WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: decrease(Cons(x,xs)) -> decrease(xs) decrease(Nil()) -> number42(Nil()) goal(x) -> decrease(x) number42(x) -> 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() ,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() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Cons(Nil() ,Nil())))))))))))))))))))))))))))))))))))))))))) - Signature: {decrease/1,goal/1,number42/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {decrease,goal,number42} and constructors {Cons,Nil} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(0) x "A"(8)] -(8)-> "A"(8) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "Nil") :: [] -(0)-> "A"(8) F (TrsFun "Nil") :: [] -(0)-> "A"(15) F (TrsFun "decrease") :: ["A"(8)] -(15)-> "A"(0) F (TrsFun "goal") :: ["A"(14)] -(16)-> "A"(0) F (TrsFun "number42") :: ["A"(0)] -(14)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"Cons\")_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))