WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(a()) -> a() mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) - Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,f,g} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- a :: [] -(0)-> "A"(4) a :: [] -(0)-> "A"(14) a :: [] -(0)-> "A"(10) a__f :: ["A"(4)] -(5)-> "A"(4) f :: ["A"(4)] -(4)-> "A"(4) f :: ["A"(14)] -(14)-> "A"(14) f :: ["A"(0)] -(0)-> "A"(0) g :: ["A"(0)] -(0)-> "A"(14) mark :: ["A"(14)] -(8)-> "A"(4) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "a_A" :: [] -(0)-> "A"(1) "f_A" :: ["A"(1)] -(1)-> "A"(1) "g_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(?,O(n^1))