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 {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- Cons :: [A(0) x A(6)] -(6)-> A(6) Cons :: [A(0) x A(0)] -(0)-> A(0) False :: [] -(0)-> A(0) Nil :: [] -(0)-> A(6) Nil :: [] -(0)-> A(0) True :: [] -(0)-> A(0) even :: [A(6)] -(8)-> A(0) evenodd :: [A(6)] -(9)-> A(0) notEmpty :: [A(0)] -(1)-> A(0) odd :: [A(6)] -(8)-> A(0) Cost-free Signatures used: -------------------------- Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) False :: [] -(0)-> A_cf(0) Nil :: [] -(0)-> A_cf(0) True :: [] -(0)-> A_cf(0) even :: [A_cf(0)] -(0)-> A_cf(0) odd :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- Cons_A :: [A(0) x A(1)] -(1)-> A(1) False_A :: [] -(1)-> A(1) Nil_A :: [] -(0)-> A(1) True_A :: [] -(1)-> A(1) * Step 2: Open MAYBE - 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} Following problems could not be solved: - 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} WORST_CASE(?,O(n^1))