WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: append(cons(x,xs),ys) -> cons(x,append(xs,ys)) append(nil(),ys) -> ys attach(x,cons(y,ys)) -> cons(pair(x,y),attach(x,ys)) attach(x,nil()) -> nil() pairs(cons(x,xs)) -> append(attach(x,xs),pairs(xs)) pairs(nil()) -> nil() - Signature: {append/2,attach/2,pairs/1} / {cons/2,nil/0,pair/2} - Obligation: innermost runtime complexity wrt. defined symbols {append,attach,pairs} and constructors {cons,nil,pair} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- append :: ["A"(5, 0) x "A"(0, 0)] -(3)-> "A"(0, 0) attach :: ["A"(0, 0) x "A"(13, 0)] -(2)-> "A"(5, 0) cons :: ["A"(5, 0) x "A"(5, 0)] -(5)-> "A"(5, 0) cons :: ["A"(13, 0) x "A"(13, 0)] -(13)-> "A"(13, 0) cons :: ["A"(0, 0) x "A"(15, 15)] -(15)-> "A"(0, 15) cons :: ["A"(0, 0) x "A"(0, 0)] -(0)-> "A"(0, 0) nil :: [] -(0)-> "A"(5, 0) nil :: [] -(0)-> "A"(13, 0) nil :: [] -(0)-> "A"(0, 15) nil :: [] -(0)-> "A"(11, 7) nil :: [] -(0)-> "A"(6, 7) pair :: ["A"(0, 0) x "A"(7, 0)] -(0)-> "A"(8, 7) pairs :: ["A"(0, 15)] -(1)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "cons_A" :: ["A"(1, 0) x "A"(1, 0)] -(1)-> "A"(1, 0) "cons_A" :: ["A"(0, 0) x "A"(1, 1)] -(1)-> "A"(0, 1) "nil_A" :: [] -(0)-> "A"(1, 0) "nil_A" :: [] -(0)-> "A"(0, 1) "pair_A" :: ["A"(0, 0) x "A"(0, 0)] -(0)-> "A"(1, 0) "pair_A" :: ["A"(0, 0) x "A"(1, 0)] -(0)-> "A"(0, 1) WORST_CASE(?,O(n^2))