WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: group3(@l) -> group3#1(@l) group3#1(::(@x,@xs)) -> group3#2(@xs,@x) group3#1(nil()) -> nil() group3#2(::(@y,@ys),@x) -> group3#3(@ys,@x,@y) group3#2(nil(),@x) -> nil() group3#3(::(@z,@zs),@x,@y) -> ::(tuple#3(@x,@y,@z),group3(@zs)) group3#3(nil(),@x,@y) -> nil() zip3(@l1,@l2,@l3) -> zip3#1(@l1,@l2,@l3) zip3#1(::(@x,@xs),@l2,@l3) -> zip3#2(@l2,@l3,@x,@xs) zip3#1(nil(),@l2,@l3) -> nil() zip3#2(::(@y,@ys),@l3,@x,@xs) -> zip3#3(@l3,@x,@xs,@y,@ys) zip3#2(nil(),@l3,@x,@xs) -> nil() zip3#3(::(@z,@zs),@x,@xs,@y,@ys) -> ::(tuple#3(@x,@y,@z),zip3(@xs,@ys,@zs)) zip3#3(nil(),@x,@xs,@y,@ys) -> nil() - Signature: {group3/1,group3#1/1,group3#2/2,group3#3/3,zip3/3,zip3#1/3,zip3#2/4,zip3#3/5} / {::/2,nil/0,tuple#3/3} - Obligation: innermost runtime complexity wrt. defined symbols {group3,group3#1,group3#2,group3#3,zip3,zip3#1,zip3#2 ,zip3#3} and constructors {::,nil,tuple#3} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- :: :: ["A"(15) x "A"(15)] -(15)-> "A"(15) :: :: ["A"(10) x "A"(10)] -(10)-> "A"(10) :: :: ["A"(6) x "A"(6)] -(6)-> "A"(6) :: :: ["A"(13) x "A"(13)] -(13)-> "A"(13) :: :: ["A"(2) x "A"(2)] -(2)-> "A"(2) group3 :: ["A"(15)] -(12)-> "A"(2) group3#1 :: ["A"(15)] -(9)-> "A"(2) group3#2 :: ["A"(15) x "A"(1)] -(15)-> "A"(2) group3#3 :: ["A"(15) x "A"(1) x "A"(9)] -(12)-> "A"(2) nil :: [] -(0)-> "A"(15) nil :: [] -(0)-> "A"(10) nil :: [] -(0)-> "A"(6) nil :: [] -(0)-> "A"(13) nil :: [] -(0)-> "A"(7) nil :: [] -(0)-> "A"(5) tuple#3 :: ["A"(0) x "A"(7) x "A"(7)] -(0)-> "A"(7) tuple#3 :: ["A"(0) x "A"(3) x "A"(3)] -(0)-> "A"(3) zip3 :: ["A"(10) x "A"(6) x "A"(13)] -(11)-> "A"(2) zip3#1 :: ["A"(10) x "A"(6) x "A"(13)] -(2)-> "A"(2) zip3#2 :: ["A"(6) x "A"(13) x "A"(5) x "A"(10)] -(8)-> "A"(2) zip3#3 :: ["A"(13) x "A"(3) x "A"(10) x "A"(3) x "A"(6)] -(2)-> "A"(2) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "::_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "nil_A" :: [] -(0)-> "A"(1) "tuple#3_A" :: ["A"(0) x "A"(0) x "A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^1))