WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cond_prefix_s1_s2_2(False(),x2,x1) -> False() cond_prefix_s1_s2_2(True(),x2,x1) -> prefix#2(x2,x1) eq#2(0(),0()) -> True() eq#2(0(),S(x16)) -> False() eq#2(S(x16),0()) -> False() eq#2(S(x4),S(x2)) -> eq#2(x4,x2) main(x2,x1) -> prefix#2(x2,x1) prefix#2(Cons(x4,x2),Nil()) -> False() prefix#2(Cons(x8,x6),Cons(x4,x2)) -> cond_prefix_s1_s2_2(eq#2(x8,x4),x6,x2) prefix#2(Nil(),x2) -> True() - Signature: {cond_prefix_s1_s2_2/3,eq#2/2,main/2,prefix#2/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_prefix_s1_s2_2,eq#2,main ,prefix#2} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(15) 0 :: [] -(0)-> "A"(0) Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15) Cons :: ["A"(13) x "A"(13)] -(13)-> "A"(13) False :: [] -(0)-> "A"(1) False :: [] -(0)-> "A"(14) Nil :: [] -(0)-> "A"(13) Nil :: [] -(0)-> "A"(15) S :: ["A"(0)] -(0)-> "A"(0) S :: ["A"(15)] -(15)-> "A"(15) True :: [] -(0)-> "A"(1) True :: [] -(0)-> "A"(10) True :: [] -(0)-> "A"(12) cond_prefix_s1_s2_2 :: ["A"(1) x "A"(15) x "A"(13)] -(11)-> "A"(0) eq#2 :: ["A"(15) x "A"(0)] -(15)-> "A"(2) main :: ["A"(15) x "A"(15)] -(15)-> "A"(0) prefix#2 :: ["A"(15) x "A"(13)] -(8)-> "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))