WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(x) -> list(x) list(Cons(x,xs)) -> list(xs) list(Nil()) -> True() list(Nil()) -> isEmpty[Match](Nil()) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Signature: {goal/1,list/1,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0,isEmpty[Match]/1} - Obligation: innermost runtime complexity wrt. defined symbols {goal,list,notEmpty} and constructors {Cons,False,Nil,True ,isEmpty[Match]} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(0) x "A"(15)] -(15)-> "A"(15) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "Nil") :: [] -(0)-> "A"(15) F (TrsFun "Nil") :: [] -(0)-> "A"(0) F (TrsFun "Nil") :: [] -(0)-> "A"(14) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "goal") :: ["A"(15)] -(16)-> "A"(0) F (TrsFun "isEmpty[Match]") :: ["A"(0)] -(0)-> "A"(14) F (TrsFun "list") :: ["A"(15)] -(15)-> "A"(0) F (TrsFun "notEmpty") :: ["A"(0)] -(7)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"Cons\")_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"False\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"True\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"isEmpty[Match]\")_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(?,O(n^1))