "A"(8, 8) x "A"(0, 13)] -(14)-> "A"(13, 5) loop[Ite] :: ["A"(7, 7) x "A"(0, 0) x "A"(9, 0) x "A"(8, 8) x "A"(0, 13)] -(5)-> "A"(13, 5) match1 :: ["A"(15, 15) x "A"(15, 14)] -(16)-> "A"(2, 2) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1, 0) "0_A" :: [] -(0)-> "A"(0, 1) "Cons_A" :: ["A"(1, 0) x "A"(1, 0)] -(1)-> "A"(1, 0) "Cons_A" :: ["A"(0, 0) x "A"(1, 1)] -(1)-> "A"(0, 1) "False_A" :: [] -(0)-> "A"(1, 0) "False_A" :: [] -(0)-> "A"(0, 1) "Nil_A" :: [] -(0)-> "A"(1, 0) "Nil_A" :: [] -(0)-> "A"(0, 1) "S_A" :: ["A"(1, 0)] -(1)-> "A"(1, 0) "S_A" :: ["A"(1, 1)] -(1)-> "A"(0, 1) "True_A" :: [] -(0)-> "A"(1, 0) "True_A" :: [] -(0)-> "A"(0, 1) WORST_CASE(?,O(n^2))