WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,xs)) -> odd(xs) even(Nil()) -> True() evenodd(x) -> even(x) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() odd(Cons(x,xs)) -> even(xs) odd(Nil()) -> False() - Signature: {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False ,Nil,True} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(0) x "A"(2)] -(2)-> "A"(2) F (TrsFun "Cons") :: ["A"(0) x "A"(3)] -(3)-> "A"(3) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "Nil") :: [] -(0)-> "A"(2) F (TrsFun "Nil") :: [] -(0)-> "A"(3) F (TrsFun "True") :: [] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "even") :: ["A"(2)] -(8)-> "A"(0) F (TrsFun "evenodd") :: ["A"(14)] -(11)-> "A"(0) F (TrsFun "notEmpty") :: ["A"(3)] -(3)-> "A"(0) F (TrsFun "odd") :: ["A"(2)] -(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) WORST_CASE(?,O(n^1))