WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__zeros()) -> zeros() tail(cons(X,XS)) -> activate(XS) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(0) activate :: [A(12)] -(8)-> A(0) cons :: [A(0) x A(12)] -(0)-> A(12) cons :: [A(0) x A(0)] -(0)-> A(0) n__zeros :: [] -(0)-> A(12) n__zeros :: [] -(0)-> A(4) n__zeros :: [] -(0)-> A(14) tail :: [A(12)] -(9)-> A(0) zeros :: [] -(7)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0) x A(1)] -(0)-> A(1) n__zeros_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__zeros()) -> zeros() tail(cons(X,XS)) -> activate(XS) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__zeros()) -> zeros() tail(cons(X,XS)) -> activate(XS) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros} WORST_CASE(?,O(n^1))