WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2)) fold#3(Nil()) -> 0() main(x1) -> fold#3(x1) plus#2(0(),x12) -> x12 plus#2(S(x4),x2) -> S(plus#2(x4,x2)) - Signature: {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {fold#3,main,plus#2} and constructors {0,Cons,Nil,S} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(15) 0 :: [] -(0)-> A(5) Cons :: [A(15) x A(15)] -(15)-> A(15) Nil :: [] -(0)-> A(15) S :: [A(15)] -(15)-> A(15) S :: [A(3)] -(3)-> A(3) fold#3 :: [A(15)] -(13)-> A(3) main :: [A(15)] -(14)-> A(0) plus#2 :: [A(15) x A(3)] -(8)-> A(3) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Nil :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) fold#3 :: [A_cf(0)] -(0)-> A_cf(0) plus#2 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) Cons_A :: [A(1) x A(1)] -(1)-> A(1) Nil_A :: [] -(0)-> A(1) S_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2)) fold#3(Nil()) -> 0() main(x1) -> fold#3(x1) plus#2(0(),x12) -> x12 plus#2(S(x4),x2) -> S(plus#2(x4,x2)) - Signature: {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {fold#3,main,plus#2} and constructors {0,Cons,Nil,S} Following problems could not be solved: - Strict TRS: fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2)) fold#3(Nil()) -> 0() main(x1) -> fold#3(x1) plus#2(0(),x12) -> x12 plus#2(S(x4),x2) -> S(plus#2(x4,x2)) - Signature: {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {fold#3,main,plus#2} and constructors {0,Cons,Nil,S} WORST_CASE(?,O(n^1))