WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- Cons :: [A(15) x A(15)] -(15)-> A(15) Cons :: [A(0) x A(0)] -(0)-> A(0) Nil :: [] -(0)-> A(15) Nil :: [] -(0)-> A(7) fleft_op_e_xs_1 :: [] -(0)-> A(3) fleft_op_e_xs_1 :: [] -(0)-> A(13) foldr#3 :: [A(15)] -(1)-> A(6) main :: [A(15)] -(15)-> A(0) rev_l :: [] -(0)-> A(0) rev_l :: [] -(0)-> A(14) rev_l#2 :: [A(0) x A(0)] -(1)-> A(0) step_x_f :: [A(3) x A(3) x A(3)] -(3)-> A(3) step_x_f :: [A(6) x A(6) x A(6)] -(6)-> A(6) step_x_f#1 :: [A(0) x A(0) x A(3) x A(0)] -(5)-> A(0) Cost-free Signatures used: -------------------------- Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Nil :: [] -(0)-> A_cf(0) fleft_op_e_xs_1 :: [] -(0)-> A_cf(0) foldr#3 :: [A_cf(0)] -(0)-> A_cf(0) rev_l :: [] -(0)-> A_cf(0) rev_l#2 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) step_x_f :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) step_x_f#1 :: [A_cf(0) x A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- Cons_A :: [A(1) x A(1)] -(1)-> A(1) Nil_A :: [] -(0)-> A(1) fleft_op_e_xs_1_A :: [] -(0)-> A(1) rev_l_A :: [] -(0)-> A(1) step_x_f_A :: [A(0) x A(0) x A(0)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} Following problems could not be solved: - Strict TRS: foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6)) foldr#3(Nil()) -> fleft_op_e_xs_1() main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil()) main(Nil()) -> Nil() rev_l#2(x8,x10) -> Cons(x10,x8) step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5) step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5)) - Signature: {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3} - Obligation: innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons ,Nil,fleft_op_e_xs_1,rev_l,step_x_f} WORST_CASE(?,O(n^1))