WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,Nil())) -> False() even(Cons(x',Cons(x,xs))) -> even(xs) even(Nil()) -> True() goal(x,y) -> and(lte(x,y),even(x)) lte(Cons(x,xs),Nil()) -> False() lte(Cons(x',xs'),Cons(x,xs)) -> lte(xs',xs) lte(Nil(),y) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Weak TRS: and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() - Signature: {and/2,even/1,goal/2,lte/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,even,goal,lte,notEmpty} and constructors {Cons,False ,Nil,True} + Applied Processor: Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- F (TrsFun "Cons") :: ["A"(0) x "A"(4)] -(4)-> "A"(4) F (TrsFun "Cons") :: ["A"(0) x "A"(8)] -(8)-> "A"(8) F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "False") :: [] -(0)-> "A"(12) F (TrsFun "Nil") :: [] -(0)-> "A"(4) F (TrsFun "Nil") :: [] -(0)-> "A"(0) F (TrsFun "Nil") :: [] -(0)-> "A"(8) F (TrsFun "True") :: [] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(12) F (TrsFun "True") :: [] -(0)-> "A"(6) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "and") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "even") :: ["A"(4)] -(2)-> "A"(0) F (TrsFun "goal") :: ["A"(14) x "A"(14)] -(15)-> "A"(0) F (TrsFun "lte") :: ["A"(8) x "A"(0)] -(7)-> "A"(6) F (TrsFun "notEmpty") :: ["A"(8)] -(8)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "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 \"True\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))