WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(C(x1,x2),y) -> C(a(x1,y),a(x2,C(x1,x2))) a(Z(),y) -> Z() 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() first(C(x1,x2)) -> x1 second(C(x1,x2)) -> x2 - Weak TRS: and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() - Signature: {a/2,and/2,eqZList/2,first/1,second/1} / {C/2,False/0,True/0,Z/0} - Obligation: innermost runtime complexity wrt. defined symbols {a,and,eqZList,first,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"(12) x "A"(12)] -(12)-> "A"(12) C :: ["A"(8) x "A"(8)] -(8)-> "A"(8) C :: ["A"(7) x "A"(7)] -(7)-> "A"(7) C :: ["A"(1) x "A"(1)] -(1)-> "A"(1) C :: ["A"(0) x "A"(0)] -(0)-> "A"(0) False :: [] -(0)-> "A"(0) False :: [] -(0)-> "A"(6) False :: [] -(0)-> "A"(14) True :: [] -(0)-> "A"(0) True :: [] -(0)-> "A"(6) True :: [] -(0)-> "A"(14) Z :: [] -(0)-> "A"(15) Z :: [] -(0)-> "A"(8) Z :: [] -(0)-> "A"(12) Z :: [] -(0)-> "A"(7) a :: ["A"(15) x "A"(0)] -(5)-> "A"(1) and :: ["A"(0) x "A"(0)] -(3)-> "A"(12) eqZList :: ["A"(12) x "A"(8)] -(1)-> "A"(0) first :: ["A"(7)] -(8)-> "A"(0) second :: ["A"(7)] -(8)-> "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))