WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(++) = {1,2} Following symbols are considered usable: {rev} TcT has computed the following interpretation: p(++) = 3 + x1 + x2 p(a) = 8 p(b) = 8 p(rev) = 2 + 2*x1 Following rules are strictly oriented: rev(++(x,x)) = 8 + 4*x > 2 + 2*x = rev(x) rev(++(x,y)) = 8 + 2*x + 2*y > 7 + 2*x + 2*y = ++(rev(y),rev(x)) rev(a()) = 18 > 8 = a() rev(b()) = 18 > 8 = b() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))