WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__add(X1,X2) -> add(X1,X2) a__add(0(),X) -> mark(X) a__add(s(X),Y) -> s(add(X,Y)) a__and(X1,X2) -> and(X1,X2) a__and(false(),Y) -> false() a__and(true(),X) -> mark(X) a__first(X1,X2) -> first(X1,X2) a__first(0(),X) -> nil() a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) a__from(X) -> cons(X,from(s(X))) a__from(X) -> from(X) a__if(X1,X2,X3) -> if(X1,X2,X3) a__if(false(),X,Y) -> mark(Y) a__if(true(),X,Y) -> mark(X) mark(0()) -> 0() mark(add(X1,X2)) -> a__add(mark(X1),X2) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(X1,X2) mark(false()) -> false() mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) mark(from(X)) -> a__from(X) mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) mark(nil()) -> nil() mark(s(X)) -> s(X) mark(true()) -> true() - Signature: {a__add/2,a__and/2,a__first/2,a__from/1,a__if/3,mark/1} / {0/0,add/2,and/2,cons/2,false/0,first/2,from/1 ,if/3,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__add,a__and,a__first,a__from,a__if ,mark} and constructors {0,add,and,cons,false,first,from,if,nil,s,true} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(0) 0 :: [] -(0)-> "A"(13) 0 :: [] -(0)-> "A"(7) a__add :: ["A"(0) x "A"(13)] -(8)-> "A"(0) a__and :: ["A"(0) x "A"(13)] -(2)-> "A"(0) a__first :: ["A"(0) x "A"(0)] -(1)-> "A"(0) a__from :: ["A"(13)] -(3)-> "A"(0) a__if :: ["A"(0) x "A"(13) x "A"(13)] -(9)-> "A"(0) add :: ["A"(13) x "A"(13)] -(13)-> "A"(13) add :: ["A"(0) x "A"(0)] -(0)-> "A"(0) and :: ["A"(13) x "A"(13)] -(13)-> "A"(13) and :: ["A"(0) x "A"(0)] -(0)-> "A"(0) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(13) cons :: ["A"(0) x "A"(0)] -(0)-> "A"(9) false :: [] -(0)-> "A"(0) false :: [] -(0)-> "A"(13) false :: [] -(0)-> "A"(7) first :: ["A"(13) x "A"(13)] -(13)-> "A"(13) first :: ["A"(0) x "A"(0)] -(0)-> "A"(0) from :: ["A"(13)] -(13)-> "A"(13) from :: ["A"(0)] -(0)-> "A"(0) if :: ["A"(13) x "A"(13) x "A"(13)] -(13)-> "A"(13) if :: ["A"(0) x "A"(0) x "A"(0)] -(0)-> "A"(0) mark :: ["A"(13)] -(1)-> "A"(0) nil :: [] -(0)-> "A"(13) nil :: [] -(0)-> "A"(7) s :: ["A"(0)] -(0)-> "A"(0) s :: ["A"(0)] -(0)-> "A"(13) s :: ["A"(0)] -(0)-> "A"(9) s :: ["A"(0)] -(0)-> "A"(1) true :: [] -(0)-> "A"(0) true :: [] -(0)-> "A"(13) true :: [] -(0)-> "A"(7) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "add_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "and_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "cons_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(1) "false_A" :: [] -(0)-> "A"(1) "first_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "from_A" :: ["A"(1)] -(1)-> "A"(1) "if_A" :: ["A"(1) x "A"(1) x "A"(1)] -(1)-> "A"(1) "nil_A" :: [] -(0)-> "A"(1) "s_A" :: ["A"(0)] -(0)-> "A"(1) "true_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))