WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(x,xs) -> member(x,xs) member(x,Nil()) -> False() member(x',Cons(x,xs)) -> member[Ite][True][Ite](!EQ(x',x),x',Cons(x,xs)) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) member[Ite][True][Ite](False(),x',Cons(x,xs)) -> member(x',xs) member[Ite][True][Ite](True(),x,xs) -> True() - Signature: {!EQ/2,goal/2,member/2,member[Ite][True][Ite]/3,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,goal,member,member[Ite][True][Ite] ,notEmpty} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "!EQ") :: ["A"(0) x "A"(0)] -(0)-> "A"(14) F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "Cons") :: ["A"(0) x "A"(15)] -(15)-> "A"(15) F (TrsFun "Cons") :: ["A"(0) x "A"(5)] -(5)-> "A"(5) F (TrsFun "False") :: [] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "Nil") :: [] -(0)-> "A"(15) F (TrsFun "Nil") :: [] -(0)-> "A"(5) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(10) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "goal") :: ["A"(12) x "A"(15)] -(16)-> "A"(0) F (TrsFun "member") :: ["A"(0) x "A"(15)] -(15)-> "A"(0) F (TrsFun "member[Ite][True][Ite]") :: ["A"(0) x "A"(0) x "A"(15)] -(1)-> "A"(0) F (TrsFun "notEmpty") :: ["A"(5)] -(2)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"0\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Cons\")_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "F (TrsFun \"False\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Nil\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"S\")_A" :: ["A"(0)] -(0)-> "A"(1) "F (TrsFun \"True\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))