WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: eqNat#2(0(),0()) -> True() eqNat#2(0(),S(x20)) -> False() eqNat#2(S(x20),0()) -> False() eqNat#2(S(x4),S(x2)) -> eqNat#2(x4,x2) eval2#5(x10,x8,x6,x4,Not(x2)) -> lnot#1(eval2#5(x10,x8,x6,x4,x2)) eval2#5(x12,x10,x8,x6,And(x4,x2)) -> land#2(eval2#5(x12,x10,x8,x6,x4),eval2#5(x12,x10,x8,x6,x2)) eval2#5(x12,x10,x8,x6,Or(x4,x2)) -> lor#2(eval2#5(x12,x10,x8,x6,x4),eval2#5(x12,x10,x8,x6,x2)) eval2#5(x22,x20,x14,x10,Var(x6)) -> ite_b#2(eqNat#2(x6,x22),x20,ite#3(eqNat#2(x6,x14),x10)) ite#3(False(),x1) -> bot[0]#1() ite#3(True(),x1) -> x1 ite_b#2(False(),x20,x24) -> x24 ite_b#2(True(),x20,x24) -> x20 land#2(False(),x28) -> False() land#2(True(),x28) -> x28 lnot#1(False()) -> True() lnot#1(True()) -> False() lor#2(False(),x32) -> x32 lor#2(True(),x32) -> True() main(x3,x2,x1) -> Cons(Triple(True(),True(),eval2#5(x3,True(),x2,True(),x1)) ,Cons(Triple(True(),False(),eval2#5(x3,True(),x2,False(),x1)) ,Cons(Triple(False(),True(),eval2#5(x3,False(),x2,True(),x1)) ,Cons(Triple(False(),False(),eval2#5(x3,False(),x2,False(),x1)),Nil())))) - Signature: {eqNat#2/2,eval2#5/5,ite#3/2,ite_b#2/3,land#2/2,lnot#1/1,lor#2/2,main/3} / {0/0,And/2,Cons/2,False/0,Nil/0 ,Not/1,Or/2,S/1,Triple/3,True/0,Var/1,bot[0]#1/0} - Obligation: innermost runtime complexity wrt. defined symbols {eqNat#2,eval2#5,ite#3,ite_b#2,land#2,lnot#1,lor#2 ,main} and constructors {0,And,Cons,False,Nil,Not,Or,S,Triple,True,Var,bot[0]#1} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(1) 0 :: [] -(0)-> "A"(0) And :: ["A"(7) x "A"(7)] -(7)-> "A"(7) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Cons :: ["A"(0) x "A"(0)] -(1)-> "A"(1) False :: [] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(0) Not :: ["A"(7)] -(7)-> "A"(7) Or :: ["A"(7) x "A"(7)] -(7)-> "A"(7) S :: ["A"(0)] -(0)-> "A"(0) S :: ["A"(1)] -(1)-> "A"(1) Triple :: ["A"(0) x "A"(0) x "A"(0)] -(0)-> "A"(0) Triple :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(1) True :: [] -(0)-> "A"(0) Var :: ["A"(7)] -(0)-> "A"(7) bot[0]#1 :: [] -(0)-> "A"(0) eqNat#2 :: ["A"(1) x "A"(0)] -(1)-> "A"(0) eval2#5 :: ["A"(0) x "A"(0) x "A"(0) x "A"(0) x "A"(7)] -(5)-> "A"(0) ite#3 :: ["A"(0) x "A"(0)] -(1)-> "A"(0) ite_b#2 :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(0) land#2 :: ["A"(0) x "A"(0)] -(1)-> "A"(0) lnot#1 :: ["A"(0)] -(1)-> "A"(0) lor#2 :: ["A"(0) x "A"(0)] -(1)-> "A"(0) main :: ["A"(0) x "A"(0) x "A"(28)] -(23)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "And_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "Cons_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "Not_A" :: ["A"(1)] -(1)-> "A"(1) "Or_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "Triple_A" :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) "Var_A" :: ["A"(1)] -(0)-> "A"(1) "bot[0]#1_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))