WORST_CASE(?,O(1)) * Step 1: Ara WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: filter(cons(X),0(),M) -> cons(0()) filter(cons(X),s(N),M) -> cons(X) nats(N) -> cons(N) sieve(cons(0())) -> cons(0()) sieve(cons(s(N))) -> cons(s(N)) zprimes() -> sieve(nats(s(s(0())))) - Signature: {filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(0) cons :: ["A"(0)] -(0)-> "A"(0) filter :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(0) nats :: ["A"(0)] -(1)-> "A"(0) s :: ["A"(0)] -(0)-> "A"(0) sieve :: ["A"(0)] -(1)-> "A"(0) zprimes :: [] -(3)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "cons_A" :: ["A"(0)] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(1))