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