WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: first(0(),X) -> nil() first(s(X),cons(Y)) -> cons(Y) from(X) -> cons(X) - Signature: {first/2,from/1} / {0/0,cons/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {first,from} and constructors {0,cons,nil,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(0) cons :: [A(0)] -(1)-> A(1) cons :: [A(0)] -(3)-> A(3) cons :: [A(0)] -(14)-> A(14) first :: [A(0) x A(1)] -(13)-> A(0) from :: [A(14)] -(15)-> A(0) nil :: [] -(0)-> A(14) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0)] -(1)-> A(1) nil_A :: [] -(0)-> A(1) s_A :: [A(0)] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: first(0(),X) -> nil() first(s(X),cons(Y)) -> cons(Y) from(X) -> cons(X) - Signature: {first/2,from/1} / {0/0,cons/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {first,from} and constructors {0,cons,nil,s} Following problems could not be solved: - Strict TRS: first(0(),X) -> nil() first(s(X),cons(Y)) -> cons(Y) from(X) -> cons(X) - Signature: {first/2,from/1} / {0/0,cons/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {first,from} and constructors {0,cons,nil,s} WORST_CASE(?,O(n^1))