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