WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6) foldl#3(x2,Nil()) -> x2 main(x1) -> foldl#3(Nil(),x1) - Signature: {foldl#3/2,main/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {foldl#3,main} TcT has computed the following interpretation: p(Cons) = [0] p(Nil) = [4] p(foldl#3) = [2] x1 + [2] p(main) = [1] x1 + [11] Following rules are strictly oriented: foldl#3(x2,Nil()) = [2] x2 + [2] > [1] x2 + [0] = x2 main(x1) = [1] x1 + [11] > [10] = foldl#3(Nil(),x1) Following rules are (at-least) weakly oriented: foldl#3(x16,Cons(x24,x6)) = [2] x16 + [2] >= [2] = foldl#3(Cons(x24,x16),x6) * Step 2: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6) - Weak TRS: foldl#3(x2,Nil()) -> x2 main(x1) -> foldl#3(Nil(),x1) - Signature: {foldl#3/2,main/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: none Following symbols are considered usable: {foldl#3,main} TcT has computed the following interpretation: p(Cons) = 4 + x2 p(Nil) = 4 p(foldl#3) = 2*x1 + 4*x2 p(main) = 8 + 9*x1 Following rules are strictly oriented: foldl#3(x16,Cons(x24,x6)) = 16 + 2*x16 + 4*x6 > 8 + 2*x16 + 4*x6 = foldl#3(Cons(x24,x16),x6) Following rules are (at-least) weakly oriented: foldl#3(x2,Nil()) = 16 + 2*x2 >= x2 = x2 main(x1) = 8 + 9*x1 >= 8 + 4*x1 = foldl#3(Nil(),x1) * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6) foldl#3(x2,Nil()) -> x2 main(x1) -> foldl#3(Nil(),x1) - Signature: {foldl#3/2,main/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))