WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) sqr(0()) -> 0() sqr(s(x)) -> +(sqr(x),s(double(x))) sqr(s(x)) -> s(+(sqr(x),double(x))) - Signature: {+/2,double/1,sqr/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,sqr} and constructors {0,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- + :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0) 0 :: [] -(0)-> "A"(1, 0) 0 :: [] -(0)-> "A"(3, 0) 0 :: [] -(0)-> "A"(4, 3) 0 :: [] -(0)-> "A"(0, 0) double :: ["A"(3, 0)] -(1)-> "A"(1, 0) s :: ["A"(1, 0)] -(1)-> "A"(1, 0) s :: ["A"(3, 0)] -(3)-> "A"(3, 0) s :: ["A"(7, 3)] -(4)-> "A"(4, 3) s :: ["A"(0, 0)] -(0)-> "A"(0, 0) sqr :: ["A"(4, 3)] -(1)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^2))