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