WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(xs,ys) -> merge(xs,ys) merge(Cons(x,xs),Nil()) -> Cons(x,xs) merge(Cons(x',xs'),Cons(x,xs)) -> merge[Ite](<=(x',x),Cons(x',xs'),Cons(x,xs)) merge(Nil(),ys) -> ys - Weak TRS: <=(0(),y) -> True() <=(S(x),0()) -> False() <=(S(x),S(y)) -> <=(x,y) merge[Ite](False(),xs',Cons(x,xs)) -> Cons(x,merge(xs',xs)) merge[Ite](True(),Cons(x,xs),ys) -> Cons(x,merge(xs,ys)) - Signature: {<=/2,goal/2,merge/2,merge[Ite]/3} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<=,goal,merge,merge[Ite]} and constructors {0,Cons,False ,Nil,S,True} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "<=") :: ["A"(0) x "A"(0)] -(0)-> "A"(14) F (TrsFun "Cons") :: ["A"(13) x "A"(13)] -(13)-> "A"(13) F (TrsFun "Cons") :: ["A"(9) x "A"(9)] -(9)-> "A"(9) F (TrsFun "Cons") :: ["A"(8) x "A"(8)] -(8)-> "A"(8) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(3) F (TrsFun "False") :: [] -(0)-> "A"(15) F (TrsFun "Nil") :: [] -(0)-> "A"(9) F (TrsFun "Nil") :: [] -(0)-> "A"(13) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(3) F (TrsFun "True") :: [] -(0)-> "A"(15) F (TrsFun "goal") :: ["A"(15) x "A"(15)] -(16)-> "A"(0) F (TrsFun "merge") :: ["A"(13) x "A"(9)] -(12)-> "A"(0) F (TrsFun "merge[Ite]") :: ["A"(3) x "A"(13) x "A"(9)] -(3)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"0\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Cons\")_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"False\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"S\")_A" :: ["A"(1)] -(0)-> "A"(1) "F (TrsFun \"True\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))