WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cond_prefix_s1_s2_2(False(),x2,x1) -> False() cond_prefix_s1_s2_2(True(),x2,x1) -> prefix#2(x2,x1) eq#2(0(),0()) -> True() eq#2(0(),S(x16)) -> False() eq#2(S(x16),0()) -> False() eq#2(S(x4),S(x2)) -> eq#2(x4,x2) main(x2,x1) -> prefix#2(x2,x1) prefix#2(Cons(x4,x2),Nil()) -> False() prefix#2(Cons(x8,x6),Cons(x4,x2)) -> cond_prefix_s1_s2_2(eq#2(x8,x4),x6,x2) prefix#2(Nil(),x2) -> True() - Signature: {cond_prefix_s1_s2_2/3,eq#2/2,main/2,prefix#2/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_prefix_s1_s2_2,eq#2,main ,prefix#2} 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"(8) F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "Cons") :: ["A"(14) x "A"(14)] -(14)-> "A"(14) F (TrsFun "Cons") :: ["A"(3) x "A"(3)] -(3)-> "A"(3) F (TrsFun "False") :: [] -(0)-> "A"(0) F (TrsFun "False") :: [] -(0)-> "A"(14) F (TrsFun "Nil") :: [] -(0)-> "A"(3) F (TrsFun "Nil") :: [] -(0)-> "A"(14) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(8)] -(8)-> "A"(8) F (TrsFun "True") :: [] -(0)-> "A"(0) F (TrsFun "True") :: [] -(0)-> "A"(14) F (TrsFun "cond_prefix_s1_s2_2") :: ["A"(0) x "A"(14) x "A"(3)] -(2)-> "A"(0) F (TrsFun "eq#2") :: ["A"(8) x "A"(0)] -(15)-> "A"(0) F (TrsFun "main") :: ["A"(14) x "A"(15)] -(9)-> "A"(0) F (TrsFun "prefix#2") :: ["A"(14) x "A"(3)] -(1)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"0\")_A" :: [] -(0)-> "A"(1) "F (TrsFun \"Cons\")_A" :: ["A"(1) 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"(1)] -(1)-> "A"(1) "F (TrsFun \"True\")_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))