WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) -> Nil() goal(x) -> duplicate(x) - Signature: {duplicate/1,goal/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- Cons :: [A(11) x A(11)] -(11)-> A(11) Cons :: [A(0) x A(0)] -(0)-> A(0) Nil :: [] -(0)-> A(11) Nil :: [] -(0)-> A(0) duplicate :: [A(11)] -(4)-> A(0) goal :: [A(12)] -(5)-> A(0) Cost-free Signatures used: -------------------------- Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Nil :: [] -(0)-> A_cf(0) duplicate :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- Cons_A :: [A(1) x A(1)] -(1)-> A(1) Nil_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) -> Nil() goal(x) -> duplicate(x) - Signature: {duplicate/1,goal/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil} Following problems could not be solved: - Strict TRS: duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) -> Nil() goal(x) -> duplicate(x) - Signature: {duplicate/1,goal/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil} WORST_CASE(?,O(n^1))