WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2)) eqZList(C(x1,x2),Z()) -> False() eqZList(Z(),C(y1,y2)) -> False() eqZList(Z(),Z()) -> True() f(C(x1,x2)) -> C(f(x1),f(x2)) f(Z()) -> Z() first(C(x1,x2)) -> x1 g(x) -> x second(C(x1,x2)) -> x2 - Weak TRS: and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() - Signature: {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False ,True,Z} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- C :: ["A"(15) x "A"(15)] -(15)-> "A"(15) C :: ["A"(11) x "A"(11)] -(11)-> "A"(11) C :: ["A"(0) x "A"(0)] -(0)-> "A"(0) C :: ["A"(1) x "A"(1)] -(1)-> "A"(1) False :: [] -(0)-> "A"(0) False :: [] -(0)-> "A"(14) True :: [] -(0)-> "A"(0) True :: [] -(0)-> "A"(12) Z :: [] -(0)-> "A"(15) Z :: [] -(0)-> "A"(11) Z :: [] -(0)-> "A"(14) and :: ["A"(0) x "A"(0)] -(0)-> "A"(10) eqZList :: ["A"(15) x "A"(15)] -(8)-> "A"(0) f :: ["A"(11)] -(3)-> "A"(0) first :: ["A"(0)] -(6)-> "A"(0) g :: ["A"(14)] -(12)-> "A"(0) second :: ["A"(1)] -(2)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "C_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) "Z_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))