WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cond_string_dec_s_s0_3(False(),x2,x1) -> False() cond_string_dec_s_s0_3(True(),x2,x1) -> string_dec#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) -> string_dec#2(x2,x1) string_dec#2(Cons(x4,x2),Nil()) -> False() string_dec#2(Cons(x8,x6),Cons(x4,x2)) -> cond_string_dec_s_s0_3(eq#2(x8,x4),x6,x2) string_dec#2(Nil(),Cons(x4,x2)) -> False() string_dec#2(Nil(),Nil()) -> True() - Signature: {cond_string_dec_s_s0_3/3,eq#2/2,main/2,string_dec#2/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_string_dec_s_s0_3,eq#2,main ,string_dec#2} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(2) 0 :: [] -(0)-> "A"(12) Cons :: ["A"(12) x "A"(12)] -(12)-> "A"(12) Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15) False :: [] -(0)-> "A"(0) False :: [] -(0)-> "A"(12) False :: [] -(0)-> "A"(14) False :: [] -(0)-> "A"(8) Nil :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(12) S :: ["A"(12)] -(12)-> "A"(12) S :: ["A"(2)] -(2)-> "A"(2) True :: [] -(0)-> "A"(0) True :: [] -(0)-> "A"(14) True :: [] -(0)-> "A"(12) cond_string_dec_s_s0_3 :: ["A"(0) x "A"(12) x "A"(15)] -(12)-> "A"(0) eq#2 :: ["A"(2) x "A"(12)] -(5)-> "A"(0) main :: ["A"(14) x "A"(15)] -(16)-> "A"(0) string_dec#2 :: ["A"(12) x "A"(15)] -(7)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))