WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: divp(x,y) -> =(rem(x,y),0()) prime(0()) -> false() prime(s(0())) -> false() prime(s(s(x))) -> prime1(s(s(x)),s(x)) prime1(x,0()) -> false() prime1(x,s(0())) -> true() prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y))) - Signature: {divp/2,prime/1,prime1/2} / {0/0,=/2,and/2,false/0,not/1,rem/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {divp,prime,prime1} and constructors {0,=,and,false,not ,rem,s,true} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(2) 0 :: [] -(0)-> "A"(0) = :: ["A"(0) x "A"(0)] -(0)-> "A"(0) and :: ["A"(0) x "A"(0)] -(0)-> "A"(0) divp :: ["A"(0) x "A"(0)] -(1)-> "A"(0) false :: [] -(0)-> "A"(0) not :: ["A"(0)] -(0)-> "A"(0) prime :: ["A"(2)] -(1)-> "A"(0) prime1 :: ["A"(0) x "A"(2)] -(1)-> "A"(0) rem :: ["A"(0) x "A"(0)] -(0)-> "A"(0) s :: ["A"(2)] -(2)-> "A"(2) s :: ["A"(0)] -(0)-> "A"(0) true :: [] -(0)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "=_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "and_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "false_A" :: [] -(0)-> "A"(0) "not_A" :: ["A"(0)] -(0)-> "A"(0) "rem_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) "true_A" :: [] -(0)-> "A"(0) WORST_CASE(?,O(n^1))