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