WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dec(Cons(Cons(x,xs),Nil())) -> dec(Nil()) dec(Cons(Cons(x',xs'),Cons(x,xs))) -> dec(Cons(x,xs)) dec(Cons(Nil(),Cons(x,xs))) -> dec(Cons(x,xs)) dec(Cons(Nil(),Nil())) -> Nil() goal(x) -> nestdec(x) isNilNil(Cons(Cons(x,xs),Nil())) -> False() isNilNil(Cons(Cons(x',xs'),Cons(x,xs))) -> False() isNilNil(Cons(Nil(),Cons(x,xs))) -> False() isNilNil(Cons(Nil(),Nil())) -> True() nestdec(Cons(x,xs)) -> nestdec(dec(Cons(x,xs))) nestdec(Nil()) -> Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Nil()))))))))))))))))) number17(n) -> Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Nil()))))))))))))))))) - Signature: {dec/1,goal/1,isNilNil/1,nestdec/1,number17/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {dec,goal,isNilNil,nestdec ,number17} and constructors {Cons,False,Nil,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- Cons :: ["A"(0) x "A"(1)] -(1)-> "A"(1) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Cons :: ["A"(0) x "A"(9)] -(9)-> "A"(9) False :: [] -(0)-> "A"(13) Nil :: [] -(0)-> "A"(1) Nil :: [] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(9) Nil :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(13) Nil :: [] -(0)-> "A"(12) Nil :: [] -(0)-> "A"(14) True :: [] -(0)-> "A"(13) dec :: ["A"(1)] -(1)-> "A"(12) goal :: ["A"(15)] -(16)-> "A"(0) isNilNil :: ["A"(1)] -(11)-> "A"(3) nestdec :: ["A"(9)] -(10)-> "A"(0) number17 :: ["A"(0)] -(16)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))