WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: -(x,0()) -> x -(0(),s(y)) -> 0() -(s(x),s(y)) -> -(x,y) div(x,0()) -> 0() div(0(),y) -> 0() div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y)))) if(false(),x,y) -> y if(true(),x,y) -> x lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) - Signature: {-/2,div/2,if/3,lt/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {-,div,if,lt} and constructors {0,false,s,true} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- - :: ["A"(4, 1) x "A"(0, 0)] -(1)-> "A"(4, 1) 0 :: [] -(0)-> "A"(0, 0) 0 :: [] -(0)-> "A"(4, 1) 0 :: [] -(0)-> "A"(1, 0) div :: ["A"(4, 1) x "A"(0, 0)] -(1)-> "A"(0, 0) false :: [] -(0)-> "A"(0, 0) if :: ["A"(0, 0) x "A"(0, 0) x "A"(0, 0)] -(1)-> "A"(0, 0) lt :: ["A"(1, 0) x "A"(0, 0)] -(1)-> "A"(0, 0) s :: ["A"(0, 0)] -(0)-> "A"(0, 0) s :: ["A"(5, 1)] -(4)-> "A"(4, 1) s :: ["A"(1, 0)] -(1)-> "A"(1, 0) true :: [] -(0)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "false_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) "true_A" :: [] -(0)-> "A"(0) WORST_CASE(?,O(n^2))