WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs)) addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs)) addlist(Nil(),ys) -> Nil() goal(xs,ys) -> addlist(xs,ys) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Signature: {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {addlist,goal,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 "0") :: [] -(0)-> "A"(0) F (TrsFun "Cons") :: ["A"(0) x "A"(1)] -(1)-> "A"(1) F (TrsFun "Cons") :: ["A"(0) x "A"(12)] -(12)-> "A"(12) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "Nil") :: [] -(0)-> "A"(1) F (TrsFun "Nil") :: [] -(0)-> "A"(12) F (TrsFun "Nil") :: [] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(14) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "addlist") :: ["A"(1) x "A"(1)] -(9)-> "A"(0) F (TrsFun "goal") :: ["A"(15) x "A"(15)] -(16)-> "A"(0) F (TrsFun "notEmpty") :: ["A"(12)] -(1)-> "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))