WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: group3(l) -> group3#1(l) group3#1(cons(x,xs)) -> group3#2(xs,x) group3#1(nil()) -> nil() group3#2(cons(y,ys),x) -> group3#3(ys,x,y) group3#2(nil(),x) -> nil() group3#3(cons(z,zs),x,y) -> cons(tuple#3(x,y,z),group3(zs)) group3#3(nil(),x,y) -> nil() zip3(l1,l2,l3) -> zip3#1(l1,l2,l3) zip3#1(cons(x,xs),l2,l3) -> zip3#2(l2,l3,x,xs) zip3#1(nil(),l2,l3) -> nil() zip3#2(cons(y,ys),l3,x,xs) -> zip3#3(l3,x,xs,y,ys) zip3#2(nil(),l3,x,xs) -> nil() zip3#3(cons(z,zs),x,xs,y,ys) -> cons(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} / {cons/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 {cons,nil,tuple#3} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "cons") :: ["A"(7) x "A"(7)] -(7)-> "A"(7) F (TrsFun "cons") :: ["A"(14) x "A"(14)] -(14)-> "A"(14) F (TrsFun "cons") :: ["A"(1) x "A"(1)] -(1)-> "A"(1) F (TrsFun "cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "group3") :: ["A"(7)] -(2)-> "A"(0) F (TrsFun "group3#1") :: ["A"(7)] -(1)-> "A"(0) F (TrsFun "group3#2") :: ["A"(7) x "A"(0)] -(4)-> "A"(0) F (TrsFun "group3#3") :: ["A"(7) x "A"(0) x "A"(0)] -(7)-> "A"(0) F (TrsFun "nil") :: [] -(0)-> "A"(7) F (TrsFun "nil") :: [] -(0)-> "A"(14) F (TrsFun "nil") :: [] -(0)-> "A"(1) F (TrsFun "nil") :: [] -(0)-> "A"(0) F (TrsFun "nil") :: [] -(0)-> "A"(10) F (TrsFun "tuple#3") :: ["A"(0) x "A"(0) x "A"(0)] -(3)-> "A"(3) F (TrsFun "tuple#3") :: ["A"(0) x "A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "zip3") :: ["A"(14) x "A"(1) x "A"(0)] -(4)-> "A"(0) F (TrsFun "zip3#1") :: ["A"(14) x "A"(1) x "A"(0)] -(1)-> "A"(0) F (TrsFun "zip3#2") :: ["A"(1) x "A"(0) x "A"(0) x "A"(14)] -(11)-> "A"(0) F (TrsFun "zip3#3") :: ["A"(0) x "A"(0) x "A"(14) x "A"(0) x "A"(1)] -(7)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"cons\")_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"tuple#3\")_A" :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))