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