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())) -> c(f(g(f(a())))) mark(a()) -> a() mark(c(X)) -> c(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(mark(X)) - Signature: {a__f/1,mark/1} / {a/0,c/1,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,c,f,g} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- a :: [] -(0)-> "A"(0) a :: [] -(0)-> "A"(2) a__f :: ["A"(0)] -(1)-> "A"(0) c :: ["A"(2)] -(2)-> "A"(2) c :: ["A"(0)] -(0)-> "A"(0) f :: ["A"(0)] -(0)-> "A"(0) f :: ["A"(2)] -(2)-> "A"(2) g :: ["A"(2)] -(2)-> "A"(2) g :: ["A"(0)] -(0)-> "A"(0) mark :: ["A"(2)] -(1)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "a_A" :: [] -(0)-> "A"(0) "c_A" :: ["A"(0)] -(0)-> "A"(0) "f_A" :: ["A"(0)] -(0)-> "A"(0) "g_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^1))