WORST_CASE(?,O(n^2)) * Step 1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} + Applied Processor: NaturalPI {shape = Mixed 2, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(mixed(2)): The following argument positions are considered usable: uargs(cons) = {1}, uargs(copy) = {3} Following symbols are considered usable: {copy,f} TcT has computed the following interpretation: p(0) = 2 p(cons) = x1 + x2 p(copy) = 1 + 3*x1 + 4*x1*x2 + 2*x1^2 + 3*x2 + 2*x3 p(f) = 3 + 2*x1 p(n) = 0 p(nil) = 0 p(s) = 2 + x1 Following rules are strictly oriented: copy(0(),y,z) = 15 + 11*y + 2*z > 3 + 2*z = f(z) copy(s(x),y,z) = 15 + 11*x + 4*x*y + 2*x^2 + 11*y + 2*z > 7 + 3*x + 4*x*y + 2*x^2 + 7*y + 2*z = copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) = 9 + 4*y + 2*z > 1 + 3*y + 2*z = copy(n(),y,z) f(cons(nil(),y)) = 3 + 2*y > y = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^2))