WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2} / {=/2,false/0,nil/0,set/1,true/0,union/2} - Obligation: innermost runtime complexity wrt. defined symbols {mem,or} and constructors {=,false,nil,set,true,union} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- = :: ["A"(0) x "A"(0)] -(0)-> "A"(14) false :: [] -(0)-> "A"(0) false :: [] -(0)-> "A"(14) mem :: ["A"(0) x "A"(15)] -(1)-> "A"(0) nil :: [] -(0)-> "A"(15) or :: ["A"(0) x "A"(0)] -(9)-> "A"(0) set :: ["A"(0)] -(0)-> "A"(15) true :: [] -(0)-> "A"(0) true :: [] -(0)-> "A"(14) union :: ["A"(15) x "A"(15)] -(15)-> "A"(15) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "=_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "false_A" :: [] -(0)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "set_A" :: ["A"(0)] -(0)-> "A"(1) "true_A" :: [] -(0)-> "A"(1) "union_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))