WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: checkF(queue(cons(x,xs),r)) -> queue(cons(x,xs),r) checkF(queue(nil(),r)) -> queue(rev(r),nil()) empty() -> queue(nil(),nil()) enq(0()) -> empty() enq(s(n)) -> snoc(enq(n),n) head(queue(cons(x,f),r)) -> x head(queue(nil(),r)) -> errorHead() rev(xs) -> rev'(xs,nil()) rev'(cons(x,xs),ys) -> rev'(xs,cons(x,ys)) rev'(nil(),ys) -> ys snoc(queue(f,r),x) -> checkF(queue(f,cons(x,r))) tail(queue(cons(x,f),r)) -> checkF(queue(f,r)) tail(queue(nil(),r)) -> errorTail() - Signature: {checkF/1,empty/0,enq/1,head/1,rev/1,rev'/2,snoc/2,tail/1} / {0/0,cons/2,errorHead/0,errorTail/0,nil/0 ,queue/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {checkF,empty,enq,head,rev,rev',snoc ,tail} and constructors {0,cons,errorHead,errorTail,nil,queue,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(15) checkF :: ["A"(7)] -(5)-> "A"(7) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) cons :: ["A"(0) x "A"(1)] -(1)-> "A"(1) cons :: ["A"(0) x "A"(7)] -(7)-> "A"(7) empty :: [] -(11)-> "A"(7) enq :: ["A"(15)] -(12)-> "A"(7) errorHead :: [] -(0)-> "A"(6) errorTail :: [] -(0)-> "A"(7) head :: ["A"(11)] -(9)-> "A"(0) nil :: [] -(0)-> "A"(0) nil :: [] -(0)-> "A"(1) nil :: [] -(0)-> "A"(15) nil :: [] -(0)-> "A"(7) queue :: ["A"(0) x "A"(7)] -(7)-> "A"(7) queue :: ["A"(0) x "A"(11)] -(11)-> "A"(11) queue :: ["A"(0) x "A"(8)] -(8)-> "A"(8) rev :: ["A"(1)] -(4)-> "A"(0) rev' :: ["A"(1) x "A"(0)] -(2)-> "A"(0) s :: ["A"(15)] -(15)-> "A"(15) snoc :: ["A"(7) x "A"(0)] -(14)-> "A"(7) tail :: ["A"(11)] -(3)-> "A"(1) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "errorHead_A" :: [] -(0)-> "A"(1) "errorTail_A" :: [] -(0)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "queue_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "s_A" :: ["A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))