WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) - Signature: {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(15) activate :: [A(12)] -(8)-> A(12) cons :: [A(0) x A(12)] -(0)-> A(12) from :: [A(0)] -(14)-> A(12) n__from :: [A(0)] -(12)-> A(12) n__from :: [A(0)] -(13)-> A(13) s :: [A(15)] -(15)-> A(15) s :: [A(0)] -(0)-> A(0) sel :: [A(15) x A(12)] -(12)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) activate :: [A_cf(0)] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) from :: [A_cf(0)] -(0)-> A_cf(0) n__from :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) sel :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0) x A(1)] -(0)-> A(1) n__from_A :: [A(0)] -(1)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) - Signature: {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) - Signature: {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s} WORST_CASE(?,O(n^1))